python_financial_data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import datetime as dt\n",
    "import time\n",
    "\n",
    "import scipy as sp\n",
    "import scipy.stats as stats\n",
    "from scipy import stats\n",
    "from scipy.stats import norm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 475,
   "metadata": {},
   "outputs": [],
   "source": [
    "# conda install -c anaconda pandas-datareader\n",
    "from pandas_datareader import data, wb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 476,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pip install bs4\n",
    "from bs4 import BeautifulSoup\n",
    "import requests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the instruments to download. We would like to see Apple, Microsoft and the S&P500 index.\n",
    "tickers = ['AAPL', 'MSFT', '^GSPC']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We would like all available data from 01/01/2000 until 12/31/2016.\n",
    "start_date = '2010-01-01'\n",
    "end_date = '2016-12-31'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "data_source='google' is not implemented",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-6-f3351d1f6ea3>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# User pandas_reader.data.DataReader to load the desired data. As simple as that.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mpanel_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mDataReader\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'INPX'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'google'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstart_date\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mend_date\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\util\\_decorators.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m    206\u001b[0m                 \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    207\u001b[0m                     \u001b[0mkwargs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnew_arg_name\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnew_arg_value\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 208\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    209\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    210\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas_datareader\\data.py\u001b[0m in \u001b[0;36mDataReader\u001b[1;34m(name, data_source, start, end, retry_count, pause, session, api_key)\u001b[0m\n\u001b[0;32m    374\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mdata_source\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mexpected_source\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    375\u001b[0m         \u001b[0mmsg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m\"data_source=%r is not implemented\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[0mdata_source\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 376\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    377\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    378\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mdata_source\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m\"yahoo\"\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNotImplementedError\u001b[0m: data_source='google' is not implemented"
     ]
    }
   ],
   "source": [
    "# User pandas_reader.data.DataReader to load the desired data. As simple as that.\n",
    "panel_data = data.DataReader('INPX', 'google', start_date, end_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Open</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Adj Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2015-01-02</td>\n",
       "      <td>535.799988</td>\n",
       "      <td>527.880005</td>\n",
       "      <td>532.599976</td>\n",
       "      <td>529.549988</td>\n",
       "      <td>1324000</td>\n",
       "      <td>529.549988</td>\n",
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       "    <tr>\n",
       "      <td>2015-01-05</td>\n",
       "      <td>527.989990</td>\n",
       "      <td>517.750000</td>\n",
       "      <td>527.150024</td>\n",
       "      <td>519.460022</td>\n",
       "      <td>2059100</td>\n",
       "      <td>519.460022</td>\n",
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       "    <tr>\n",
       "      <td>2015-01-06</td>\n",
       "      <td>521.210022</td>\n",
       "      <td>505.549988</td>\n",
       "      <td>520.500000</td>\n",
       "      <td>506.640015</td>\n",
       "      <td>2722800</td>\n",
       "      <td>506.640015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2015-01-07</td>\n",
       "      <td>511.489990</td>\n",
       "      <td>503.649994</td>\n",
       "      <td>510.950012</td>\n",
       "      <td>505.149994</td>\n",
       "      <td>2345900</td>\n",
       "      <td>505.149994</td>\n",
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       "    <tr>\n",
       "      <td>2015-01-08</td>\n",
       "      <td>507.500000</td>\n",
       "      <td>495.019989</td>\n",
       "      <td>501.510010</td>\n",
       "      <td>506.910004</td>\n",
       "      <td>3652700</td>\n",
       "      <td>506.910004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>2019-10-25</td>\n",
       "      <td>1268.000000</td>\n",
       "      <td>1249.150024</td>\n",
       "      <td>1252.000000</td>\n",
       "      <td>1264.300049</td>\n",
       "      <td>1352200</td>\n",
       "      <td>1264.300049</td>\n",
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       "      <td>2019-10-28</td>\n",
       "      <td>1299.239990</td>\n",
       "      <td>1272.310059</td>\n",
       "      <td>1275.000000</td>\n",
       "      <td>1288.979980</td>\n",
       "      <td>3271400</td>\n",
       "      <td>1288.979980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-10-29</td>\n",
       "      <td>1280.800049</td>\n",
       "      <td>1255.609985</td>\n",
       "      <td>1276.000000</td>\n",
       "      <td>1260.660034</td>\n",
       "      <td>2622500</td>\n",
       "      <td>1260.660034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-10-30</td>\n",
       "      <td>1268.020020</td>\n",
       "      <td>1250.650024</td>\n",
       "      <td>1255.150024</td>\n",
       "      <td>1260.699951</td>\n",
       "      <td>1458600</td>\n",
       "      <td>1260.699951</td>\n",
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       "    <tr>\n",
       "      <td>2019-10-31</td>\n",
       "      <td>1266.520020</td>\n",
       "      <td>1249.479980</td>\n",
       "      <td>1260.000000</td>\n",
       "      <td>1258.800049</td>\n",
       "      <td>159500000</td>\n",
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       "<p>1217 rows × 6 columns</p>\n",
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      "text/plain": [
       "                   High          Low         Open        Close     Volume  \\\n",
       "Date                                                                        \n",
       "2015-01-02   535.799988   527.880005   532.599976   529.549988    1324000   \n",
       "2015-01-05   527.989990   517.750000   527.150024   519.460022    2059100   \n",
       "2015-01-06   521.210022   505.549988   520.500000   506.640015    2722800   \n",
       "2015-01-07   511.489990   503.649994   510.950012   505.149994    2345900   \n",
       "2015-01-08   507.500000   495.019989   501.510010   506.910004    3652700   \n",
       "...                 ...          ...          ...          ...        ...   \n",
       "2019-10-25  1268.000000  1249.150024  1252.000000  1264.300049    1352200   \n",
       "2019-10-28  1299.239990  1272.310059  1275.000000  1288.979980    3271400   \n",
       "2019-10-29  1280.800049  1255.609985  1276.000000  1260.660034    2622500   \n",
       "2019-10-30  1268.020020  1250.650024  1255.150024  1260.699951    1458600   \n",
       "2019-10-31  1266.520020  1249.479980  1260.000000  1258.800049  159500000   \n",
       "\n",
       "              Adj Close  \n",
       "Date                     \n",
       "2015-01-02   529.549988  \n",
       "2015-01-05   519.460022  \n",
       "2015-01-06   506.640015  \n",
       "2015-01-07   505.149994  \n",
       "2015-01-08   506.910004  \n",
       "...                 ...  \n",
       "2019-10-25  1264.300049  \n",
       "2019-10-28  1288.979980  \n",
       "2019-10-29  1260.660034  \n",
       "2019-10-30  1260.699951  \n",
       "2019-10-31  1258.800049  \n",
       "\n",
       "[1217 rows x 6 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import pandas_datareader as pdr\n",
    "from pandas_datareader import data as wb\n",
    "\n",
    "ticker = 'GOOGL'\n",
    "start_date = '2015-01-01'\n",
    "end_date = '2019-10-31'\n",
    "data_source = 'yahoo'\n",
    "\n",
    "# get stock prices\n",
    "ticker_data=wb.DataReader(ticker, data_source=data_source, start=start_date, end=end_date)\n",
    "df = pd.DataFrame(ticker_data)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 473,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pandas_datareader import Options\n",
    "\n",
    "# >>> aapl = Options('AAPL')\n",
    "# FutureWarning: Options(symbol) is deprecated, use Options(symbol, data_source) instead\n",
    "#                after removing the cwd from sys.path.\n",
    "\n",
    "# >>> aapl = Options('AAPL', 'google')\n",
    "# NotImplementedError: currently only yahoo supported\n",
    "\n",
    "# >>> aapl = Options('AAPL', 'yahoo')\n",
    "# ImmediateDeprecationError: \n",
    "# Yahoo Options has been immediately deprecated due to large breaks in the API without the\n",
    "# introduction of a stable replacement. Pull Requests to re-enable these data\n",
    "# connectors are welcome.\n",
    "\n",
    "# >>> puts, calls = appl.get_options_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pip install yahoo-finance\n",
    "# >>> from yahoo_finance import Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 479,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This fetches the page’s full HTML content\n",
    "data_url = \"https://finance.yahoo.com/quote/SPY/options\"\n",
    "data_html = requests.get(data_url).content"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {},
   "outputs": [],
   "source": [
    "# BeautifulSoup is the perfect tool for working with HTML data in Python.\n",
    "content = BeautifulSoup(data_html, \"html.parser\")\n",
    "options_tables = content.find_all(\"table\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 484,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Break it down into two tables, for calls and puts\n",
    "options_tables = [] \n",
    "tables = content.find_all(\"table\")\n",
    "for i in range(len(content.find_all(\"table\"))):\n",
    "    options_tables.append(tables[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Yahoo’s data contains options that are pretty deep in- and out-of-the-money, \n",
    "# which might be great for certain purposes. \n",
    "# calls\n",
    "calls = options_tables[0].find_all(\"tr\")[1:] # first row is header\n",
    "# puts\n",
    "puts = options_tables[1].find_all(\"tr\")[1:]  # first row is header"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let’s find these, using BeautifulSoup and Yahoo’s differential table entries for in-the-money and out-of-the-money options:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [],
   "source": [
    "itm_calls = []\n",
    "otm_calls = []\n",
    "\n",
    "itm_puts = []\n",
    "otm_puts = []\n",
    "for call_option in calls:\n",
    "    if \"in-the-money\" in str(call_option):  \n",
    "        itm_calls.append(call_option)\n",
    "    else:\n",
    "        otm_calls.append(call_option)\n",
    "for put_option in puts:\n",
    "    if \"in-the-money\" in str(put_option):\n",
    "        itm_puts.append(put_option)\n",
    "    else:\n",
    "        otm_puts.append(put_option)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "57\n"
     ]
    }
   ],
   "source": [
    "def options5(put_call, moneyness):\n",
    "    moneyness = moneyness.upper()\n",
    "    put_call = put_call.upper()\n",
    "    \n",
    "    # SPDR S&P 500 ETF (SPY)\n",
    "    data_url = \"https://finance.yahoo.com/quote/SPY/options\"\n",
    "    data_html = requests.get(data_url).content\n",
    "    content = BeautifulSoup(data_html, \"html.parser\")\n",
    "    tables = [v for v in content.find_all(\"table\")]\n",
    "    \n",
    "    if put_call == \"C\":\n",
    "        t = tables[0].find_all(\"tr\")[1:]\n",
    "    elif put_call == \"P\":\n",
    "        t = tables[1].find_all(\"tr\")[1:]\n",
    "    \n",
    "    if moneyness == \"ITM\":\n",
    "        g = [option for option in t if \"in-the-money\" in str(option)]\n",
    "    elif moneyness == \"OTM\":\n",
    "        g = [option for option in t if not \"in-the-money\" in str(option)]\n",
    "\n",
    "    x = [[td.text for td in BeautifulSoup(str(opt), \"html.parser\").find_all(\"td\")] for opt in g]        \n",
    "    header = ['Contract Name', 'Last Trade Date', 'Strike', 'Last Price', 'Bid', 'Ask', \n",
    "              'Change', 'Change (%)', 'Volume', 'Open Interest', 'Implied Volatility']\n",
    "    return pd.DataFrame(data=x, columns=header)\n",
    "print(len(options5(\"C\", \"ITM\")))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "121\n"
     ]
    }
   ],
   "source": [
    "def options6(put_call):\n",
    "    # moneyness = moneyness.upper()\n",
    "    put_call = put_call.upper()\n",
    "    \n",
    "    # SPDR S&P 500 ETF (SPY)\n",
    "    data_url = \"https://finance.yahoo.com/quote/SPY/options\"\n",
    "    data_html = requests.get(data_url).content\n",
    "    content = BeautifulSoup(data_html, \"html.parser\")\n",
    "    tables = [v for v in content.find_all(\"table\")]\n",
    "    \n",
    "    g = [option for t in tables for option in t.find_all(\"tr\")[1:]]\n",
    "\n",
    "    x = [[td.text for td in BeautifulSoup(str(opt), \"html.parser\").find_all(\"td\")] for opt in g]        \n",
    "    header = ['Contract Name', 'Last Trade Date', 'Strike', 'Last Price', 'Bid', 'Ask', \n",
    "              'Change', 'Change (%)', 'Volume', 'Open Interest', 'Implied Volatility']\n",
    "    return pd.DataFrame(data=x, columns=header)\n",
    "print(len(options6(\"C\")))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "metadata": {},
   "outputs": [],
   "source": [
    "def options8(underlying, date=[]):\n",
    "    \n",
    "    if date == [] or date == \"\":\n",
    "        z = \"\"\n",
    "    else:\n",
    "        if type(date) == dt.datetime:\n",
    "            date = date.date()\n",
    "        elif type(date) == str or type(date) == int:\n",
    "            date = dt.datetime.strptime(str(date), \"%Y%m%d\")\n",
    "            print(date)\n",
    "        time_stamp = int(date.replace(tzinfo=datetime.timezone.utc).timestamp())\n",
    "            #date = dt.datetime.strptime(date,\"%Y%m%d\").date()\n",
    "        # date_stamp = str(int(time.mktime(date.timetuple())))\n",
    "        z = \"?date=\" + str(time_stamp)\n",
    "    # moneyness = moneyness.upper()\n",
    "    # put_call = put_call.upper()\n",
    "    \n",
    "    # ^ = \"5E\" -- honnan jön a % jel ?\n",
    "    underlying = underlying.replace(\"^\",\"%5E\")\n",
    "    # data_url = \"https://finance.yahoo.com/quote/\" + underlying + \"/options\"\n",
    "    \n",
    "    data_url = \"https://finance.yahoo.com/quote/\" + underlying + \"/options\" + z\n",
    "    print(data_url)\n",
    "    # NASDAQ Composite (^IXIC)\n",
    "    # SPDR S&P 500 ETF (SPY)\n",
    "    # CBOE Volatility Index (^VIX)\n",
    "    # FTSE 100 (^FTSE)\n",
    "    # Nikkei 225 (^N225)\n",
    "    data_html = requests.get(data_url).content\n",
    "    content = BeautifulSoup(data_html, \"html.parser\")\n",
    "    \n",
    "    g = [o for t in [v for v in content.find_all(\"table\")] for o in t.find_all(\"tr\")[1:]]\n",
    "    x = [[td.text for td in BeautifulSoup(str(opt), \"html.parser\").find_all(\"td\")] for opt in g]\n",
    "    \n",
    "    header = ['Contract Name', 'Last Trade Date', 'Strike', 'Last Price', 'Bid', 'Ask', \n",
    "              'Change', 'Change (%)', 'Volume', 'Open Interest', 'Implied Volatility']\n",
    "    return pd.DataFrame(data=x, columns=header)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 569,
   "metadata": {},
   "outputs": [],
   "source": [
    "def options9(underlying, date=[]):\n",
    "    if date == [] or date == \"\":\n",
    "        z = \"\"\n",
    "    else:\n",
    "        if type(date) == dt.datetime:\n",
    "            # date = date.date()\n",
    "            s = dt.datetime.strftime(date, \"%Y%m%d\")\n",
    "        elif type(date) == str or type(date) == int:\n",
    "            s = str(date)   \n",
    "        time_stamp = int(dt.datetime.strptime(s, \"%Y%m%d\").replace(tzinfo=datetime.timezone.utc).timestamp())\n",
    "        #time_stamp = int(dt.datetime.strptime(str(s), \"%Y%m%d\").replace(tzinfo=datetime.timezone.utc).timestamp())\n",
    "        \n",
    "        z = \"?date=\" + str(time_stamp)\n",
    "    \n",
    "    # ^ = \"5E\" -- honnan jön a % jel ?\n",
    "    underlying = underlying.replace(\"^\",\"%5E\")\n",
    "    data_url = \"https://finance.yahoo.com/quote/\" + underlying + \"/options\" + z\n",
    "    data_html = requests.get(data_url).content\n",
    "    content = BeautifulSoup(data_html, \"html.parser\")\n",
    "    \n",
    "    g = [o for t in [v for v in content.find_all(\"table\")] for o in t.find_all(\"tr\")[1:]]\n",
    "    x = [[td.text for td in BeautifulSoup(str(opt), \"html.parser\").find_all(\"td\")] for opt in g]\n",
    "    \n",
    "    header = ['Contract Name', 'Last Trade Date', 'Strike', 'Last Price', 'Bid', 'Ask', \n",
    "              'Change', 'Change (%)', 'Volume', 'Open Interest', 'Implied Volatility']\n",
    "    df = pd.DataFrame(data=x, columns=header)\n",
    "    df.insert(0, \"Expiry Date\", date)\n",
    "    if len(df) > 0:\n",
    "        print(date.date())\n",
    "        print(data_url)\n",
    "        print(len(df))\n",
    "        \n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "metadata": {},
   "outputs": [],
   "source": [
    "def options(ticker):\n",
    "    # ^ = \"5E\" -- honnan jön a % jel ?\n",
    "    # VIX Dec Futures Index (^VIXDEC)\n",
    "    # VIX Nov Futures Index (^VIXNOV) ...\n",
    "    ticker = ticker.replace(\"^\",\"%5E\")\n",
    "    \n",
    "    data_url = \"https://finance.yahoo.com/quote/\" + ticker + \"/options\"\n",
    "    data_html = requests.get(data_url).content\n",
    "    r = str(BeautifulSoup(data_html, \"html.parser\"))\n",
    "    r=r[r.index(\"OptionContracts-Proxy\"):]\n",
    "    r=r[r.index(\"expirationDates\"):].split(\"[\")[1].split(\"]\")[0].split(\",\")\n",
    "    df = pd.DataFrame([])\n",
    "    header = ['Contract Name', 'Last Trade Date', 'Strike', 'Last Price', 'Bid', 'Ask', \n",
    "              'Change', 'Change (%)', 'Volume', 'Open Interest', 'Implied Volatility']\n",
    "    for stamp in r:\n",
    "        data_html1 = requests.get(data_url + \"?date=\" + stamp).content\n",
    "        content = BeautifulSoup(data_html1, \"html.parser\")\n",
    "\n",
    "        g = [o for t in [v for v in content.find_all(\"table\")] for o in t.find_all(\"tr\")[1:]]\n",
    "        x = [[td.text for td in BeautifulSoup(str(opt), \"html.parser\").find_all(\"td\")] for opt in g]\n",
    "    \n",
    "        df1 = pd.DataFrame(data=x, columns=header)\n",
    "        df1.insert(0, \"Expiry Date\", dt.datetime.utcfromtimestamp(int(stamp)))\n",
    "        df = pd.concat([df, df1])\n",
    "    \n",
    "    df.reset_index(drop=True, inplace=True)\n",
    "    df[\"Expiry Date\"] = pd.to_datetime(df[\"Expiry Date\"], format=\"%Y-%m-%d\")\n",
    "    df[\"Option Type\"] = df[\"Contract Name\"].apply(lambda y : y[[i for (i, v) in enumerate([not z.isdigit() for z in y]) if v][-1]])\n",
    "    df.drop([\"Last Trade Date\", \"Bid\", \"Ask\"], axis=1, inplace=True)\n",
    "    # there are some \"-\" in Bid prices, Ask can be used (what changing if we remove \"-\" lines in Bid and recalc?)\n",
    "    for x in [\"Strike\", \"Last Price\"]:\n",
    "        df[x] = df[x].astype(np.float)\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Expiry Date</th>\n",
       "      <th>Contract Name</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Change</th>\n",
       "      <th>Change (%)</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Open Interest</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>Option Type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00010000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>4.40</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>52</td>\n",
       "      <td>298</td>\n",
       "      <td>352.34%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00010500</td>\n",
       "      <td>10.5</td>\n",
       "      <td>3.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>4</td>\n",
       "      <td>54</td>\n",
       "      <td>271.09%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00011000</td>\n",
       "      <td>11.0</td>\n",
       "      <td>3.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>10</td>\n",
       "      <td>-</td>\n",
       "      <td>262.50%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00012000</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0.69</td>\n",
       "      <td>-1.01</td>\n",
       "      <td>-59.41%</td>\n",
       "      <td>21</td>\n",
       "      <td>55</td>\n",
       "      <td>191.80%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00012500</td>\n",
       "      <td>12.5</td>\n",
       "      <td>0.80</td>\n",
       "      <td>-0.40</td>\n",
       "      <td>-33.33%</td>\n",
       "      <td>48</td>\n",
       "      <td>80</td>\n",
       "      <td>125.00%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Expiry Date        Contract Name  Strike  Last Price Change Change (%)  \\\n",
       "0  2019-11-06  VIXW191106C00010000    10.0        4.40   0.00          -   \n",
       "1  2019-11-06  VIXW191106C00010500    10.5        3.20   0.00          -   \n",
       "2  2019-11-06  VIXW191106C00011000    11.0        3.70   0.00          -   \n",
       "3  2019-11-06  VIXW191106C00012000    12.0        0.69  -1.01    -59.41%   \n",
       "4  2019-11-06  VIXW191106C00012500    12.5        0.80  -0.40    -33.33%   \n",
       "\n",
       "  Volume Open Interest Implied Volatility Option Type  \n",
       "0     52           298            352.34%           C  \n",
       "1      4            54            271.09%           C  \n",
       "2     10             -            262.50%           C  \n",
       "3     21            55            191.80%           C  \n",
       "4     48            80            125.00%           C  "
      ]
     },
     "execution_count": 488,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test call\n",
    "options(\"^VIX\").head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C'"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the last charachter from a string (what is not a digit)\n",
    "y = \"VIXW191106C00010000\"\n",
    "b =[not z.isdigit() for z in y]\n",
    "b\n",
    "y[[i for (i, value) in enumerate([not z.isdigit() for z in y]) if value][-1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 489,
   "metadata": {},
   "outputs": [],
   "source": [
    "def stocks(ticker):\n",
    "\n",
    "    ticker = ticker.replace(\"^\",\"%5E\")\n",
    "    data_url = \"https://finance.yahoo.com/quote/\" + ticker + \"/history\"\n",
    "    data_html = requests.get(data_url).content\n",
    "    content = BeautifulSoup(data_html, \"html.parser\")\n",
    "    g = [o for t in [v for v in content.find_all(\"table\")] for o in t.find_all(\"tr\")[1:-1]]\n",
    "    x = [[td.text for td in BeautifulSoup(str(opt), \"html.parser\").find_all(\"td\")] for opt in g]\n",
    "    \n",
    "    header = [\"Date\", \"Open\", \"High\", \"Low\", \"Close\", \"Adj Close\", \"Volume\"]\n",
    "    df = pd.DataFrame(data=x, columns=header)\n",
    "    # Date is in format Mar 04, 2019 (format=\"%b %d, %Y\")--> it has to be converted to dataframe\n",
    "    df[\"Date\"] = pd.to_datetime(pd.to_datetime(df[\"Date\"], format=\"%b %d, %Y\"), format=\"%Y-%m-%d\")\n",
    "    \n",
    "    for x in [\"Open\", \"High\", \"Low\", \"Close\", \"Adj Close\"]:\n",
    "        df[x] = df[x].astype(np.float)\n",
    "    \n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 541,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2019-11-04</td>\n",
       "      <td>12.68</td>\n",
       "      <td>13.13</td>\n",
       "      <td>12.44</td>\n",
       "      <td>12.83</td>\n",
       "      <td>12.83</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2019-11-01</td>\n",
       "      <td>12.50</td>\n",
       "      <td>12.60</td>\n",
       "      <td>12.26</td>\n",
       "      <td>12.30</td>\n",
       "      <td>12.30</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2019-10-31</td>\n",
       "      <td>13.51</td>\n",
       "      <td>13.95</td>\n",
       "      <td>13.18</td>\n",
       "      <td>13.22</td>\n",
       "      <td>13.22</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>2019-10-30</td>\n",
       "      <td>13.08</td>\n",
       "      <td>13.37</td>\n",
       "      <td>12.27</td>\n",
       "      <td>12.33</td>\n",
       "      <td>12.33</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>2019-10-29</td>\n",
       "      <td>13.16</td>\n",
       "      <td>13.52</td>\n",
       "      <td>13.07</td>\n",
       "      <td>13.20</td>\n",
       "      <td>13.20</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>95</td>\n",
       "      <td>2019-06-20</td>\n",
       "      <td>14.04</td>\n",
       "      <td>16.03</td>\n",
       "      <td>13.19</td>\n",
       "      <td>14.75</td>\n",
       "      <td>14.75</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>96</td>\n",
       "      <td>2019-06-19</td>\n",
       "      <td>15.05</td>\n",
       "      <td>15.71</td>\n",
       "      <td>14.15</td>\n",
       "      <td>14.33</td>\n",
       "      <td>14.33</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>2019-06-18</td>\n",
       "      <td>14.89</td>\n",
       "      <td>15.54</td>\n",
       "      <td>14.62</td>\n",
       "      <td>15.15</td>\n",
       "      <td>15.15</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>98</td>\n",
       "      <td>2019-06-17</td>\n",
       "      <td>15.65</td>\n",
       "      <td>15.76</td>\n",
       "      <td>15.24</td>\n",
       "      <td>15.35</td>\n",
       "      <td>15.35</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>2019-06-14</td>\n",
       "      <td>16.00</td>\n",
       "      <td>16.40</td>\n",
       "      <td>15.21</td>\n",
       "      <td>15.28</td>\n",
       "      <td>15.28</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Date   Open   High    Low  Close  Adj Close Volume\n",
       "0  2019-11-04  12.68  13.13  12.44  12.83      12.83      -\n",
       "1  2019-11-01  12.50  12.60  12.26  12.30      12.30      -\n",
       "2  2019-10-31  13.51  13.95  13.18  13.22      13.22      -\n",
       "3  2019-10-30  13.08  13.37  12.27  12.33      12.33      -\n",
       "4  2019-10-29  13.16  13.52  13.07  13.20      13.20      -\n",
       "..        ...    ...    ...    ...    ...        ...    ...\n",
       "95 2019-06-20  14.04  16.03  13.19  14.75      14.75      -\n",
       "96 2019-06-19  15.05  15.71  14.15  14.33      14.33      -\n",
       "97 2019-06-18  14.89  15.54  14.62  15.15      15.15      -\n",
       "98 2019-06-17  15.65  15.76  15.24  15.35      15.35      -\n",
       "99 2019-06-14  16.00  16.40  15.21  15.28      15.28      -\n",
       "\n",
       "[100 rows x 7 columns]"
      ]
     },
     "execution_count": 541,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test call\n",
    "stocks(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 493,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24197072451914337"
      ]
     },
     "execution_count": 493,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.pdf(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 494,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 494,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# normal cummulative distribution function\n",
    "norm.cdf(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 576,
   "metadata": {},
   "outputs": [],
   "source": [
    "# norm.cdf is the cumulative distribution function of the standard normal distribution\n",
    "# T-t is the time to maturity (expressed in years)\n",
    "# S_{t} is the spot price of the underlying asset\n",
    "# K is the strike price\n",
    "# r is the risk free rate (annual rate, expressed in terms of continuous compounding)\n",
    "# sigma  is the volatility of returns of the underlying asset\n",
    "\n",
    "def BSoption_price(St, K, r, sigma, time_to_expiry, option_type):\n",
    "    T=time_to_expiry\n",
    "    t=0\n",
    "    if sigma != 0:\n",
    "        d1 = (np.log(St / K) + (r + (sigma ** 2) / 2) * (T - t)) / (sigma * np.sqrt(T - t))\n",
    "        d2 = d1 - sigma * np.sqrt(T - t)\n",
    "        if option_type == \"C\":\n",
    "            price = norm.cdf(d1) * St - norm.cdf(d2) * K * np.exp(- r * (T - t))\n",
    "        elif option_type == \"P\":\n",
    "            price = - norm.cdf(-d1) * St + norm.cdf(-d2) * K * np.exp(- r * (T - t))\n",
    "    else:\n",
    "        if option_type == \"C\":\n",
    "            price = np.max(St - K * np.exp(- r * (T - t)), 0)\n",
    "        elif option_type == \"P\":\n",
    "            price = np.min(St - K * np.exp(- r * (T - t)), 0)\n",
    "    return price\n",
    "    \n",
    "            \n",
    "def BSCall_price(St, K, r, sigma, time_to_expiry):\n",
    "    T=time_to_expiry\n",
    "    t=0\n",
    "    d1 = (np.log(St / K) + (r + (sigma ** 2) / 2) * (T - t)) / (sigma * np.sqrt(T - t))\n",
    "    d2 = d1 - sigma * np.sqrt(T - t)\n",
    "    price = norm.cdf(d1) * St - norm.cdf(d2) * K * np.exp(- r * (T - t))\n",
    "    return price\n",
    "def BSPut_price(St, K, r, sigma, time_to_expiry):\n",
    "    T=time_to_expiry\n",
    "    t=0\n",
    "    d1 = (np.log(St / K) + (r + (sigma ** 2) / 2) * (T - t)) / (sigma * np.sqrt(T - t))\n",
    "    d2 = d1 - sigma * np.sqrt(T - t)\n",
    "    price = - norm.cdf(-d1) * St + norm.cdf(-d2) * K * np.exp(- r * (T - t))\n",
    "    return price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3938124510035834"
      ]
     },
     "execution_count": 496,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test call\n",
    "BSoption_price(100, 120, 0.1, 0.4, 0.3, \"C\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "metadata": {},
   "outputs": [],
   "source": [
    "def implied_volatility(ticker):\n",
    "    hist_stocks = stocks(ticker)\n",
    "    \n",
    "    \n",
    "    today = dt.date.today()\n",
    "    hist_stocks[\"Today\"] = pd.to_datetime(today, format=\"%Y-%m-%d\")\n",
    "    #hist_stocks[\"Date\"] = pd.to_datetime(hist_stocks[\"Date\"], format=\"%Y-%m-%d\")\n",
    "    hist_stocks[\"Date Diff\"] = hist_stocks[\"Today\"] - hist_stocks[\"Date\"]\n",
    "    hist_stocks.sort_values(by=\"Date Diff\", ascending=True,inplace=True)\n",
    "    hist_stocks.reset_index(drop=True,inplace=True)\n",
    "    # most recent stock price\n",
    "    S=hist_stocks.loc[0, \"Adj Close\"]\n",
    "    \n",
    "    opts = options(ticker)\n",
    "    #opts[\"Last Price\"] = opts[\"Last Price\"].astype(np.float)\n",
    "    opts[\"Time to Expiry\"] = (opts[\"Expiry Date\"] - pd.to_datetime(today, format=\"%Y-%m-%d\")).apply(lambda x : x.days)/252\n",
    "    opts.drop([\"Contract Name\", \"Change\", \"Change (%)\", \"Volume\", \"Open Interest\"], axis=1, inplace=True)\n",
    "       \n",
    "    r=0\n",
    "    Sigma = np.array(np.linspace(0,1,101)[1:])\n",
    "    RMS = []\n",
    "    for sigma in Sigma:\n",
    "        x = np.vectorize(BSoption_price)(S, opts['Strike'], r, sigma, opts[\"Time to Expiry\"], opts[\"Option Type\"]) \n",
    "        rms = np.sqrt(np.mean(np.array(x - opts[\"Last Price\"])**2)) # --> min by sigma\n",
    "        RMS.append(rms)\n",
    "    \n",
    "    m=np.min(RMS)\n",
    "    ind_m = RMS.index(m)\n",
    "    implied_sigma = Sigma[ind_m]\n",
    "    opts[\"Implied Price\"] = np.vectorize(BSoption_price)(S, opts['Strike'], r, implied_sigma, \n",
    "                                                         opts[\"Time to Expiry\"], opts[\"Option Type\"]) \n",
    "    opts[\"Pricing Error\"] = opts[\"Implied Price\"] - opts[\"Last Price\"]\n",
    "    Ind=[i for (i, v) in enumerate(RMS) if v == m]\n",
    "    Implied_Sigma = np.array(Sigma)\n",
    "    Implied_Sigma = Implied_Sigma[Ind]\n",
    "    Implied_Sigma_RMS = np.array(RMS)\n",
    "    Implied_Sigma_RMS = Implied_Sigma_RMS[Ind]\n",
    "    print(Implied_Sigma)\n",
    "    print(Implied_Sigma_RMS)\n",
    "\n",
    "    plot_volatility_smile(Sigma, RMS)\n",
    "    plt.plot(Implied_Sigma, Implied_Sigma_RMS, \"*r\")\n",
    "    return opts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.59]\n",
      "[2.50941586]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = implied_volatility(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.58]\n",
      "[2.24943417]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = implied_volatility(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.59]\n",
      "[2.41304381]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = implied_volatility(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.59]\n",
      "[2.45028526]\n"
     ]
    },
    {
     "data": {
      "image/png": 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MolGYP4cEPHFFHkGJyLvAO0Am8AxwJXA7MA04F5gpImeWR0hjjDFlY8uP48jWEFqfPcrrKCUqrny+oKrLC5m+HJjsjnRbca+uGWOMySdv54geTVp6HadERR5BFSxOIhIuIj1E5CR3fqaqrvN3QGOMMWVj2U+Vo3PEUcWd4hsnIp3c93WAJcB7wCIRubKc8hljjCkjVZZUjs4RRxXXi+8MVV3hvr8BWKOqXYAY4EG/JzPGGFNmtq1bTpeMRWxscSmhFbxzxFHFFajMPO8HAV8AqGqSXxMZY4wpc9t+HE2WhnLKObd5HcVnxRWogyIyVER6AKcB3wOISBhQvaQNi0gzEZkuIokiskJE7ilkmXgRSRaRxe7rkQLzQ0VkkYhMKd3HMsYYc1T64TQ67PqKZbVPp2HjaK/j+Ky447xbgVeBRsC9eY6czsK5D6ok2cD9qrpQRGoDC0TkR1VdWWC531R1aBHbuAdIBCJ82J8xxphCLP3hXXpziKpxt3odpVSKLFCqugbnfqeC038Afihpw6q6E9jpvk8VkUSgCVCwQBXKvUn4POAp4D5f1jHGGPNndVe8x+aQZnSMG+x1lFIRVS18hsirxa2oqnf7vBORaOBXoLOqpuSZHg98BmwDdgAPHO2YISKfAk8Dtd3phR5lichIYCRAVFRUzKRJk3yNBUBaWhq1atUq1TqBytoiP2uPY6wt8qtM7ZGyczUXrH6Qr+vfSO2uF5b59suiLfr3779AVWMLTi/uFN8onJtyP8YpHnI8OxaRWjhF6N68xcm1EGihqmkiMgSnI0YbERkK7FbVBW4RK5Kqvgm8CRAbG6vx8cUu/iczZswgPj6e5P17OJy6n7Dwqs6rSlVq1a5bYcdJ8YejbWEc1h7HWFvkV5naY97Lb3BYq9Lv2v/zy7Du/myL4grUycBlwBU415M+Aj5T1QO+blxEwnGK0/uqOrng/LwFS1W/FZGxIhKJ0ynjArdoVQMiRGSiql7j675La+UXzxG35Y180zI0nH0h9UkOiyStRjNyojpTOzqGZh37+OU/2hhjylLy/j10OTCNpQ3OpU8l/J1V3DWofcA4YJyINMF5Ft8KEfmbqv6vpA2LiADjgURVfbGIZRoBu1RVRaQ3Tq/Cfar6EPCQu0w8zik+vxUngJNiL2JevaZodiaanQk5GZC2h7DDu6ievpuWyXOITP4e1kDOD8Ka8DbsizqNOp3PoU3MAMKrVPVnPGOMKbXE716nr2QSGV95upbnVeLdWiLSE6c4DQK+Axb4uO3TgBHAMhFZ7E57GPf5fao6DhgG3CYi2ThPSh+uRV0U87PWXU+ldddTi11mb9IWtifO5fCGOdRLmkWvbf8lbPu7HPihNmvq96dmz8vo0HdIpbkJzhgTuHKys2m2biKJ4R3pUMLvtoqqyN+kIvI4MBSnm/ck4CFVzfZ1w6o6kxKuW6nqaGB0CcvMAGb4ul9/imzU3Bl9sv9lAKQc3Mf6uVPIWf4lXfb9QI1pX7F7Wn3WN72I6EGjOLlFO48TG2OC1bJfPqW77iKpe+V98E9xf+r/E9gAdHNf/3bO2iGAqmpX/8er2CLqNqDHOdfBOddx5FAqC375lLCl79Nn67vwzrssqdGbkLg76Hz6+UHV2cIY472Q+W+ym/p0HTTC6yjHrbgCVfGfxV6BVK9Zm5ghN8CQG9i5eTWbfhxHm22Tifz5Wtb90pqD3W+l+7k3EBZexeuoxpgAt2XNYrqmL2B2i1HEVeLr48UNt7G5sBfOPUunl1/EyufkFu2Iu/klav89kXldHidcM4hd8CBJ/+7C/C/GkJ2VWfJGjDHmOO2c+iqZGkabwXd6HeWEFDfcRoSIPCQio0XkbHHchXPa7/Lyi1h5Va1Wg96X3kuzfyxl0aljyAipQa/FD7Pj6e4kfPMWuTk5Xkc0xgSY1OT9dN7zDUvqDiCyUTOv45yQ4i6M/A9oBywDbgam4vS6u1BVy/525AAWEhpKj7OvoeXDCSyKe5Ucwoid/wDrnu5L4twSnxpljDE+W/Ht69SUdOr0q9xHT1B8gWqlqter6hs43cxjgaGquriYdUwxQkJD6XHOdbT4xyLmd3+Kutl76fDd5Sx8big7Nq7yOp4xppLLzcmhyZqJrA5rR9ue/byOc8KKK1BZR9+oag6wUVVT/R8p8IWEhtLrojup/delzG4xivZp86g/4XRmT/g7GemHvY5njKmklk7/mGa6g9Qet3gdpUwUV6C6iUiK+0oFuh59LyIFn6lnjkP1mrWJu+EZUm6excraccRtep3dz8Sw/LcvvY5mjKmEwue9zi4a0G3QtV5HKRPF9eILVdUI91VbVcPyvLfxmcpQo2an0POBr1ka/w6C0vmna5n3ylUkH9jrdTRjTCWxfuksOmUuYWOrqwPm0WvF9eIr8fnpvixjfNc1/lIi/5rA7JOvpef+78h4pReLf/zA61jGmEpg/0+vcFir0mGozyMhVXjFneL7UkReEJEzRaTm0Yki0kpEbhKRHyhkQENzYqrVqEXcra+x8eKvSAuJoPvvtzHv5StJTd7vdTRjTAW1N2kL3Q5OY1nD86hTv6HXccpMcaf4zgJ+whn6fYWIJIvIPmAizjDw16nqp+UTM/i06X4GTf82l9lNbyTmwHekvtyHlXO+9zqWMaYCWjflZcLIofG5gTX4eLEPiFPVb1X1alWNVtU6qtpAVU9V1adUNam8QgarKlWrEXfzS6wd+im5hND+u+HMfuseexKFMeYP6YfTaLftE5bW7EuzU7p4HadM2RNMK4H2vQZS7765JNQfQtz2Cax7th87N6/2OpYxpgJY8s046pFC2Gl3eB2lzFmBqiRq1q5L73s+IKHX8zTN3EjNd/uz8IcSx400xgSwnOxsGq8cz9rQU+gUd57XccqcFahKJva8W0i+7ieSwprQc/adzBl3u53yMyZILf15Es10Byk9bwvIIX1K/EQi0lpEqrrv40XkbhGp6/9opihNWnWixQO/MDfyEvomvc+a5wawd8dmr2MZY8pZ9flj2CEn0e3swLgxtyBfSu5nQI6InAKMxxknym7O8VjVajXoc+e7JPR8huiMNfDmmayaO9XrWMaYcrJq3o+0z1rJlraBO86cLwUq1x3q/WLgZVX9C3Cyf2MZX8VeMIpdV3zDEalBq2+HM/eTF7yOZIwpB0dmvMRBatH1/MDrHHGULwUqS0SuBK4DprjTwv0XyZRWy469iLj7N1ZV70mfFU8w97XryMxI9zqWMcZPtq5dQrdDs0hsejk1atXxOo7f+FKgbgDigKdUdaOItMS5WddUIHXqRdLpge+ZffK19Nn3BeteGMiBPTu9jmWM8YOd3z1HFmG0GRpYN+YWVGyBEpFQ4GFVvVtVPwRQ1Y2q+p+SNiwizURkuogkisgKEbmnkGXi3SdULHZfj/i6rvmz0LAw4m59jYTY52idsYrDY/uxedVCr2MZY8rQ7u0b6b7vOxZHnlfpR8wtSUlPksgBGorI8VyBywbuV9UOQF/gDhHpWMhyv6lqd/f1RCnXNYWIHTqSjed/RFXNoP6HQ1g64zOvIxljysiGr54hhFyaDX3I6yh+F+bDMpuA30XkK+DQ0Ymq+mJxK6nqTmCn+z5VRBKBJsDKknZ4IusaR/vYs0g6aRopE4bRcfrNzN2ziT6X3e91LGPMCTi4N4muSZNZXGcAsS3bex3H70RVi19A5NHCpqvq4z7vRCQa+BXorKopeabH43Rj3wbsAB5Q1RW+rJtn/khgJEBUVFTMpEmTfI0FQFpaGrVqBe6oIZnph6k3/1l65Szih5oXER5zLSEhoYUuG+htUVrWHsdYW+TnVXscWfg+g1M+5uuOL1P7pJblvv/ClEVb9O/ff4Gqxv5phqr69AJqA7V8XT7PerWABcAlhcyLOLpNYAiw1td1C3vFxMRoaU2fPr3U61Q2WZkZOufVa1UfjdCE5y/UI4fTCl0uGNqiNKw9jrG2yM+L9khLOaAHHz1ZFz5zbrnvuzhl0RZAghbyO92XJ0l0FpFFwHKcYTcWiEgnX6qiiITjHCG9r6qTCymOKaqa5r7/FggXkUhf1jW+CwuvQu873mVO63uISZ3OhpfOsdF6jalkln31CnU4RPUBD3gdpdz40s38TeA+VW2hqi2A+4G3SlpJRATnyROJWsT1KhFp5C6HiPR28+zzZV1TOhISQt8RT5AQ+xynZKxk/2sD2LVtvdexjDE+SD9yiFZrJ7CiSlfax57ldZxy40uBqqmq049+oaozgJpFL/6H04ARwIA83ciHiMgoERnlLjMMWC4iS4BXgeHu4V6h65bic5kixA4dyZqB79IwZze8PYjNiQu8jmSMKcGSr0ZzEvvRM//qdZRy5Usvvg0i8k/g6NgO1wAbS1pJVWcCUsIyo4HRx7OuOX6dz7iQ9XUaUmfyldT96HxWDf1fUP1VZkxlkpmRTovEN0kM70inU4d6Hadc+XIEdSPQEJjsviJxni5hKrHWXU8l87ofSJXaNP/6SpZO/9TrSMaYQiz+eiyN2EvWaQ8E5JAaxSnNkyR6uq97VfVAOeUzftS4ZXuq3TqNnWFN6DBjJMmrppe8kjGm3GRlZtB0xeusCWtLlzMv9jpOufPlSRIx5ZTFeCCyUTMa3jWNNVU7cv7OV5j78bNeRzLGuBZ98waNdTdHTr0/6I6ewLdTfItE5CsRGSEilxx9+T2ZKTcRdRvQ+i8/kBDWkz4rn2L2f//hdSRjgl52ViaNl45hXWhrusZf7nUcT/hSoOoD+4ABwPnuK7iu1AWBatVrkhr3EAkRA4nbOJrZb9yF5uZ6HcuYoLXom7doqkmk9rkvKI+eoIRefO41qKWq+lI55TEeCg0Lp+c9HzN37I3E7XyPuWPT6HXb24SEFv5oJGOMf2RlZtB4ySusC21N94FXeR3HM75cg7qgnLKYCiAkNNR56kSjq+mzdzILXr2K7KxMr2MZE1QWfT2WJrqLtFMfDNqjJ/DtFN8sERktImeISM+jL78nM56RkBD6jBzN7Oa30iv5e5a+MsxG6DWmnGSkH6b5sjGsDmtHt/7Bee3pKF9u1D3V/feJPNMU55qUCVASEkLcjc8yZ2J1+q57mcUvX0j7uydTrbovDxExxhyvxV++Rh/2sOeMZ4P66Al8KFCq2r88gpiKqe81jzP3oxr0Sfw3S185n7Z3f0W1GjbsgjH+kH44jZaJ40gM70TnMy7yOo7nfHmaeZSIjBeR79yvO4rITf6PZiqKPlf8jXldHqfzkYWsf3kIh9OSvY5kTEBa/MVLnMR+cuIfCvqjJ/DtGtQE4Aegsfv1GuBefwUyFVPvS+9lYczTtM9YyuZXBpOavN/rSMYElLSUA7Rd8ybLq3an82nnex2nQvClQEWq6sdALoCqZgM5fk1lKqTYC25jcZ8XaJOZyPbXhpBycJ/XkYwJGMs+fZr6pFDlHJ8HKw94vhSoQyLSAKdjBCLSF7BzPEEqZshNLDv1ZVpnrSFp9Lk28KExZWD/7u102fweC2ueQdue8V7HqTB8KVD3AV8BrUXkd+A94C6/pjIVWo9zrmP5aa8SnbWe3aPPIXnfLq8jGVOprfn0caqTToPznyh54SBSYoFS1YVAP5zu5rcCnVR1qb+DmYqtx9nXsPLMsbTI3sSesYOtSBlznHZuXk3PXZ+xoP4QWrS3W0zz8qmbiKpmq+oKVV2uqln+DmUqh+5nDWdV/Bs0y97C3rHncnBvkteRjKl0tn3+KIrQ/BI7eirI+jGaE9K1/zBW93+Dptlb2ff6uRzYs9PrSMZUGhtXzKXnge9Z1GgYjZqd4nWcCscKlDlhXeMvZc2AN2mSvY0DVqSM8Vnq1//gkNSgw+XWc68wvtyo27OQV2sR8eUxSSZIdOl3CWvPGk/jnO0ctCJlTImW/TKZrunzWdnmVuo0iPI6ToXkyxHUWGAO8CbwFjAbmASsEZGzi1pJRJqJyHQRSRSRFSJyTyHLxItIsogsdl+P5Jl3roisFpF1IvL3Un8yU+66nHkha88az8lWpIwpVk52NjV/eZwdEkWPS//qdZwKy5cCtQnooaqxqhoD9ACWAwOB4sYHzwbuV9UOQF/gDhHpWMhyv6lqd/f1BPwxDtUYYDDQEbiyiNdgTo8AACAASURBVHVNBWNFypiSLfh6LK1yN7Gz19+oWq2G13EqLF8KVHtVXXH0C1VdiVOwNhS3kqrudLuoo6qpQCLQxMdcvYF1qrpBVTNxjtgu9HFd47G8RcquSRmT3+G0ZKKXvMTqsHb0PPcGr+NUaKKqxS8g8hGwH6dIAFwBRAIjgJmq2qvEnYhEA78CnVU1Jc/0eOAzYBuwA3hAVVeIyDDgXFW92V1uBNBHVe8sZNsjgZEAUVFRMZMmTSq4SLHS0tKoVcuezg1l3xbJmxZwzsan2SqN2dDrSarWrFNm2y4P9r1xjLVFfifSHkcWvs/glI/5svVT1GnWuYyTlb+y+N7o37//AlWN/dMMVS32BVQH7gc+B74AHgBq4Bx91fJh/VrAAuCSQuZFHN0GMARY676/DHg7z3IjgNdK2ldMTIyW1vTp00u9TqDyR1ssnfGZpj/SQNc90U0P7NlZ5tv3J/veOMbaIr/jbY+dm9fo4UciNeG5C8o2kIfK4nsDSNBCfqf78iSJI6r6gqperKoXqerzqnpYVXNVNa24dUUkHOcI6X1VnVzItlOObkNVvwXCRSQS54iqWZ5Fm+IcYZlKpku/S1gz4E2aZm9j3+uD7WZeE9S2f/IggtLk8ue9jlIp+NLN/DQR+VFE1ojIhqMvH9YTYDyQqKovFrFMI3c5RKS3m2cfMB9oIyItRaQKMBzneYCmEurS75I/bubd+/oQeyySCUor53xPTOrPLGp+PY2at/E6TqXgy71M44G/4JymK80wG6fhnJpbJiKL3WkPA80BVHUcMAy4TUSygSPAcPdwL1tE7sQZhyoUeEfzdNQwlU/X+EtZqkq7GaPYOnYw3P6d3fthgkZOdjZVfnyYXTSg+/BHvY5TafhSoJJV9bvSblhVZwJSwjKjgdFFzPsW+La0+zUVV9f+w1iC0mHGKLaMHQx3/ECd+g29jmWM3y34cjS9c9aT0Ot5YmvW9jpOpeFLN/PpIvKciMTlfZqE35OZgNSt/2Uk9nud5tmb2T3mXJL37/E6kjF+lbxvF22WvUBieCdiBt/kdZxKxZcjqD7uv3m7ACowoOzjmGDQbcDlLCGXDr/cweaxg+GO76lTL9LrWMb4xaoPHiRWU9l/wYtIiD3+tDRKLFCq2r88gpjg0m3AcBYrdPz1djaNGQx3fGdFygScNQt/odfeL5kXdRl9u/T1Ok6lU2SBEpFrVHWiiNxX2PyieuYZ46vuZw1nMVakTGDKyc5Gvr2f/VKHjlf9x+s4lVJxx5s13X9rF/Ey5oR1P2s4K08fTXTWenaNGUzygb1eRzKmTCRMfok22WvZFPMwEXUbeB2nUiryCEpV33D/tYFKjF91H3SVcyQ18047kjIBYd+ubbRf+RIrqnQj5rxbvI5Taflyo+5/RaRunq/ricg7/o1lgk33QVex4rRX7UjKBISN799DdU2n1iUvW8eIE+BLy3VV1YNHv1DVAzhDbhhTpnqcfY2d7jOV3tLpnxKbMo0FzW+kRXu7I+dE+FKgQkSk3tEvRKQ+vnVPN6bUug+6ipVnjLEiZSqlw2nJRP76EJtDmtLz6ie8jlPp+VKgXgBmiciTIvIkMIviByo05oR0H3glK88cS3TWBruZ11QqS//3Nxrrbg6d/YINRFgGfHma+XvApcAuYDfOsBn/83cwE9y6nzWcxH5jaJG1kT1jzrEHzJoKb92SmfRKmsTc+hfQse+5XscJCEUWKBGJcP+tDyQBHwDvA0nuNGP8qtuA4STGj6NZ9hb2jj3XhuowFVZmRjohX97BAalD+xEveR0nYBR3BPWB++8CICHP6+jXxvhdt/6Xsbr/GzTJ3sr+seewf/d2ryMZ8ycLJv4frXI3se30/9gtEmWoyAKlqkPdsZr6qWqrPK+WqtqqHDOaINc1/lLWnjWexjnbSR43mL1JW72OZMwf1i+dReyWd0iIGET3gVd6HSegFHsNyh2b6fNyymJMkbqceSHrBr1DVE4Sh948l707NnsdyRgyM9Lhy9tJltq0uW6M13ECji+9+OaISC+/JzGmBJ1Pv4BNg98jMmcvR946l13b1nsdyQS5Be//k9Y5G9l22tM2AKcf+FKg+uMUqfUislRElonIUn8HM6YwHfuey9bzJlI39wA54wezY9NqryOZILVm4S/Ebh5PQsRAug+6yus4AcmXG24H+z2FMaXQvvcg1oR9RNRXV5I+YTBbr/mSZqd08TqWCSLZGUeo/vV97Je6tLl+nNdxAlZx3cyrici9wF+Bc4Htqrr56KvcEhpTiLY9+7H30slUIYvqE4eyOXGB15FMEAlZ9A5NcneyZ9Ar1Knf0Os4Aau4U3z/xRlFdxnOUdQL5ZLIGB+17tKXlCu+ACDio4tYt+R3jxOZYLDk50kMSJ/KvEbD6Xza+V7HCWjFFaiOqnqNO+zGMOCMcspkjM9adIjhyDVTyKAKJ30+jFXzp3kdyQSwfbu20eTXv7GOZvS4wcZs9bfiClTW0Teqml3aDYtIMxGZLiKJIrJCRO4pZtleIpIjIsPyTHvWXS9RRF5178ky5k+andIFveFbUqQOzadcxfKZX3kdyQSg3Jwctr97HbX1EIkd7rNn7ZWD4gpUNxFJcV+pQNej70UkxYdtZwP3q2oHoC9wh4h0LLiQiIQCzwA/5Jl2KnAa0BXoDPQC+vn8qUzQOblFO6rd8gO7Q6No8+ONLP5pkteRTICZ9/5jdE1PYHGnB6kdZc8qKA/FPUkiVFUj3FdtVQ3L8z6ipA2r6k5VXei+TwUSgSaFLHoX8BnOg2j/WB2oBlQBqgLhOA+rNaZIkY1bUPf2H9kSHk2nX28n4es3vI5kAsSqhJ+IWT+GhTXPpPewB7yOEzTEeViEn3ciEg38CnRW1ZQ805vgPPNvADAemKKqn7rzngduBgQYrar/KGLbI4GRAFFRUTGTJpXuL+e0tDRq1apVyk8UmAKlLbLSD3HSvCfpkrOKbxreTO3OQ49rO4HSHmUhmNsi40gqXebeiyIs7/MSVavXDur2KKgs2qJ///4LVDX2TzNU1a8voBbOA2YvKWTeJ0Bf9/0EYJj7/hTgG3fdWsBs4MyS9hUTE6OlNX369FKvE6gCqS2OHErVRc+co/pohM5692+am5NT6m0EUnucqGBti5zsbF34zLma+Ug9XTX/pz+mB2t7FKYs2gJI0EJ+p/vyJInjJiLhOKfv3lfVyYUsEgtMEpFNOD0Fx4rIRcDFwBxVTVPVNOA7nOtYxvikWo1adLr3SxIiBhG36XXmjhtFbk6O17FMJTN34iP0ODyLBW3vpV3sAK/jBB2/FSi31914IFFVC+2Pqc6T0aNVNRr4FLhdVb8AtgD9RCTMLXL9cK5hGeOz8CpV6XnPR8w56Qr67v6Iha9c7jzc0xgfLP/tS3pvGMOC2v3pc+X/eR0nKPnzCOo0YAQwQEQWu68hIjJKREaVsO6nwHqcm4SXAEtU9Ws/ZjUBKiQ0lD6jxjG75Z3Epkxj1UtDOZyW7HUsU8ElbV1Hk5/uZGtoU9qPnICE+PVkkymCL8/iOy6qOhOng4Ovy1+f530OcKsfYpkgJCEhxF33FPM+a0jM0sdY//JAGtzyOQ2imnodzVRA6UcOkfLfK2msWYQMn0jN2nW9jhS07M8CEzR6X3ovy04fS7OsTRwZN5DtG1Z4HclUMJqby/LXr6Nt9hrWnvY8zdt29zpSULMCZYJK90FXsXnoh9TUNKq/dy5rF/3qdSRTgcz53z+JTfmR2dG30ePsa7yOE/SsQJmg077XQFKvmkK6VKPJF8NYPO1DryOZCmDR1In02TCGhNpn0ffaf3sdx2AFygSp5m27U+XWn9ge3pwuv93G3I/+43Uk46H1y+bQ7vf7WBfehs63vWedIioI+18wQSuyUXOa3PsTy2r2pU/i08x5fRQ52aV+LrKp5JK2rqP2Z1eSJjWpd+MnVKthT4ioKKxAmaBWo1Ydutw3hbmRl9J314csffF8DqUe9DqWKSfJB/aS/u7FVNcjHLpsEg0bR3sdyeRhBcoEvdCwMPrc+Q5z2/+drodmk/RyPElb13kdy/hZRvphtr1+MY1ztrN50Ju07NTH60imACtQxrj6DH+IFfFvE5WdRNj4s0jZbg8vCVQ52dksH3M1nTKXsjTmKTqffoHXkUwhrEAZk0fX/sPYO3wKmVKFc9b8k/lfjPE6kiljmptLwtgbiEn9mdmt7ib2gtu8jmSKYAXKmAKiO8RS/fZfWRXahl6LH2bO66PIzsr0OpYpA5qby9w376TP/q+Y3fha4q590utIphhWoIwpRL2GJ7P31Cf+6Dyx8oVzObg3yetY5gTNee9h+ia9z9zIS+h78ytexzElsAJlTBFCw8Lpc+c7zOvyGO2PLOHwmDNYt2Sm17HMcZrz3j+J2/Q6CRGD6HXb23avUyVg/0PGlKD3pX9h04WfEao5NJ18EfM+f83rSKaUZv/3H/Td8CoLag+g+10fEBIa6nUk4wMrUMb4oG3PeMJv/4111TrRe8n/Me+Vq0k/nOZ1LOODORMeJm7jaBIiBtLt7o8IC6/idSTjIytQxvio/klNaP/Aj8xucj29D0xhx/OnsXXtEq9jmSJobi6zx99P301jSIgYRA8rTpWOFShjSiEsvApxt7zCkn5vUy93H/Unnk3C1294HcsUkJuTw7yxNxG39W3m1R1Cj7snERrmt+HvjJ9YgTLmOHTrfxkZN81gS5VWxC54kPkvXU5aygGvYxkgMyOdRS8Po8/eycxpdDW97n7filMlZQXKmOPUqNkptHnwF2Y3u5meB6dy8KU41iz8xetYQS3l4D5WvTSEmNSfmdPqbvqOGmu99Sox+58z5gSEhVch7qYXWH3uh4RpFi2/vJjZ7zxIVmaG19GCzo5Nq9n/ajwdjixmftcn6Gs34VZ6VqCMKQMd4wZT/e45LKnTn7gtb7Dx2dPZsmax17GCxuqEn6k6YRD1c/eyeuC79LrkHq8jmTLgtwIlIs1EZLqIJIrIChEp8jtGRHqJSI6IDMszrbmITHXXXyki0f7KakxZqFO/IbH3fcaC3i9yUvYOTnp/IHMmPmZjTPnZ/C/G0OLry0mXahy48js6n3Gh15FMGfHnEVQ2cL+qdgD6AneISMeCC4lIKPAM8EOBWe8Bz7nr9wZ2+zGrMWUmZshNZI+cxaoaMfRd9xLr/xPHxpXzvY4VcDIz0pk7+gZ6LX6Y9VU7Uv226bRo193rWKYM+a1AqepOVV3ovk8FEoEmhSx6F/AZeQqQW8jCVPVHd/00VT3sr6zGlLXIxi3o9tfvSIh9jobZSTT56Bxmj7+f9COHvI4WEHZtW8/G5/rRZ+9kZp98De3+Oo36JxX268VUZuVyDco9PdcDmFtgehPgYmBcgVXaAgdFZLKILBKR59wjLWMqDQkJIXboSPT2OSyt05+4rW+z99meLJ3xmdfRKrWF30+g2ttn0DRrEwv7vkLcrWPsBtwAJarq3x2I1AJ+AZ5S1ckF5n0CvKCqc0RkAjBFVT91r0WNxylqW4CPgG9VdXwh2x8JjASIioqKmTRpUqnypaWlUatWrdJ/sABkbZFfWbdH8qaFdN/0Ji3YyazwvhzsdAM16jYqs+37U0X43sjKOEz4wreIz/iZRGnN+s73UatBU0+yVIT2qCjKoi369++/QFVj/zRDVf32AsJxri3dV8T8jcAm95WGc5rvIpxrVjPyLDcCGFPS/mJiYrS0pk+fXup1ApW1RX7+aI/0I4d01jsP6uFHIvXIIw101lv3alrKgTLfT1nz+ntj+e/f6NbH2mnOI3V01ht3aWZGuqd5vG6PiqQs2gJI0EJ+p/uzF5/gHAUlquqLhS2jqi1VNVpVo4FPgdtV9QtgPlBPRBq6iw4AVvorqzHlpWq1GsTd8AzJN89meZ1+xG17h0Mv9GDeZy/boIiFSDm4j7mvXUunqVci5JJ4zgfEjXyV8CpVvY5myoE/r0GdhnPkM0BEFruvISIySkRGFbeiquYADwA/icgyQIC3/JjVmHLVqNkpxN73GavO+4wDYQ3pvexRdjzdnYXfT0Bzc72O5znNzWXBN2+T/nIssXu/Yk7UldR/YAGdTh3idTRTjvz2gCpVnYlTWHxd/voCX/8IdC3jWMZUKO17DURjBrBo2gfUn/Mfes65h3XzXyW1z310O+vKoBy3aN2S38mc8iAxWctZH9qKg+dNoG/Pfl7HMh6wJ0kY4zEJCaHH2dfQ9OHFzOv2L6rlHqLHrDvY/FRPFnw7Pmhu9N2xaTXzXr6SVpPP4+SsLczt9AjRD82nrRWnoGUFypgKIjQsjN4X30Wjh5eR0PM/hJBNzLz72PVUB+Z88CSpyfu9jugXu7dvZO5r1xH5bhzdDvzIvEZXEHLPIvpcdr89hTzI2f++MRVMWHgVYi+4jZwht7Dop/eplvAGfdc8T+rqMcw96TxOih9Jy059vI55wjaunM+eqS/S/cBUeqAsijyf6IsfoW/T1l5HMxWEFShjKqjQsDB6nHMdnHMdaxb+QsqMV+mx+wuqfPIpqz9vT3KHK2k34Brq1Iv0OqrPsrMyWT7jU0IWjKdregKNtAqLGl5As/P+Rp+W7b2OZyoYK1DGVAJte/aDnv04sGcnC6e+xcnrP6bdskfJXPoki2r2IbfzpbQ7/RJqRdTzOmqhNicuYMev79Bm5xS6c5C91GV29G10GHovfSIrx83KpvxZgTKmEqnX8GT6Xv0Imvt/rFn8G/vnfkDrXT/QcN7vZM59kKXVu3G4xUCa9Dqfpq06eTZYX25ODuuX/s7ehM9ovHMaLXK30URDWFazL9t6jKBTv0uJs3uZTAmsQBlTCUlIyB9HVTnZ2ayYN5XUJV/RZPcvdF39DKx+ht3UZ0tET3KaxVG/TR+at4+harUavu1g504YPhw++ggalXyEk5WZwZZVC9ib+BvhW2bS6tBC2pBGSw1hVbWuzG11La37XUmPRs1P8JObYGIFyphKLjQszLmB1b2JdevaJexYNJWwrb8TnZJA5IppsAIyNZR1YdEcrNmSrDotCW94CrWiWlGrQWPqRTWlZu26xzb65JMwcyY88QSMHQtA+pFDJO9LImXvDlJ2rCNzzzpCD26kbupaWmRtpLVk0RpIoiFr6p5JSKszaR13EZ0bnuxBq5hAYAXKmADTrE03mrXpBvwVzc1l+6ZEklbNIXPrYmrtX06TlCVEJf9EyNb8D4pO13Cq/nsfkve2q9dfh9dfp18YyD8iqAZE5Zm9jzrsrNqSRZGXE9asByd3OJ3G0e1o5NGpRRNYrEAZE8AkJIQmrTrRpFWnfNPTjxwiaVMiKUmbyEhOIidlFxzeR5XH9tF88hzqLdtOaFYOOeGhHOjajJWDu1EluiNSswHhESdRp3Ebolq0o0FEPRp49NlM4LMCZUwQqla9JtEdYqHDn0c4YNttsPhNqFaN0MxMInsPJvesy+kbH1/uOU1ws+NwY0x+u3bBqFEwZ47zb1KS14lMkLIjKGNMfpPzjCs6Zozz74wZnkQxwc2OoIwxxlRIVqCMMcZUSFagjDHGVEhWoIwxxlRIVqCMMcZUSFagjDHGVEiiqiUvVUmIyB5gcylXiwT2+iFOZWRtkZ+1xzHWFvlZexxTFm3RQlUbFpwYUAXqeIhIgqoWcjt98LG2yM/a4xhri/ysPY7xZ1vYKT5jjDEVkhUoY4wxFZIVKHjT6wAViLVFftYex1hb5GftcYzf2iLor0EZY4ypmOwIyhhjTIVkBcoYUyIREa8zmOBjBcoY44s6XgcwwSeor0GJSHcgA0BVEz2O4ykR6QxkASHB3hYAIjIQyAZ+U9Ucr/N4SUTOAW4BblfV3V7n8ZqInAo0BpJV9Uev81QkIhKiqrlltb2gPYISkcHA18DtwCcicoPHkTwjIkOAD4H7gXdE5FyPI3lKRMKBp4GngN4iErQDe4pIP+AN4C0rTiAiZwMTgE7ApyJypreJvCUi54nI4yLytIg0KMviBEFYoMRRC7gLuENV7wJuBv4hIqO8TVf+RCQWeBGnDW4FXgcGu+0UdN8frmxgjvvvP4DTIWivw7QDnlHVH0SkkYicGqy/lEWkIfAEcK+qPg48CYSISBtvk3lDRPoAo4HVQD3gK/f7I7ys9hF0v4DUkQYkABEiEq6qc4DhwN9E5DpvE5a7SOApVZ2rzvneDUBXnFN9ZfrXUGXhtsO3wOPAZ8BfRORu4F4RCfU0XPnLBGJEpCVOmwwH/iciD3gbyxMHgflApntK/GHgJuAXEbnd02Te6AxMVdUPVHUUzs/Kg0BPcE73negOgq5A5ZEEnAVUB1DVBGAEcJf7wxgUVPV7YFqeSYuBI0evu4hII0+CeU+BO1X1XWA78BJQIwivR80HjgBXA/9T1buBIcCt7mnyoKGqWUAacCXwMfCKqo4ALgD+JSKne5nPA/OB6iLSHkBVXwRmAi+LSN2y+AM36ArU0dM0qjoWqAGME5E67pHUTGApzi+ngJenLXbmmRwGNBWRUBG5HhgvIjWC5fRWns85DVgiInE4f8iMBwa4F8iDhqquwDlyuAA4WURqudM+xf3jLhgcPRpQ1YeA23BOhf/mTksAJuL87ASTJJzT4INEJBJAVZ8HluNcLjhhQdGgItIOqI9zWi8XyAFQ1StEZBLwMjDHvRjeD6fRA1JhbVGg580RnNN8f8P5pXSTqh72JGw5KNgeqpojIqKq2e459keBC1X1axG5A9jmZV5/KqwtAFT1nyKSCTQH7haRNJxTfW97FrYcFPKzgvu9ken+IXOTiGwDzgAG4hxlBzQRCc3zfbFbRF4D/uXOm6Gqy4D1lNEf+QHfzVxELgH+jXOaZjvON9sEVU3Js8yNON1GuwGPuX8hBpzi2iJvkRKR2Tj3vVwayF3OS/recDvTtFPVBd6lLB8+/pwMAFoDHYE3g/l7w13mA5zbVNoAI1V1pRdZy4OItFXVNe770Dx/yKmI9MA5YqqLU5h6Axe5xerE9hvIBcrtTTIReFVVfxeRS4G+ON9Uz6lqcoHlq6pqhgdR/a40bSEiDwOTVXWVN2n97zi+NwK208hxtEWYqgbyWYbS/KyEADVVNdWbtP4nIkNxrrl9oapXudOOFqkQVc11T/HVA3oBs1V1Y1nsOxiuQUXg/IUD8DkwBaiCc6ETEektIj3d+ZnlH69cldQWfdy/lP4dyMUpj5LaI1acm7kJ1OKUR0lt0SvPz0kwdBTx5Welu6rmBnhxqgncCdyL03txIoBbnMLy/Fxkq+pat0dfmRQnCPAC5fa6eRG4RETOcBtzJk5PtTNFpDpwGrDDXT5gDyd9bItTgYD9YcvLx/Y4A+dCcEDzsS1OJwh+TqBUPyvB8L1xCLgR+AB4AKiWp0hlA4hIN+AaEalW1p2pAvoUH4CIVMO5CbUrMFFVf3Wnz8DpALDew3jlytoiP2uPY6wt8rP2KJyINMAZ/+mIql4jIl1xjjR/88eTRgK+F5+qpovI+zgX7x5y++xnAA1x7mkIGtYW+Vl7HGNtkZ+1R+FUdZ+I3Ao8JyKrcc7CnemP4gRBcAR1lIhUwTmddyuQjnOT3SJvU3nD2iI/a49jrC3ys/YonIj8BedWlEFl0VuvyP0ES4E6SpxH1WgQXPQukbVFftYex1hb5GftcYyI1MPp1Xe/qi71676CrUAZY4w5MSJSTVXT/b4fK1DGGGMqooDuZm6MMabysgJljDGmQrICZYwxpkKyAmWMMaZCsgJlgp47fERZbCdeRKa47y8Qkb+Xcv1N7kM3806b4N4YmXfaRSLybQnbKvYziUhdyTMKrIg0FpFPi/sc7n47luYzGXMirEAZ4weq+pWq/qcMNvUhzthLeQ13p5+IusAfBUpVd6jqsIILFfgcF+EMtWFMubACZYzLPXL4RUQ+FpE1IvIfEblaROaJyDIRae0uN0FExonIb+5yQwvZ1vUiMtp931BEPhOR+e7rNHd6AxGZKiKLROQNoLAHbU4D2ovIye46NXAGx/vC/fo+EVnuvu4tJEctEflJRBa6n+FCd9Z/gNYislhEnhORaBFZXtTnEGck4QtwHnGzWERai8jCPMu1EZGAHzfLlC8rUMbk1w24B+gCjADaqmpvnNFj78qzXDTO6MvnAePch4sW5RXgJVXtBVzKsZFoHwVmqmoP4CucEWvzcUcvnQxc7k66AJiuqqkiEgPcAPTBGa/oFnEGj8srHbhYVXsC/YEX3CdO/x1Yr6rdVfWvJbQJqjrLzfhXd531QLK4w5G4OSaUtB1jSsMKlDH5zVfVne7AleuBqe70ZThF6aiP3bGA1gIbgPbFbHMgMFpEFuP8ko8QkdrAmTgD46Gq3wAHilg/72m+vKf3Tgc+V9VDqpqGU8jOKLCuAP8WkaU4R2NNgKhispbG28AN7mOArsAZksGYMhPwTzM3ppTyjqicm+frXPL/vBR8BEtxj2QJAeJU9Ujeie7QOb48yuV34GR33J1TOVasfBl752qcJ3DHqGqWiGwCijvaK43PcI4CfwYWqOq+MtquMYAdQRlzvC4TkRD3ulQrYHUxy07FGZUUgDynxX7FKSCIyGCcIbP/xB0g8GPgv8C3eZ6B9itwkYjUEGfk04uB3wqsXgfY7Ran/kALd3oqUNunT3pMvnXcHD8ArwPvlnJb5v/bu0PcBIIoDuPfOwGH4Ao9AYKzrEJRiajmCghM0woSTJPqCkQbgkAQsPU9w6vYIVQ0pSVNdkK+n5xkZ96qf3bfZEZnGVDSZQ7AC/AMNGcOzhwBNxGxjYgd0JTxO9obWjfAEHj/YY4H2v7Y43EgMze0fZ834BWYfXMVxH1Ze00bhvvy7AewKpsrpr94X8rat2VTR//L/MnpV6j0bzwsVvqjiJgDT5m56LqWrkXEGOhl5qTrWnR97EFJukhELIE+MOi6Fl0nv6AkSVWyByVJqpIBJUmqkgElSaqSASVJqpIBJUmqokNhMQAAAAZJREFU0icUMTAgAhsOpAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = implied_volatility(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 670,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:12: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.59]\n",
      "[2.21999505]\n"
     ]
    },
    {
     "data": {
      "image/png": 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EGuK6JcbvwGxgjqrmeT2hMcaYMrNm4dd00j0s7Xyf01FKVGSBEpF3gUbA17huibEPCAXaAIOAv4jIw6o6vzyCGmOMOXcnEqe6B0eMdjpKiYrbgvqXqv5eyPTfgVkiEoL75oPGGGMqvgMpO+icvoBlkVcTVy3M6TglKvIY1OnFSUSCRaS7iNR3zz+hqhu9HdAYY0zZ2PDdWwRLLuf1H+90FI8UWaBEZLKIdHQ/DwdWAu8Dv4nI9eWUzxhjTBnIy82l6ZZPWBPSmWbtejgdxyPFjeK7UFWT3M9vA9aramcgGniopDcWkSYiEi8iySKSJCJnHJETkeEiskpEVojIUhG5wD29m4gsci+3SkRGncVnM8YY4/b7L/+hke4ls3PFP/Z0UnHHoE7ke34p8BmAqqaIiCfvnQNMUNXlIlIDWCYi36vqmnxtfgS+VFUVkS7Ap0A7IBO4WVU3iEhD97Lfqmqa5x/NGGPMSbmLp5BKOJ0vrTwFqrgtqDQRGSYi3YE+wFwAEQkCqpb0xqq6R1WXu5+nA8m4RgXmb5Ohqup+WR1Q9/T1qrrB/Xw3rhGE9UrzwYwxxrjs2baOLkcXsb7RCKqEVnM6jsfkVH04bYZIG+AVoAHwkqpOc0+/DBioqhM8XolIFDAf6KSqR06bNwJ4HqgPDFXVRafN7wW8B3Qs7LwrERkHjAOIjIyMnjFjhqexAMjIyCAsrOKPZikP1hcFWX+cYn1RUGXrj6yl07gk/T982/1NqtWKLNP3Lou+6Nev3zJVjTljhqp69QGEAcuAkSW0uwj44bRp5wHrgDhP1hUdHa2lFR8fX+plfJX1RUHWH6dYXxRUmfrj+LGjmvpEY13+wiCvvH9Z9AWwVAv5nV7cibqvFFfxVPXekqqiiAQDnwMfquqsEt5vvoi0FJEIVT0gIjVxXbHir6qaUNK6jDHGnGn19x8QwxF2xd7udJRSK26QxHhcJ+V+CuwGPBoZcZK4RlJMBZJVdVIRbVoBm1RVRaQHEAKkuk8C/gJ4X1U/K816z9aBlO1kZx2jQZPWSIBdotAY4xvCVk1jp5xHxwuGOx2l1IorUOcB1wCjcI3I+wT4XFUPefjefYDRwGoRWeGe9ijuq0+o6mTgKuBmEcnGdZ2/Ue5idS2uXX51ReRW97K3quoKvGTDnNfovW0yaYSxo0prMup0pGrLC2gefSnhtSO8tVpjjPGaTasTaJe9hoTWD9I4MNDpOKVWZIFS1VRgMjBZRBoB1wNJIvJnVf2gpDdW1QWUsNWlqi/gus7f6dOnA9NLWkdZanj+9SRWr4ukrKL24WTa7p5ByJ7p5P4ibAhqyYH6cdToNIg2MZcSUiW0PKMZY8xZSf3p/2ioIbQfVDmuHHG6Yq9mDuDe9XY9rnOh5uAa8OBzmrXtRrO23f73+vixoyQtn8eRtT8RnpJAzO6PCd4znczvqpBUPZqcVoNodeG11K53noOpjTGmcGkHUuhy8FtW1R1Er7plO3KvvBQ3SOIpYBiu85dmAI+oak55BXNaaNXqdOwzFPoMBSDjyCGSEueQtfZbmqX+SoNVC8ld+QRJVTqR0fJy2vS/2YqVMabCWPvNa8RJNvUG3ON0lLNW3BbUY8BmoKv78Zz7ChICqKp28X68iiOsZm26XXoDXHoDmpfHxtWLOLDkcxrs/o6Oyc+RveYFVlTrSW7n6+g84HrbDWiMcUxO9gmiNn9MUkhXOnaMdTrOWSuuQDUvtxSVjAQE0KprH1p17YPm5bEpaTH7f32fFilzqL/4fg4sfpINja6k2aV30jCqrdNxjTF+ZvVPH9Od/eyJedLpKOekuEES2wqbLiKBuO6yW+h8fyMBAbTsHEfLznHk5uSw8pcvyFvyDr12voe8+x7Lwy6ker8HaBvT3+moxhg/EbJsCnuoR5f+1zkd5ZwUd7uNmiLyiIi8KiIDxeUeXLv9ri2/iJVHYFAQXftdQ/eH5rB/7FISG91Mq6PLaPv1CNY824dV8TPRvDOu1mSMMWVm8++JdDyxim0tbyAwqMRxcBVacWekfgC0BVYDY4HvgKuB4apa+c74KmcNmrSi97hXCHgwiYQ2E6mTnUKXn8ew7rnzWT3/CytUxhivOPDjKxzTENoPucvpKOesuPLaQl33f0JEpgAHgKbqujK58VBYzdrE3fAYJ7L+ROKXr9Is6Q0a/HQraxZ0JnDg07brzxhTZg7t30OXg9+ysu5gYivp0PL8ituCyj75RFVzgS1WnM5eSJVQYq+ZSO2HV5PY/hHqn9hB269HsOxfI9i9Za3T8YwxPmDt1y8RKtk0GPiA01HKRHEFqquIHHE/0oEuJ5+LyJFiljPFqBJajdhRDxP64AoSGo+hw5EFREzrw6K37yMz47DT8YwxlVTW8Uxab5vBqtCeleaW7iUpskCpaqCq1nQ/aqhqUL7nNcszpC8Kq1mbuLGTSB+3mFXh/ei9axpHXoxm+bcf2PEpY0yprZr7DhGkIb3vdDpKmSluFF+Jd6DypI0pXv1GzYl5cCZrBn3CsYDq9Fh0N6v+eRkp2zc4Hc0YU0loXh51Vk9ha0BTOl14pdNxykxxu/j+KyL/EpGLRKT6yYki0kJExojIt8Ag70f0Dx3iBtHkkSUktJlI68yV1Jh6AYkznicvN9fpaMaYCi5p4de0zN3Cvo5jfOp2QcXt4hsA/Aj8EddVzA+LSCquq4w3AG5R1ZnlE9M/BAWHEHfDY6Td9gubqnYkdu3fWf/3C9ixcbXT0YwxFVjOr69xkJp0GVL5bkpYnGJLrap+o6o3qmqUqoaral1VPV9Vn1XVlPIK6W8aRrWl80M/sKTbczTM3kbdDwaQ+MnfbWvKGHOG7etX0O1YAuuaXEto1eolL1CJ+M62oI+RgAB6XnkXx2//lY1VOxOb/DxJ/xjA3p2bnI5mjKlAUua+SJYG03ro/U5HKXNWoCq4+o2a0/mh70ns+Bgtj6+hypSL+O27cr2XozGmgjqQsoOuqXNZETGEiAZNnI5T5qxAVQISEEDsNRNJvel7DgRG0n3hXSS+ehvHMzOcjmaMcdCGr/5FMDk0HPwnp6N4RYkFSkRaikgV9/O+InKviNTyYLkmIhIvIskikiQi9xXSZriIrBKRFSKyVEQuyDfvFhHZ4H7cUtoP5ouatO5Kkz8tICHyemIPzGLPi33YsWGl07GMMQ44mp5Gh12fsiLsApq06ux0HK/wZAvqcyBXRFoBU3HdJ+ojD5bLASaoansgDrhLRDqc1uZHoKuqdgP+AEwBEJE6wBNALNALeEJEanuwTp9XJbQacXdMZtXFU6mVl0qd6QNZ9s1Up2MZY8rZ6q9eJZyjVOvnG5c1KownBSrPfav3EcBLqvoAUOK9zVV1j6oudz9Px3Xr+EantclQVXW/rA6cfH4Z8L2qHlTVQ8D32DlXBXTpdzVZY+axI7g50YsfJPHVP3Ai67jTsYwx5SD7RBZR66eRHNyRdjEDnI7jNXKqPhTRQCQReAn4C3C5qm4Rkd9VtZPHKxGJAuYDnVT1yGnzRgDPA/WBoaq6SEQmAqGq+jd3m8eAY6r6YiHvPQ4YBxAZGRk9Y8YMT2MBkJGRQVhY5b0gRm5ONrr8XS7JnM3v0oYd3f9M1ZoRZ/Velb0vypr1xynWFwU53R+H18YzPOUl/tvkYcJb9nYsB5RNX/Tr12+ZqsacMUNVi30AHYBXgOvdr5sDD5e0XL7lw4BlwMgS2l0E/OB+/ifgr/nmPYZrd2Gx64qOjtbSio+PL/UyFdHS2VP06OP1dN8TzTQ58buzeg9f6YuyYv1xivVFQU72R15urm5+qotufaqj5ubkOJbjpLLoC2CpFvI7vdhdfO7buz+qqveq6sfugrZFVf/uSVUUkWBcx7A+VNVZxbVV1flASxGJAHYC+cdMNgZ2e7JOfxU9ZAx7r/2KLKlCi9mjSPzsX05HMsZ4wcr4T2met5V9Xe4gIDDQ6TheVdKVJHKBeiISUto3FhHBNagiWVUnFdGmlbsdItIDCAFSgW+BgSJS2z04YqB7milG846x1LhnAWur9iA26WkSXxtDTvYJp2MZY8qI5uURuugl9lCPbkPGOh3H6zy5Yf1W4FcR+RI4enJiUUUnnz7AaGC1iKxwT3sUaOpefjJwFXCziGQDx4BR7s29gyLyDLDEvdzTqnrQs4/k38Lr1KPjxLkkvH03cXs/ZvWLm2j6x88Ir1PP6WjGmHO0JmEuHXOSSWz/COeFVHE6jtd5UqB2ux8BQA1P31hVFwBSQpsXgBeKmPcO8I6n6zOnBAYFEXfHZBZ/0YFuK55k7/9dxJEbP/XZcyWM8Re5818klXC6Xn6301HKRYkFSlWfAhCRGq6XapcvqCR6jbiX5IZtaTBnLDJ9EGsGTaVDnI3WN6Yy2rDiF7ocX8aiFvfSu5p/jKj05EoSnUTkN+B3XLfdWCYiHb0fzZSF9rGXkXnzXI4EhNNqzo0s/fINpyMZY85C+vf/4AjV6DTcd0/MPZ0nJ+q+BTyoqs1UtRkwAXjbu7FMWWrUoiPhd//MhiodiFn+MIve/bPdVt6YSmRr8lK6ZfxCUqNR1Aiv43SccuNJgaquqvEnX6jqPFxXfTCVSHiderSe8D1LwgfSe9tklrx6s43wM6aSOPDNcxwnhPYjHnY6SrnypEBtFpHHRCTK/fgrsMXbwUzZC6kSSsx9n7Co0W30OvgVSZOGcjQ9zelYxphibFu3gh5HfmJlw1HUimjgdJxy5UmB+gNQD5jlfkQAt3kzlPEeCQig9+0vkdjxMTplLmH3y5dwcN8up2MZY4qw75tnOU4Iba78s9NRyl2xo/jyX0minPKYchJ7zURW1G5Eu1/uYf8bl3D85i+cjmSMOc3Ojb/TI+17ljS4jrjIxk7HKXeeXEkiupyymHLW7ZLr2TrkI2rqYULeu4z0lI1ORzLG5LP762fJJohWIx51OoojPNnF95uIfCkio0Vk5MmH15OZctEudiCHRn1JLoH0Tf4raxLmOh3JGAPs2pxMj0NzWRE5kogGTZ2O4whPClQdXNfH6w9c7n4M82YoU76i2segY74jVWrTYs5NrPypdLcsMcaUvd1fPkUOgbS80j+3nsCzY1CrVPXf5ZTHOKRBk1bM7fk82cufoePPd7A0I42YK8Y7HcsYv7Rjw0p6HJrLkgajiGsY5XQcx3hyDOqKcspiHBZavRYN7v2edVU6E7P8zyR+4tFdVYwxZWzvV0+TRQitRz7mdBRHebKLb6GIvCoiF4pIj5MPryczjqgRXoeWD8zht2rnE5v8PIve89/dC8Y4YWvyUnoc/pGVDUdR1w9H7uXnydXMz3f/+3S+aYrrmJTxQaFVq9Pp/v+w9NUb6L3lNRa9mU7c7S8jAZ78PWOMORcHZz9FBKG0v+ovTkdxnCdXM+9XHkFMxRIcUoUe931K4uu30XvP+yS+nkHPO6b4/B08jXHSplUL6ZExn4QmY4jzs6tGFMaTq5lHishUEZnjft1BRMZ4P5pxWkBgIL3umkZCgxuJPTCLZf93I7k5OU7HMsZnpc95iiNUo/1VtmsdPDsGNQ3X7dYbul+vB+73ViBTsUhAALHjXmVR03H0TJvDipevJvtEltOxjPE5yYnf0u1YAknNbyO8doTTcSoETwpUhKp+CuQBqGoOkOvVVKZCkYAAev/hnyS0vI/o9Hh+f+lKso5nOh3LGJ+heXnww5McoBZdr/K/a+4VxZMCdVRE6uIaGIGIxAGHS1pIRJqISLyIJItIkojcV0ibG0VklfuxUES65pv3gHu530XkYxEJLcXnMl4QN/ppEts/QvfMhax76QqOZ9rNlY0pC6vmfUr77DVs6nA31cLCnY5TYXhSoB4EvgRaisivwPvAPR4slwNMUNX2QBxwl4h0OK3NFuBiVe0CPIPr5oiISCPgXiBGVTsBgcB1HqzTeFnsqIdZ3PlJOh1bysaXh5KZUeLfKsaYYuTm5FBzwfPslPPocaVdlzu/EguUqi4HLsY13PyPQEdVXeXBcnvcy6Kq6UAy0Oi0NgtV9ZD7ZQKQf9B/EFBVRIKAasDukj+OKQ+9rnqAZd2fpf3xlWx9ZSgZRw6VvJAxplC/ffM2zfO2sjdmIsEhVZyOU6GIqnp/JSJRwHygk6oeKfv2HE4AACAASURBVKLNRKCdqo51v74PeBY4BnynqjcWsdw4YBxAZGRk9IwZpbuOXEZGBmFhYaVaxleVti8Or/uZobtfYl1AS3bHPkVwqG/daNm+G6dYXxRUVv2Rk3OC9gvu4qhUY+eFkwgIqHyncZRFX/Tr12+ZqsacMUNVvfoAwoBlwMhi2vTDtYVV1/26NvATrhslBgP/AW4qaV3R0dFaWvHx8aVexledTV8snztNTzxeW9c9E6NpB/eXfSgH2XfjFOuLgsqqPxZNf0r1iZq66udZZfJ+TiiLvgCWaiG/0716aQARCQY+Bz5U1VlFtOkCTAGGq2qqe/IlwBZV3a+q2bju5Ht+YcsbZ3W/7BZ+7/MKUdmb2PfqZRxO3et0JGMqhcOpe2m/YTKrQnvS+aIRTsepkDw5UbdHIY+W7mNDxS0nwFQgWVUnFdGmKa7iM1pV1+ebtR2IE5Fq7vcZgGsLy1RA3QfexJqLXqdZzlb2vz6YtAMpTkcypsJL/vQJwjSTGlc873SUCsuTa/G9DvQAVgECdHI/rysi41X1uyKW6wOMBlaLyAr3tEeBpgCqOhl4HKgLvO6qQ+SoaoyqJorITGA5rtGAv+Ee4Wcqpm4DrmNVQBBt541n5xuD0PFzqF3vPKdjGVMh7dqcTI+UT1lWZyi9OvR0Ok6F5UmB2gqMUdUkcF3qCPgTrmHhs4BCC5SqLsBV0IqkrgERY4uY9wTwhAf5TAXRpd/VrA4IoPVP49jzxiB0/DfUqd+o5AWN8TMpsx6mNkG0uOY5p6NUaJ4cg2p3sjgBqOoaoLuqbvZeLFNZdb54JBsGTKVB7m4OTx5M6t6dTkcypkJZu+QHojPmsbLpzUQ0bOZ0nArNkwK1TkTeEJGL3Y/XgfUiUgXI9nI+Uwl1vmg4my6dSoPcPaS/OYgDKTucjmRMhZCXm0vAt4+wn9p0ufavTsep8DwpULcCG3FdIPYBYLN7Wjau4eHGnKHTBVeweeA06ufu4+hbgzmQst3pSMY4btlXb9AmZz1buz9E9Rq1nI5T4XlyJYljqvovVR2hqleq6ouqmqmqeapqF2MzRerYZyhbLptGvZNFavc2pyMZ45iMI4dovuKfrAtqS/SwPzodp1LwZJh5HxH5XkTWi8jmk4/yCGcqv47nD3EXqf0cnTLEipTxW6tnPE4EaciQf9iNPz3kyS6+qcAk4AKgZ76HMR7peP4Qtg5+n3q5+8mcYltSxv/s2pxE9K6PWBI+iDY9+jodp9LwpEAdVtU5qrpPVVNPPryezPiUDnGD2Dr4fSJyD1iRMn5n38yJZBNE81H/cDpKpeJJgYoXkX+KSO/8V5PwejLjczrEDWLbkA+om5vKsbcHsX/3VqcjGeN1K3+aQffMhaxuOc6GlZeSJyfqxrr/zX+lWQX6l30c4+vax17GWj6gyTejOfj2YPaN/Yb6jZo7HcsYrziemUG9Xx5nW0ATeoz6i9NxKh1PRvH1K+RhxcmctXaxA9kx5APq5B0ka8oQ9u3a4nQkY7zit4+foKHuJX3A84RUsZuCl1aRW1AicpOqTheRBwubX9QFYI3xRLvYgayV6TSePZq0KYPZO2Y2kY1bOh3LmDKzc+Pv9Nj+HktrDiCmz+VOx6mUituCOnn3uRpFPIw5J+16XcrOYdOplZdG9tQhpOzY6HQkY8qE5uWROvN+sgmi2fX2t/zZKnILSlXfdP/7VPnFMf6mXc9LWCsf0uirGznyzhBSbptNg6atnY5lzDlZPvc9oo8vIaHNBOIaRjkdp9Ly5ETd90SkVr7XtUXkHe/GMv6kXcwA9gyfQQ1NJ+/doezZts7pSMactcMH99Ns8ZNsDGxJzLUPOx2nUvNkmHkXVU07+UJVDwHdvRfJ+KM2PfqScsUMwjQdnTaM3VutSJnKae30B6mth+GKVwgKDnE6TqXmSYEKEJHaJ1+ISB08G55uTKm06XExe6/8lOp6lIBpQ9m12W6ibCqXNQlziT34JUsaXEerrhc4HafS86RA/QtYKCLPiMgzwELAToc2XtG624XsH/EpoRwj8P1h7NqcVPJCxlQAWcczqf7dBPZQjy6jX3A6jk/w5Dyo94GrgL3APmCkqn7g7WDGf7XqegGpV31OFbIIfn8YOzasdDqSMSX6bfpfaZa3k/0X/51qYeFOx/EJRRYoEanp/rcOkAJ8BHwIpLinFUtEmohIvIgki0iSiNxXSJsbRWSV+7FQRLrmm1dLRGaKyFr3e/Q+mw9oKqeWneNIu+Zzgsgh9MPhbFu73OlIxhRp48pfid4xjaU1L6VLv6udjuMzituC+sj97zJgab7HydclyQEmqGp7IA64S0Q6nNZmC3CxqnYBngHeyjfvZWCuqrYDugJ2QMLPNO8YS/qo/yAoYTOuZMuaJU5HMuYMJ7KOI1/exWGpQetbXnM6jk8pskCp6jAREVwFpEW+R3NVbVHSG6vqHlVd7n6ejqvANDqtzUL3qECABKAx/G/r7SJct/pAVU/kH0lo/Eez9tFk3vBfcgmk1qcj2LRqodORjClg2YeP0TJ3Czv7PE943Uin4/gUUdXiG4gsU9Xoc1qJSBQwH+ikqkeKaDMRaKeqY0WkG66tqTW4tp6WAfep6tFClhsHjAOIjIyMnjFjRqmyZWRkEBYWVqplfFVF7oujqbvosfoxqukxfm77BDUbtvP6Oityf5Q364uCTvZHespGBiU/RGKV3uSc/yenYzmiLL4b/fr1W6aqMWfMUNViH8BrQM+S2hWzfBiuAjOymDb9cG1h1XW/jsG1izDW/fpl4JmS1hUdHa2lFR8fX+plfFVF74tdW9bqridba/rjkZqc8K3X11fR+6M8WV8UFB8fr1nHj+nGp7vq/ieaatqBFKcjOaYsvhvAUi3kd7onw8z7AQkissk9mGG1iKzypCqKSDDwOfChqs4qok0XYAowXE/dCHEnsFNVE92vZwJ2Dyo/1zCqLQF/+IZDAbVp+s1NJP062+lIxo8tm/Yn1669C/5uu/a8xJMCNRhogev+T5cDw9z/Fst9/GoqkKxFXPlcRJoCs4DRqrr+5HRVTQF2iEhb96QBuHb3GT/XoEkrqt4+l32B9Wn53S2sip/pdCTjh45sX0Xs7g9YXOdyul1yvdNxfFZxt9sIBcYDrYDVwFRVzSnFe/cBRgOrRWSFe9qjQFMAVZ0MPA7UBV531TNy9NR+yHuAD0UkBNgM3FaKdRsfFtGwGQHjv2XXm8NoN28cv2Ufp/vAm5yOZfzEkbRUYja/zO6ABnS87VWn4/i04i5Z9B6QDfyCayuqA3DGuUxFUdUFgJTQZiwwtoh5Kyh4F19j/qdO/UYE3v09W14bSudf72HpiUxiho1zOpbxA+vevYPuepCNw2bSuEatkhcwZ624XXwdVPUmdd1242rgwnLKZIxHwmtH0Ojeuayr0okeSx5i8Uy7747xrmWzp9Dz8Lf8UHMk7WIGOB3H5xVXoLJPPinlrj1jyk1Yzdq0vH8Oq6v1pNfvT5Ew/UmnIxkftWtzEm0X/5W1Qe0J7nqd03H8QnEFqquIHHE/0oEuJ5+LSKHnMhnjhNBqYbS//yuWhfUlbuO/WTTlATQvz+lYxoecyDpO5ke3kCcBhI9+j8CgYKcj+YXiriQRqKo13Y8aqhqU73nN8gxpTElCqoTS7f7PWVx7GL13vsPiN24nLzfX6VjGRyx/535a52xgU+/nOa9Z25IXMGXCk2HmxlQKgUFB9LznAxIiryd2/0yWv3wt2SeynI5lKrmVP80gbu/HJEaMpPtltzgdx69YgTI+RQICiP3j6yxqfhcxR35gzb+HcexoutOxTCW1e8taouY/yKbAFnQdY0PKy5sVKONzJCCA3rc8R2LHx+mcuYStLw3k8MH9TscylczxzAwyp9+AAKE3Tie0anWnI/kdK1DGZ8VeM4HfYv9NyxPrOfRqf/bu3OR0JFNJaF4eq966nVa5m9h84SQatejodCS/ZAXK+LToIbex/tJ3icjdj04ZaDc+NB5ZMusleqV9w6LGf6DbABtS7hQrUMbndbrgClJGuu7OGz7jctYu/t7pSKYCW7vkB7qtfpZVodH0uvWfTsfxa1agjF9o1bUPWTfPJUNqEDX7epZ/+4HTkUwFlLJjIxGzx7AvIIJmt39MYFBxV4Mz3mYFyviNRi3aU+2OH9kW3IJuC+8hccbzTkcyFUhmxmEypl1LqGaRe+1HdguNCsAKlPErdeo3oukDP7Kyem9i1/6dhMl32gm9hrzcXNZOvokWOZvZdPErNGt/TjcRN2XECpTxO1Wr16DLg1+RGDGSuJQPWTHpSo5nZjgdyzgo8Z0J9MiYz+JW99K1/7VOxzFuVqCMXwoMCqLXnVNJaD2Bbhm/sG1Sfw6k7HA6lnHA4pmT6L3rXRbXHkrsjU86HcfkYwXK+C0JCCDuxsdZ2edVmmZv4cSb/dmyZonTsUw5Whn/GT1WP8Oq0J50v+NdJMB+JVYk9r9h/F73gTexY/hMgjWb+p8MY+VPM5yOZMrBxpULaD3vLrYGNafFnZ8RHFLF6UjmNFagjAHa9LiYvLE/sieoEZ1/Hk/C9Cftlh0+bMeGldT+4gaOSE3Cx8wirGZtpyOZQnitQIlIExGJF5FkEUkSkTNuFy8iN4rIKvdjoYh0PW1+oIj8JiJfeyunMSdFNm5JwwfiWRF2IXEb/01gwkscP3bU6VimjKXs2EjwhyMRlBM3zKRewyinI5kieHMLKgeYoKrtgTjgLhHpcFqbLcDFqtoFeAZ467T59wHJXsxoTAHVwsLp9uB/WNTkdi468TPb/9WXfbu2OB3LlJHUvTs58e4VVNejHBwxg6ZtujkdyRTDawVKVfeo6nL383RchabRaW0Wquoh98sEoPHJeSLSGBgKTPFWRmMKExAYSO8xL/Lfxg/RKHs7AW/3ZW3id07HMufo8MH9HHrrCurl7mfH4Gm06trH6UimBKKq3l+JSBQwH+ikqoXeLl5EJgLtVHWs+/VM4HmgBjBRVYcVsdw4YBxAZGRk9IwZpTvAnZGRQVhYWKmW8VXWFwVlZGRA5gG6rnmeSN3PtxG3EtZxmF+O9Krs342sY+lELX6c5nnbmdPsz4S36HVO71fZ+6MslUVf9OvXb5mqxpwxQ1W9+gDCgGXAyGLa9MO1hVXX/XoY8Lr7eV/ga0/WFR0draUVHx9f6mV8lfVFQSf7I+3gfv3thctUn6ipS/41Uo+mpzkbzAGV+buRlrpP1z/dQ7Mer6MrfvykTN6zMvdHWSuLvgCWaiG/0736p6CIBAOfAx+q6qwi2nTBtRtvuKqmuif3Aa4Qka3ADKC/iEz3ZlZjihJeO4IuE2azKOoOehz+kb2TLmTbuhVOxzIeOJy6l/2vXUaznK0kX/yGXSWikvHmKD4BpgLJqjqpiDZNgVnAaFVdf3K6qj6iqo1VNQq4DvhJVW/yVlZjShIQGEjvW/9O0oB3qZV3iHofDWTJf193OpYpxoHd2zj42kCa5mwjue9kK06VkDe3oPoAo3Ft/axwP4aIyHgRGe9u8zhQF3jdPX+pF/MYc846XzSC7Nvns7VKG3r+9ghLXrqOzIzDTscyp9m1OZmsty8lMncP6y95h679rnE6kjkLXrvZiaouAKSENmOBsSW0mQfMK7Ngxpyj+o2aU+dPP7HovT8Tu+Nddk7qzYnhb9uosApiS1IiNT67liBy2Dn8Uzr16Ot0JHOW/G84kjFlICg4hN5j/82aS94jNO8YTWddTsL0J+zWHQ5bPf+/1P3sSvII4PCoL2ljxalSswJlzDnodOFwQu5eRFL1OOI2vsSaf/QnZfsGp2P5pcWf/5t2P95GakA9cm+ba/d08gFWoIw5R7UiGtBt4tcs7vQELY4nU33qhSz+4hW7ll85ycvNZdFb99Br9ZMkV+1G3XvjOa9ZW6djmTJgBcqYMiABAfS6+kEO3fIzO6q0otfKx1j5z8Hs373V6Wg+7fChA6x+cTC9d79PYp0raP/gHGrWqut0LFNGrEAZU4YatWhPuz//TEKbibTLXEbom3EkfvYvOzblBVuSEkl/pQ8dMpeS2P4Ret39nt0yw8dYgTKmjAUEBhJ3w2PsHx3P9iqtiU16muQXLmb7eju5t6ws/fINIj+9nCqaxaYhM4gd9bBfXoLK19n/qDFe0qRVZzo8/DOLOz9FkxObaPDhABa9fT/HjqY7Ha3SSj98kKWTriZm+cNsDWmNjPuZdrEDnY5lvMQKlDFeJAEB9Lrqfk6MT2Rlrf703vUuaf/szm/fTbdBFKW0bulPHHkpju6Hf2BR03G0eSieiIbNnI5lvMgKlDHlIKJBU3o+8BlrLptBVkBVui+8i6QX+rFpdYLT0Sq845kZLHrzHlp9NZJAzWP9kE/o/Yd/EhQc4nQ042VWoIwpRx16D6bRw0tJbPcwjbM20nzmIBa/fION9itCcuK37P9nT3rveZ9ltQdT9b4E2sde5nQsU06sQBlTzoJDqhB73SPIvStY3OA6uh2cS403Y0iYfCeH9u9xOl6FkLp3J4tfvpG234wiSLNZ3X8ave7/mPDaEU5HM+XICpQxDgmvU4+4Oyaz/5ZfWV2rPz33fETwq91JmPIgaQdSnI7niOwTWSR8/CzBb/Sk+8E5LG5wHTUnLKXzRSOcjmYc4LWLxRpjPNOoRXsaPfAp25KXkfr1k8TtnErm/00nocFIWg5/mHoNo5yO6HV5ubn8Nvdd6i2bRFzeLlaFRhM+YhJxbbs5Hc04yAqUMRVEs/bRNGv/FVuTl3JgzvP0TJlB7pufsaTWJdTuf69PXi1d8/JY+dMn1Fj0AtG5W9ga0JQVfd6g64Dr7LwmYwXKmIomqn0MUe0/Z9fmJHZ+8yKd98+m2hdzWfN1JzK73Uqn/jcQWrW60zHPyYms46z45m3qr36Lbnnb2SkNWNrjBboPGUtUkP1aMi72TTCmgmrUoiON7n6Xw4cOkPDNazTd+CEdlkwkbcmTrKg/hHoXjqFFx16VaksjZcdGtnz/Fi23f0YvDrIlIIol3Z+n2+AxNLbLFJnTWIEypoILrx1B3I1PkJf7V1b/+iUnlrxHj72zCPn8U7Z90ZjdjQbTsM8NNGvXw+mohcrMOEzy/FkErfqQzseW0kCUVaHRpMS9SOeLRtC8EhVYU76sQBlTSQQEBrpGs100grQDKfwWP52wDf8ldvsUAna8zU45j531LqR6x8G07nWZo7sB0w6ksDHhSwKSv6J9RgLRcoJ91CGxyW00G/BHujRv51g2U3l4rUCJSBPgfaABkAe8paovn9bmRuDP7pcZwB2qutKTZY3xZ7UiGhB7zURgIvt3b2XzLzMI3foj3fZ+Qei+TznxUxDJIW1Jq9+Tai370KhDHBENmnq+gj174Lrr4JNPoEGDEpsfSNnBzqRfObbxV+rt+5UWOZuJEeUAtVhVbxhh3a+mXexl1LfjS6YUvPltyQEmqOpyEakBLBOR71V1Tb42W4CLVfWQiAwG3gJiPVzWGAPUaxhFvVEPAw9z7Gg6KxPncGz9POocWELPne8TtGsazIcD1GJ3aGsyazaH2s2pGtmKmpHNqFH3PGrVbVDw0kHPPAMLFsDTT8Prr6N5eRxO3UvagT2kH9jB0d3r0dRNVDmyhYaZ64gklQggWwPZENKexKg/UrvzQFp3u5hYK0rmLHntm6Oqe4A97ufpIpIMNALW5GuzMN8iCUBjT5c1xpypavUadO1/LfS/FoCj6WmsW/Ur6duWE7j3d+pkrKfV3lVU25cF6woue4Rq1Hg2BcnJN/GNN+CNN+gbBPKXmoTnm5WlwewJPI8dNbqxpUFXaraMJapTbzqEhWNMWRBV9f5KRKKA+UAnVT1SRJuJQDtVHVuaZUVkHDAOIDIyMnrGjBmlypaRkUFYWFiplvFV1hcF+Wp/aF4eWUcPk3V4N2SmEpB1mKAThwnJSSf0cDqtZq8iInkPgdl55AYHsq9jI5KGxnC8XmNyq9SCqrUJDm9AaM16BAQEOv1xHOGr342zURZ90a9fv2WqGnPGDFX16gMIA5YBI4tp0w9IBuqWdtn8j+joaC2t+Pj4Ui/jq6wvCvLb/hg/XjUgQDU01PXvHXf4b18UwfrjlLLoC2CpFvI73avjO0UkGPgc+FBVZxXRpgswBRiuqqmlWdYY4wV798L48ZCQ4Po3xT+vC2ic581RfAJMBZJVdVIRbZoCs4DRqrq+NMsaY7xkVr6/B197zfXvvHmORDH+zZvDa/oAo4HVIrLCPe1RoCmAqk4GHgfqAq+7ahI56toPWeiyqvqNF/MaY4ypQLw5im8BICW0GQuMLWR6icsaY4zxbXaNEWOMMRWSFShjjDEVkhUoY4wxFZIVKGOMMRVSuVxJoryIyH5gWykXiwAOeCFOZWR9UZD1xynWFwVZf5xSFn3RTFXrnT7RpwrU2RCRpVrYJTb8kPVFQdYfp1hfFGT9cYo3+8J28RljjKmQrEAZY4ypkKxAue5BZVysLwqy/jjF+qIg649TvNYXfn8MyhhjTMVkW1DGGGMqJCtQxpgSue8wYEy5sgJljPGE3cfdlDu/PgYlIt2ALABVTXY4jqNEpBOQDQT4e18AiMglQA7wi6rmOp3HSSJyGXA7cKeq7nM6j9NE5HygIXBYVb93Ok9FIiIBqppXVu/nt1tQIjIY+Aq4E/hMRG5zOJJjRGQI8DEwAXhHRAY5HMlR7rs5Pw88C/QSEW/eN61CE5GLgTeBt604gYgMBKYBHYGZInKRs4mcJSJDReQpEXleROqWZXECPyxQ4hIG3APcpar34Lon1V9EZLyz6cqfiMQAk3D1wR+BN4DB7n7yu++HWw6Q4P73L8AF4LfHYdoCL6jqtyLSQETO99dfyiJSD3gauF9VnwKeAQJEpLWzyZwhIrHAq8A6oDbwpfv7EVxW6/C7X0DqkgEsBWqKSLCqJgDXAX8WkVucTVjuIoBnVTVRXft7NwNdcO3qK9O/hioLdz98AzwFfA48ICL3AveLSKCj4crfCSBaRJrj6pPrgA9EZKKzsRyRBiwBTrh3iT8KjAF+FpE7HU3mjE7Ad6r6kaqOx/Wz8hDQA1y7+851BX5XoPJJAQYAVQFUdSmu28zf4/5h9AuqOhf4Id+kFcCxk8ddRKSBI8Gcp8DdqvousAv4N1DND49HLQGOATcCH6jqvcAQ4I/u3eR+Q1WzgQzgeuBT4GVVHQ1cAfxNRC5wMp8DlgBVRaQdgKpOAhYAL4lIrbL4A9fvCtTJ3TSq+jpQDZgsIuHuLakFwCpcv5x8Xr6+2JNvchDQWEQCReRWYKqIVPOX3Vv5PucPwEoR6Y3rD5mpQH/3AXK/oapJuLYcrgDOE5Ew97SZuP+48wcntwZU9RHgDly7wn9xT1sKTMf1s+NPUnDtBr9URCIAVPVF4HdchwvOmV90qIi0Berg2q2XB+QCqOooEZkBvAQkuA+GX4yr031SYX1x2sibY7h28/0Z1y+lMaqa6UjYcnB6f6hqroiIqua497E/AQxX1a9E5C5gp5N5vamwvgBQ1cdE5ATQFLhXRDJw7eqb4ljYclDIzwru78YJ9x8yY0RkJ3AhcAmurWyfJiKB+b4X+0Tk/4C/uefNU9XVwCbK6I98nx9mLiIjgedw7abZhevLNk1Vj+Rr8wdcw0a7Ak+6/0L0OcX1Rf4iJSKLcJ33cpUvDzkv6bvhHkzTVlWXOZeyfHj4c9IfaAl0AN7y5++Gu81HuE5TaQ2MU9U1TmQtDyLSRlXXu58H5vtDTkWkO64tplq4ClMv4Ep3sTq39fpygXKPJpkOvKKqv4rIVUAcri/VP1X18Gntq6hqlgNRva40fSEijwKzVHWtM2m97yy+Gz47aOQs+iJIVX15L0NpflYCgOqqmu5MWu8TkWG4jrn9R1VvcE87WaQCVDXPvYuvNtATWKSqW8pi3f5wDKomrr9wAL4AvgZCcB3oRER6iUgP9/wT5R+vXJXUF7Huv5Se8+XilE9J/REjrpO58dXilE9JfdEz38+JPwwU8eRnpZuq5vl4caoO3A3cj2v04nQAd3EKyvdzkaOqG9wj+sqkOIGPFyj3qJtJwEgRudDdmQtwjVS7SESqAn2A3e72Prs56WFfnA/47A9bfh72x4W4DgT7NA/74gL84OcESvWz4g/fjaPAH4CPgIlAaL4ilQMgIl2Bm0QktKwHU/n0Lj4AEQnFdRJqF2C6qs53T5+HawDAJgfjlSvri4KsP06xvijI+qNwIlIX1/2fjqnqTSLSBdeW5i/euNKIz4/iU9XjIvIhroN3j7jH7GcB9f6/vXsLjauI4zj+/fVBpFhbEZHqg8WgFEG8VCveihUVRIkpXqEI7YO0L1pvgb6I+CKBICIUrFAwPkgltFZKrRi80NYKtpqGtIhRIsUHBSGIVDEg9O/DTNxz4mY3m2y6a/b3gYXs5MycmYHkz5zL/EnvNHQMz0WZ56PCc1Hm+aguIiYkbQH6JY2RrsKtW4jgBB2wgpoi6TzS5bwtwCTpJbsTre1Va3guyjwfFZ6LMs9HdZKeI72Kcm8zntab8TydEqCmKG1VEx1w07suz0WZ56PCc1Hm+aiQdBHpqb4XImJ0Qc/VaQHKzMzmR9L5ETG54OdxgDIzs3a0qB8zNzOz/y8HKDMza0sOUGZm1pYcoMzMrC05QFnHy+kjmtHOXZIO5J+7JW1vsP7pvOlmsWwgvxhZLOuRdLBOWzXHJGmFCllgJV0maU+tceTzXtPImMzmwwHKbAFExP6I6GtCU7tJuZeKnsjl87EC+DdARcTPEfHI9IOmjaOHlGrD7JxwgDLL8srhkKRBSd9L6pO0UdIxSScldeXjBiTtlHQkH/dglbY2SdqRf75E0l5Jx/Pn9lx+saQhSSckvQVU22jzE2C1pJW5zlJScrwP8vfnJZ3Kn2er9OMCSZ9KGs5jeCj/qg/okjQiqV/SKkmnZhqHUibhbtIWNyOSHsbVXAAAAlZJREFUuiQNF467StKiz5tl55YDlFnZdcA24FrgSeDqiFhLyh77dOG4VaTsyw8AO/PmojN5A3g9Im4GHqaSifZl4IuIuAHYT8pYW5Kzl74PPJaLuoHPI+KMpDXAZuAWUr6ip5SSxxVNAhsi4kZgPfBa3nF6OzAeEddHRG+dOSEivsx97M11xoHfldOR5H4M1GvHrBEOUGZlxyPil5y4chwYyuUnSUFpymDOBfQD8COwukab9wA7JI2Q/slfKGkZsI6UGI+I+BD4bYb6xct8xct7dwD7IuLPiPiDFMjunFZXwKuSRkmrscuBS2v0tRG7gM15G6DHSSkZzJpm0e9mbtagYkbls4XvZyn/vUzfgqXWlixLgFsj4q9iYU6dM5utXI4CK3PenduoBKvZ5N7ZSNqBe01E/C3pNFBrtdeIvaRV4GfANxEx0aR2zQCvoMzm6lFJS/J9qSuBsRrHDpGykgJQuCx2mBRAkHQ/KWX2f+QEgYPAO8DBwh5oh4EeSUuVMp9uAI5Mq74c+DUHp/XAFbn8DLBsViOtKNXJ/fgYeBN4u8G2zOpygDKbmzHgEPARsLXOxpnPADdJGpX0LbA1l79CytA6DNwH/FSjjd2k+2PvTRVExDDpvs8x4CtgV5VUEO/mc39NCobf5boTwNH8cEX/LMZLPndvfqijq9B+ULkUatY03izWrEGSBoADEbGn1X1pNUkvAssj4qVW98UWH9+DMrM5kbQP6ALubnVfbHHyCsrMzNqS70GZmVlbcoAyM7O25ABlZmZtyQHKzMzakgOUmZm1pX8ARGdTI7dA3dsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = implied_volatility(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 671,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:12: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.61]\n",
      "[2.3688186]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = implied_volatility(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 672,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.61]\n",
      "[2.60689306]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = implied_volatility(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 673,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.6]\n",
      "[2.66150263]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = implied_volatility(\"^VIX\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.sort_values(by=[\"Pricing Error\"],ascending=True,inplace=True)\n",
    "df.reset_index(drop=True,inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 674,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pricing_errors(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 596,
   "metadata": {},
   "outputs": [],
   "source": [
    "def volatility_smile(df, ind=0, S=0):\n",
    "    S = 12.83\n",
    "    date=df.loc[0,\"Expiry Date\"]\n",
    "    df1=df[df[\"Expiry Date\"]==date]\n",
    "    df1=df1[df1[\"Option Type\"]==\"P\"]\n",
    "    df1.sort_values(by=\"Strike\", ascending=True, inplace=True)\n",
    "    df1.reset_index(drop=True,inplace=True)\n",
    "    r = 0\n",
    "    Implied_Vol = []\n",
    "    Implied_Price = []\n",
    "    #print(len(df1.index))\n",
    "    for i in [df1.index[ind]]:\n",
    "        Sigma = np.array(np.linspace(0,0.3,100001)[1:])\n",
    "        Error = []\n",
    "        for sigma in Sigma:\n",
    "            x = BSoption_price(S, df1.loc[i, 'Strike'], r, sigma, df1.loc[i, \"Time to Expiry\"], df1.loc[i, \"Option Type\"]) \n",
    "            error = np.abs(x - df1.loc[i, \"Last Price\"])\n",
    "            Error.append(error)\n",
    "        \n",
    "        plt.plot(Sigma, Error)\n",
    "        plt.grid()\n",
    "        \n",
    "        m=np.min(Error)\n",
    "        print(\"minError:\", m)\n",
    "        Ind=[i for (i, v) in enumerate(Error) if v == m]\n",
    "        print(\"Ind: \", Ind)\n",
    "        print(\"Sigma[Ind]: \", Sigma[Ind])\n",
    "        Implied_Sigma = Sigma[Ind]\n",
    "        \n",
    "        if len(Implied_Sigma)>1:\n",
    "            print(\"multiple solutions for optimal implied volatility\")\n",
    "        implied_sigma = Implied_Sigma[0]\n",
    "        print(\"implied_vol: \", implied_sigma)\n",
    "        #p = BSoption_price(S, df1.loc[i, 'Strike'], r, implied_sigma, df1.loc[i, \"Time to Expiry\"], df1.loc[i, \"Option Type\"]) \n",
    "        \n",
    "        #Implied_Price.append(p)\n",
    "        #Implied_Vol.append(implied_sigma)\n",
    "    #df1[\"Implied Volatility\"] = Implied_Vol\n",
    "    #df1[\"Implied Price\"] = Implied_Price\n",
    "    #df1[\"Pricing Error\"] = df1[\"Implied Price\"] - df1[\"Last Price\"]\n",
    "    \n",
    "    #plt.plot(df1[\"Strike\"], df1[\"Implied Volatility\"])\n",
    "    #plt.grid()\n",
    "    #return df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 526,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 528,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 530,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 532,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 536,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 539,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 540,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aaa953cd48>]"
      ]
     },
     "execution_count": 540,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(u[\"Strike\"], u[\"Implied Volatility\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 537,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aaa70ef148>]"
      ]
     },
     "execution_count": 537,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(u[\"Strike\"], u[\"Implied Volatility\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 534,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aaa7f13a88>]"
      ]
     },
     "execution_count": 534,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(u[\"Strike\"], u[\"Implied Volatility\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 544,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yj6bDnfGOIiIyZKld6JNL6Ox2lr65J95RRESGLKULvaZyODmZaTy/QcMuIhJ8KV3o2RnpnDehmCXrd8U7iojIkKV0oQNcVFXCxl3NbNvfGu8oIiJDokKvKgU0fVFEgi/lC31KeYiygmwNu4hI4KV8oZsZc6pKeGHDbrq7+z+VsIhIokr5QofwOPq+lg5e26ZPMRKR4FKhA7Mnh0+h+9wGDbuISHCp0IGyghyqKwpY8oYKXUSCS4UecfnpFSzduJe/6KhREQkoFXrE5y+ZxPjiPG5+aDUt7Tq3i4gEjwo9IjcrnX/58Ay27G3hX55cF+84IiInTYXew3kTi7nhgvHc/eJmXtq0N95xREROigr9OF+bX83YEbl87cFVtLZ3xTuOiMiAqdCPk5+dwS0fnsHmPS385I8aehGR4FCh9+LCSSV88vxx3PXCJuq362AjEQkGFXofvvreajLT01j40pZ4RxERGRAVeh+K8jK5/PQKHl21jcOdGksXkcSnQj+Ba2rGsL+lg8X1jfGOIiLSr34L3czuMrNGM1vTx/JPmNnqyOVFMzsz+jHjY87kEioKc3hwRUO8o4iI9Gsge+h3A/NPsHwTcIm7zwC+B9wehVwJIT3N+NDZo3l2XSONB9viHUdE5IT6LXR3XwL0eZSNu7/o7vsiN5cCY6KULSFcUzOGboffv/x2vKOIiJyQuff/oQ5mVgkscvfp/az3T0C1u3+uj+ULgAUA5eXlNQsXLjzZvAA0NTURCoUG9djB+P7SVlo6nB/MycXMTvrxpzrvUAQpKwQrb5CyQrDyBikrDC1vbW3tCnef1etCd+/3AlQCa/pZpxaoB4oH8pw1NTU+WHV1dYN+7GD8btlbPv7mRf7yln2DevypzjsUQcrqHqy8QcrqHqy8QcrqPrS8wHLvo1ejMsvFzGYAdwBXu3vSnX/2/TNGkpOZxgPLt8Y7iohIn4Zc6GY2DngYuN7d3xh6pMRTmJPJ/NMreGzVNto6NCddRBLTQKYt3gf8BZhqZg1m9lkz+7yZfT6yyreBYuDXZvaKmS2PYd64+cissRxq6+SPr++MdxQRkV5l9LeCu1/Xz/LPAb2+CZpMLphYzLgRefzkqXXMnVpKYU5mvCOJiBxDR4oOUFqa8dOPnsnb+1u5+cHVR94IFhFJGCr0kzCrcgRfu3wqT6zZwX++uDnecUREjqFCP0k3XjSRedVl/ODxelZt3R/vOCIiR6nQT1JamvGvHz2TsoIcbvrdSg60dMQ7kogIoEIflGF5Wfzy42ex40AbX3ngFTq7uuMdSUREhT5YZ48bzreuPI2n6xv50n+tUqmLSNz1O21R+nbDhZW0tHdxy5NrAfjZR88kI12/I0WSwYHWDg53dlFWkBPvKAOmQh+iv5s7CTP40RNrcXd+fu1MlbpIgHV3O/cv38oPH6+n+XAnV5wxkhsvmsjMscPiHa1fKvQo+Pwlk0gz+OHja3HgVpW6SCBt3NXENx5+lWWb9nL+xBHMGDOM+17awh9Wb+ecyuHceNFELp1WTlrayZ919VRQoUfJgosnYRg/eLyekvwsvnv1Cc80LCIJpKOrm9uXbOTWxevJzkjjlg+fwUdnjcXM+MK8Ku7/61buen4TC367ggkl+XxmzgSuOXsMuVnp8Y5+DBV6FN148UR2NR3m9iUbmVpRyMfPGxfvSCLSj9UN+7n5oVep336QK6ZX8N2rTqes8J1x81B2Bp+dM4EbLhjPk6/t4N+XbORbj6zhp39cx/Xnj+f6CyopLciO43fwDhV6lN08v5p1Ow7x7UfXMKk0n/MmFsc7koj0oqW9k5/96Q3ufH4TJaFsbvtkDfOnV/S5fkZ6GlfOGMX7zxjJXzfv49+f28gv6zZw25KNfHDmaD530QSqygtO4XfQS8a4vnoSSk8zfnHdWXzw1y/wd/eu5NGbZsc7kogc5/n1u/nG71ezdW8rHz9vHDfPr6Yod2An3DMzzp0wgnMnjGDjribuemETD65o4P7lW5k7tZQbL5rIhZOKB/XpZkOld+5ioCg3kzv+dhadXd3ceM9y2jp1Ii+RRLC/pZ1/emAVn7xzGRlpaSxccD4//OAZAy7z400sDfH9D5zBi1+fx5cvm8Katw/wiTuW8f5fPM/vX26g4xQfn6I99BiZWBriVx8/m0/9x0v8B+lcPs/j8htbJN6aD3fy4pt7qFvXyMtb9jN9VCGXnlbORVUl5GWdmgpydxat3s53//s19rd0cFPtJP7hPVXkZEbnTc0R+Vl8YV4VCy6eyKOvvM0dz23iS/ev4pYn1vGp2ZVcd+64Qf/SOBkq9Bi6eEopX75sCj/54xs8tmobV88cHe9IIjHn7ry5q5ln1zXy7LpdvLRpL+1d3eRnpTNjzDCefG0HD6xoICsjjQsnFXPptHLmTStjZFFuTPJsP9DKtx5Zw9P1jcwYU8Q9nzmP00YVxuS1cjLTufaccXykZix/Xr+LO57byI+eWMsvF6/no+eM5TOzJzB2RF5MXhtU6DH3+Usm8chLG/jWI2s4p3IEo4bFZqMViafW9i7+snE3dWt38ewbjWzd2wpAVVmIT82uZO6UUmZVjiArI42Orm7+unkvT7/eyOK1O/nmI2v45iMwfXQh86rLuXRaOdNHFw75L9rubufeZW9xy5Pr6Ozu5pvvn8anLqw8JceIpKUZtVPLqJ1axmvbDnDHc5v47V/e4j9f3MwVZ4xkVn4Xc2Pwuir0GMtIT2PBjGz+z9J2vvrgKn77mfMS9qAEkZOxeXczdesaqVu3i6Ub99De2U1uZjqzJxfzPy6exNyppYwZ/u690cz0NC6cVMKFk0r41pXT2NDYxNP1jSyu38kvnlnPrYvXU1GYw3umlXHZtHIumFR80kMjGxoP8fWHXmX5W/u4qKqEH3zgDMYVx27P+EROH1XEz66dydfmT+XuFzfzu2VbSB9tfDoGr6VCPwXK8tL49pWn8fWHX+XuFzfzmTkT4h1J5KS1dXSxbNNe6tY28uy6RjbvaQFgYkk+nzxvPLXVpZxTOeKkytfMqCovoKq8gL+bO4k9TYepW7eLxfU7efTlt/ndsi3kZqYzp6qEy6aVU1tddsI53+2d3dz25zf51TMbyM1K5ycfOZMPnz06Id6/GlmUyzeumMY/vKeKJUuei8lrqNBPkWvPGcvT9Tv50ZNruaiqJO7zVUUGYuveFuoiY+Evvrmbto5usiNj35+ePYG5U0sZX5wftdcrDmVzTc0YrqkZw+HOLpZu3MvTr+9kcf1O/vT6Tsxg5thhR8fdp5YXHC3rlVv28fWHVvPGzib+5sxRfPvK0xLmgJ+eQtkZ5GXG5heMCv0UMTP++UMzmP/zJXzyzmVUlRWQk5lGTmY6oewM5k0rp3Zqqc4BI3HTfLiTN3YeYu2OQ9RvP8ifVrew/ck6AMYX5/Gxc8ZxydRSLph48kMgg5Gdkc4lU0q5ZEop//fq06nffoin68Pl/uOn1vHjp9YxZngul04rZ2vDYZ556kUqCnO484ZZzJtWHvN8iUiFfgqVFmTzb584m3+r20Dz4U72NnfT1tHFnuZ2Fv51KxWFOXzs3LF87JxxVBQN/pSdOw60sXLLPg60dnDtrLEas5djdHZ1s3lPC+t2HGLdjoOs3REu8S17W46uk5eVzsSCNG6snUptdRkTSqK3Fz4YZsZpowo5bVQhX5hXRePBNhavDY+73/fSFto7u7n+gvF89fKpFOTEfnpgolKhn2LnTyzm/ONOB9DZ1c3itY3cu2wLP396Pb98ZgNnjC5iYmk+E0vyqSzJp7qikMlloV6fs62ji8dWbePP63axcss+th9oO7ps+4E2vnzZlJh+T5KY3J1dTYcjxX2I+u2HWLfzIOt3NnG4M3zAS5rBhJJ8zhhdxEdqxjC1ooDqikLGDM9lyZI/MzdB3+8pK8zhunPHcd2542ht7+LJZ/7MB+frhHj9FrqZ3QVcCTS6+7t+YhYewLoVeB/QAnzK3VdGO2gyy0hP4/LTK7j89Aq27Gnh/uVbeHnLfv7y5h4eXvn20fWmjSzkw2eP5qqZoygryGHXocP8dulb3Lv0LfY0tzN6WC6zKkdw1thhnD1+OP9v6Vv8YvF6ppYX8P4ZI+P4HUqstbZ3RYZLwnvcR0p8T3P70XVKC7Kprijgby8Yz9SKQqorCphcFjolwyexlJuVzvAcDVXCwPbQ7wZ+BdzTx/IrgKrI5TzgN5FrGYRxxXl89fLqo7db2jvZvLuFv27ey8Mvv833/1DPPz+xlpljh/FqwwHau7qZV13GZy+awAUTjz1/xLSRBWzc1cRXHniF8cV5TB9dFI9vSXro6nbaOrrCl85uWtu73rnd0U1r5OvWji4O93JfW0f30fWP3L/z4GE272nGI2eYyM1MZ0pFAZdOK6d6ZMHRve4R+Vnx/eYl5votdHdfYmaVJ1jlauAed3dgqZkNM7OR7r49ShlTWl5WxtGxwxsurGRD4yEeXvk2z6xt5NpzxvLp2ZVMLO19KCY7I53brq/h6l+9wIJ7lvPo389JyHf9E8WuQ4e564VNPLC8ATMYnpfJsLys8HVuFsPyMxl+5HZeFsPzssjPTqeprZN9LR3sb2nvcd3O/pYO9rd0sO/o/YfpfPLxQWXLTDdyMtLJyUonJzON3Mx0cjLTyclIp7qigA/MHB0p7gLGjcjT+yYpytz7P3FUpNAX9THksgj4kbs/H7m9GLjZ3Zf3su4CYAFAeXl5zcKFCwcVuqmpiVCo9xJLRPHOu/lAFz9c1sa4wjQ+MS2Lnv/VzSA73chMg6x0o7OtmeGFifmzdXf2H3YaDnXT0OS83dRNQVoHl1TmUZE/+D+5d7V088TmDp5r6KSzG84uTyeUaTR1OE3tTnOH09QBTe3OQM6zlpEGoUwjlAmhLCOUaeRnGpneQUFuFpnpkJVmZKWHf+ZZaRz3dfjfIzvdIuuGz+J5qsV7uz0ZQcoKQ8tbW1u7wt1n9bYsGm+K9ral9brZu/vtwO0As2bN8rlz5w7qBZ999lkG+9h4SIS8JRO28fe/e5nv/qWtnzWN4vwORg3LZdSwHEYNy2V05DIqcikJZfV6oEZnVzeH2jo51NbJwbaOyNfh6y53CrIzKMjJpCAng8Lc8HVBTgbZGe8ew+05hW7djnfGhve3dLzzPYWy2dPUyRNbW5kxpoirZ47mb2aMPObDCU5k3Y5D/ObZDfz36u2km3HNrLEsuHhSnzM63J2W9q6je9/7WtppauukICeTYXmZDM8P773nZqb3+vNJhO3gZAQpb5CyQuzyRqPQG4CxPW6PAbZF4Xkliq6cMYrK4nx2HDi20Du7u48Zl129dj05Iyp4e18rG3c189z63bS0dx3zmKyMNEYV5VCUl0XT0eLupLXj2PUGKisjjcKcd8p+f0vHMVPo8rPCY8JXTK+guqLw6NDCsLwsfv/kM+zJr+TRV7bxvUWv84M/vM6Fk0q4auYo5k+voLCXKWwr3trLr+veZPHaRvKy0vnM7Eo+O2div1NFzYz87AzyszMYM3xQ36pITEWj0B8D/t7MFhJ+M/SAxs8T0/TRRf2+Mfpsx1vMnXvG0dvuzsHWThr2t7Btfxvb9reybX8rDftbOdjawaiinPAed07m0UIuiJRzYY898TSzY/bYDx0OXx9sjVz3WDZ2eN7RKXTTRhYyelhun2PCw3PS+OBFE/ncRRPZ0NjEY6+8zaOrtvG1B1fzzUfWMK+6jKtnjmbu1FKWbtzDr599k5c27WV4XiZfunQKN1w4nmF5erNQksNApi3eB8wFSsysAfgOkAng7rcBjxOesriB8LTFWJxzRuLEzCjKy6Qor4jTRyX2LJnJZSG+/N6pfOmyKbyydT+PvrKNRau38cSaHWSlp9He1c3Iohy+deVpXHfu2FN2Lm6RU2Ugs1yu62e5AzdFLZHIEJkZZ40bzlnjhvPN90/jhTf3sLh+J9NHFfGBs0aTlaE5y5KctIsiSS0jPe3o+UBEkp12VUREkoQKXUQkSajQRUSShApdRCRJqNBFRJKECl1EJEmo0EVEkoQKXUQkSQzo9LkxeWGzXcBbg3x4CbA7inFiLUh5g5QVgpU3SFkhWHmDlBWGlne8u/d6pFzcCn0ozGx5X+cDTsteuMQAAAQ6SURBVERByhukrBCsvEHKCsHKG6SsELu8GnIREUkSKnQRkSQR1EK/Pd4BTlKQ8gYpKwQrb5CyQrDyBikrxChvIMfQRUTk3YK6hy4iIsdRoYuIJImEL3Qzu8vMGs1sTY/7RpjZn8xsfeQ6IT6y18zGmlmdmdWb2Wtm9sXI/YmaN8fMXjKzVZG8343cP8HMlkXy3m9mCfOhm2aWbmYvm9miyO1EzrrZzF41s1fMbHnkvkTdFoaZ2YNmtjay/V6QwFmnRn6mRy4HzewfEzjvlyL/v9aY2X2R/3cx2W4TvtCBu4H5x933dWCxu1cBiyO3E0En8BV3nwacD9xkZqeRuHkPA+9x9zOBmcB8MzsfuAX4WSTvPuCzccx4vC8C9T1uJ3JWgFp3n9ljznGibgu3Ak+6ezVwJuGfcUJmdfd1kZ/pTKCG8GcZ/54EzGtmo4EvALPcfTqQDnyMWG237p7wF6ASWNPj9jpgZOTrkcC6eGfsI/ejwGVByAvkASuB8wgfwZYRuf8C4Kl454tkGUP4P+p7gEWAJWrWSJ7NQMlx9yXctgAUApuITJJI5Ky9ZH8v8EKi5gVGA1uBEYQ/8nMRcHmsttsg7KH3ptzdtwNErsvinOddzKwSOAtYRgLnjQxhvAI0An8C3gT2u3tnZJUGwhtlIvg58DWgO3K7mMTNCuDAH81shZktiNyXiNvCRGAX8B+R4aw7zCyfxMx6vI8B90W+Tri87v428BNgC7AdOACsIEbbbVALPaGZWQh4CPhHdz8Y7zwn4u5dHv7TdQxwLjCtt9VObap3M7MrgUZ3X9Hz7l5WjXvWHma7+9nAFYSH3y6Od6A+ZABnA79x97OAZhJguKI/kXHnq4AH4p2lL5Fx/KuBCcAoIJ/w9nC8qGy3QS30nWY2EiBy3RjnPEeZWSbhMr/X3R+O3J2weY9w9/3As4TH/oeZWUZk0RhgW7xy9TAbuMrMNgMLCQ+7/JzEzAqAu2+LXDcSHuM9l8TcFhqABndfFrn9IOGCT8SsPV0BrHT3nZHbiZj3UmCTu+9y9w7gYeBCYrTdBrXQHwNuiHx9A+Gx6rgzMwPuBOrd/ac9FiVq3lIzGxb5OpfwxlcP1AHXRFZLiLzu/g13H+PulYT/zH7G3T9BAmYFMLN8Mys48jXhsd41JOC24O47gK1mNjVy1zzgdRIw63Gu453hFkjMvFuA880sL9IPR362sdlu4/2mwQDeVLiP8NhTB+E9ic8SHjtdDKyPXI+Id85I1jmE/3RaDbwSubwvgfPOAF6O5F0DfDty/0TgJWAD4T9ns+Od9bjcc4FFiZw1kmtV5PIa8L8j9yfqtjATWB7ZFh4Bhidq1kjePGAPUNTjvoTMC3wXWBv5P/ZbIDtW260O/RcRSRJBHXIREZHjqNBFRJKECl1EJEmo0EVEkoQKXUQkSajQRUSShApdRCRJ/H8Amjs58I+ZSgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 546,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n"
     ]
    },
    {
     "data": {
      "image/png": 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AOufYut7+RsJy08Va9KbbtlWFVnV6Y7ut6mS8I5p370ygTFXLAURkCbAAOFHoVXVVxP7vA3c7t28AVqpqrXPsSmA+8ELPo3ctL12sj96cN1vVyXhZNIW+GDgYcb8CmHWW/e8H/niWY4s7HyAiC4GFAEVFRT2ayW9gUoD9h+tcMRugz+dzRc4wN+WNNmtNc5BlZR28V+UnPRk+NjaV+WNSGZhcybr3K/s+qMOLP9t44aa8fZU1mkLf1bixLucZEJG7CXXTXHM+x6rqM8AzACUlJTpnzpwoYnXtV9teo6wJevIc/aW0tNQVOcPclPdcWSuPt/DUW7v5zdoKUpKEv796LP9w9diYrerkpZ9tvHFT3r7KGk2hrwBGRtwfAVR13klErge+DFyjqm0Rx87pdGxpd4JGKzddaGztoLUjYCfOzGkiV3UCuGf2KP5xzoW2qpPxtGgK/RpgnIiMASqBO4G7IncQkenAT4D5qloTsek14D9FJN+5/9fAIz1OfRZ56aE/Io40tjGyYEBfvpRxkWO+Nn789h5++d5+AkHljpIRLLp2HMV5mbGOZkyfO2ehV1W/iCwiVLSTgcWqulVEHgPWqupy4DtAFvBb5xLwA6p6i6rWisjXCf2yAHgsfGK2r+Q6hb6msdUKvTnrqk7GJIqoxoyp6gpgRafHHo24ff1Zjl0MLO5uwPOVG9GiN4mrxa/815u7T6zq9NFLhvH568dzUWFWrKMZ0+88Nzg4Lz10xaJdNJWYgkHlf97fz3febsbXsYt5k4t4aN54Jg2zVZ1M4vJcoc9OgySxFn0iKj/i44tLN7F2fx2TByXxzTsvt1WdjMGDhT5JhMFZ6dQ0WKFPFP5AkJ/9ZS9PrNxFRkoS37vjUgoadluRN8bhuUIPocnNjvis0CeCHYca+OLSTWyqqOeGi4v4+oIpFOZkUFpaFutoxsQNTxb6wux0mwbB49r9QX5UuoenVu0mJyOVp+6azs1Th9nCH8Z0wZOFfkh2OtuqG2Idw/SRzRX1/NvSjew41Mgtlw7nqx+bHLMrWo1xA08W+sLsDI762gkElWRb+cczWjsC/Nebu/nJn8oZNDCNn/5tCfMmF8U6ljFxz5OFfkh2OoGgUtfczmBr6XnCuv11fHHpRvYcaeITJSP48s2Tyc20mSWNiYYnC32hs9JUTUObFXqXa273893XdvHzd/cyPDeTX943k6vHD4l1LGNcxZOFPrykYE1jK5OxC2Xc6t09R3n4xc0cqG3mntmj+NKNE8lK9+Rb1pg+5clPTWF2aCZCu2jKnRpbO3j8jzv43w8OMGrQAJYsnM3ssYNiHcsY1/JkoT/ZordC7zalO2v4v7/bzKGGVv7+r8bw0LwJZKbZdNPG9IQnC31mWjLZ6SnWoneR+uYOvv6HbSxdV8FFhVks/cwVXHZB/rkPNMackycLPThXx1qhd4XXtx7iy8u2UNvUzqK5F/FP111Eeoq14o3pLVboTcwc87Xx77/fxu83VjFpWA4///RHmFKcG+tYxniOZwt9YU4GmyuOxzqG6YKq8vtN1fz78q00tnbwL/PG8+CcC0lNTop1NGM8ybOFfkiWtejjUU1DK19etoWV2w5z6cg8vnP7JYwvyo51LGM8zbOFvjAnnab2AE1tfgba2OuYU1WWrqvg669so80f5Ms3TeK+q8bYFBXG9APPVsAhzhWxRxrbrNDHWOXxFh753Wb+tOsIM0cX8K3bL2HMYFuz1Zj+4tkKWJhzciz9aCsqMREMKs+vPsA3V2xHgccWXMzds0aRZK14Y/qVZwt9+KIp66ePjf3HmvjSi5t4v7yWqy4azDf/z1RGFgyIdSxjEpJnC314GgRbgKR/BYLKz9/Zy3df30lqchLf+vhUPlEy0hYEMSaGPFvo8zJTSUkSmwahH5XVNPJvSzex/sBxrptYyDdum8rQ3IxYxzIm4UU1cFlE5ovIThEpE5GHu9h+tYh8KCJ+Ebm907aAiGxwvpb3VvBzSUoSu2iqn/gDQZ5eVcZNT/6FvUebePLOafzs3hIr8sbEiXO26EUkGXgamAdUAGtEZLmqbovY7QDwaeBfu3iKFlWd1gtZz9uQ7HRr0fexbVUNfPHFjWypbODmqcP491suPnF+xBgTH6LpupkJlKlqOYCILAEWACcKvaruc7YF+yBjt43Iz2R7dWOsY3hSuz/IU6vK+OGqMvIGpPGjT13GjVOHxTqWMaYLoqpn3yHUFTNfVR9w7t8DzFLVRV3s+xzwiqoujXjMD2wA/MDjqrqsi+MWAgsBioqKZixZsqTb35DP5yMrKwuAl3a3s3xPBz+ZN4C05Pg7GRiZ1Q3CecvrAyze3EaFT7lieAp3TUwjKy2+fr5u/dm6gZuygrvy9iTr3Llz16lqSVfbomnRd/UJPvtvh1NdoKpVIjIWeEtENqvqnlOeTPUZ4BmAkpISnTNnznk8/alKS0sJH+8rqOLlPespnnQZFw+Pv8myIrO6wetvruK95iJ++n45RTkZ/PzTU5k7sTDWsbrktp+tm/K6KSu4K29fZY2m0FcAIyPujwCqon0BVa1y/i0XkVJgOrDnrAf1kvAcKrsP++Ky0LvJmn21PPpOC4eay/nkzAt45KaJ5GTY4tzGuEE0hX4NME5ExgCVwJ3AXdE8uYjkA82q2iYig4ErgW93N+z5Gj1oIClJwq7D1k/fHapK6a4jPPvnvfyl7ChDMoX/fWAWV140ONbRjDHn4ZyFXlX9IrIIeA1IBhar6lYReQxYq6rLReQjwEtAPvAxEfmaql4MTAJ+4pykTSLUR7/tDC/V69JSkhgzeCC7Dvv66yU9oSMQ5MV1FTz7l73srvFRlJPOF+dPYKz/oBV5Y1woqgumVHUFsKLTY49G3F5DqEun83HvAlN7mLFHxhdls6WqPpYRXOfRl7fywuoDTB6Ww/f/5lJunjqctJQkSksrYh3NGNMNnr0yNmxcURYrtlTT0h6wRaaj8KddR3hh9QEeuGoMX755kk1dYIwHeH5Jn3GF2ajCniPWfXMuDa0dfOnFTVxUmMW/3jDBirwxHuH5Qj++KDQm1U7Intt/vLKNww2tfPeOS8lItb9+jPEKzxf60YMHkpos7K6xFv3ZrNpRw2/WVvDgNRcybWRerOMYY3qR5wt9anJo5M1ua9GfUX1zBw//bhPji7L43PXjYh3HGNPLPF/oAcYVZdsQy7N4/NXtHPW18707ppGeYl02xnhNQhT68YXZHKxrpqU9EOsocemD8lqum1jI1BF29bAxXpQYhb4oC1Uos376Lvna/OQPSIt1DGNMH0mIQj/OmfPGRt50ranNz8B0z19SYUzCSohCP3rQANKSk9hVY4W+s2BQaWoPkJVuffPGeFVCFPqU5CTGDhnIbjshe5rmjtB5i6wMa9Eb41UJUeghPPLGWvSdNbX5AazrxhgPS5hCP74wi4q6lhOFzYT4nJ9HlhV6YzwrYQr9OGcqhEQbedPU5mfnoTP/JeNrdVr0aVbojfGqBCr0zmpTCVTo2/wB/nbxam774TucaW1g67oxxvsSptCPKgiNvEmUqRBUlUde3My6/XU0twdoPsPFYtZ1Y4z3JUyhD4+8SZQTsj96ew+/W1/JBOcvGd8Zzk00tYdb9Da80hivSphCD6HVphJhzptXtxzi26/uZMG04fzj3AsBaGzt6HJfX5szvNJa9MZ4VoIV+iwqj7ecsXXrBVsq6/nCrzcwbWQe3/r4JeRkpALQ0HqGFr310RvjeQlV6McMDo28qahrjnGSvrH/WBP3PbeG/AGpPPO3M8hITSbbuRDKd5ZCLwIDbJlFYzwroQr9sLwMAKqOt8Q4Se+rPN7CXT/9gI5AkOfum0lhduh7DV/x2niGQu9r85OVlmLLBhrjYQn193pxXiYAlcdbY5ykd9U0tPKpn75PQ2sHL/z9bMY7J2ABsp2uG19b1330NqGZMd6XUC36IVnppCYL1R5q0R/ztfGpn31ATWMbz/3dTKYUnzqnfPgk65la9E1tARtxY4zHJVShT0oSinIyPNN1U9/Swd8uXs2B2maevfcjzBiVf9o+5yr0jW1+G3FjjMdFVehFZL6I7BSRMhF5uIvtV4vIhyLiF5HbO227V0R2O1/39lbw7hqel0lVvfu7bnxtfu5dvJpdhxv5yT0zuPzCQV3ul5wkZKWnnKVFb103xnjdOQu9iCQDTwM3ApOBT4rI5E67HQA+DTzf6dgC4KvALGAm8FUROb3Z2Y+G57q/Rd/SHuD+59awubKep+66jDkTCs+6f1Z6ivXRG5PAomnRzwTKVLVcVduBJcCCyB1UdZ+qbgKCnY69AVipqrWqWgesBOb3Qu5uG56XyaH6VgLBrud+iXdt/gD/8Kt1rN5XyxOfuJQbLh56zmOyM87covdZ140xnhfNJ7wYOBhxv4JQCz0aXR1b3HknEVkILAQoKiqitLQ0yqc/nc/nO+vxvpoO/EFl+euryM+I7SmKc2XtzB9UfrihjQ9rAtw3JY3c47spLd19zuOCbS0cqG7u8rWO+1qoP3o4qhznmzeW3JQV3JXXTVnBXXn7Kms0hb6rAdbRNoejOlZVnwGeASgpKdE5c+ZE+fSnKy0t5WzHB3cc5pfb1jJq8nQuuyCmvUjnzBppW1UDj768hQ9rmvnaLRdz7xWjo36dxeWrqW/pYM6cK0/b1r7yj4wfO4o5cyb2at5Yc1NWcFdeN2UFd+Xtq6zRNGkrgJER90cAVVE+f0+O7RPDnbH0bumnr2/u4Ksvb+Gj//1nyo828b07Lj2vIg+QnZ7S5Vw37f4g7YGgrRdrjMdF06JfA4wTkTFAJXAncFeUz/8a8J8RJ2D/GnjkvFP2onChr3bBRVPLN1bxteVbqWtu5+7Zo3ho3njyBqSd9/NkZ6R0OQWCzXNjTGI45ydcVf0isohQ0U4GFqvqVhF5DFirqstF5CPAS0A+8DER+ZqqXqyqtSLydUK/LAAeU9XaPvpeopKTkUpWegqVcd6i31bVwBd+vYGpxbn84r7TL4Q6H2c6GeuzQm9MQojqE66qK4AVnR57NOL2GkLdMl0duxhY3IOMvW54XgbV9fFb6INB5f+9vIW8zFR+8XczyR2Q2qPny0pPpaUjgD8QJCX5ZG+dLTpiTGJIqCtjw4blZlIVx103S9dVsG5/HY/cNKnHRR44OYNlp+mZrevGmMSQkIV+eF5m3J6MrWtq55t/3M7M0QV8/LLTRqJ2y5lmsDzZoreTscZ4WUIW+uK8DI41tdPa0fU6qrH07dd20NDq5+u3Tum1qYNzzlDom5zVpaxFb4y3JWShH5brjLyJszlv1u2v44XVB7n/qjFMGJp97gOilJUe6v7pPMTyRNdNmhV6Y7wsIQt9PI6l9weCfGXZFobmZPC568b16nOfqY/eTsYakxgStNDH30pTj/9xB9urG/jqxyb3elfKmfro7WSsMYkhIQv90NxwoY+Prpslqw/ws7/s5dNXjObGqcN6/fnDLfrGzi36dj9pKUmkpSTk28CYhJGQn/D0lGSGZKfHxVj6d/cc5SvLtnD1+CF85eZJffIaORln7qO3bhtjvC8hCz2E5qWP9dWxh5qCfOZXHzJ68ECeumv6KRcz9ab0lCRSkqTLUTe2jKAx3pe4hT7GY+nrmzv4wbpWkgSevbfkRKu7L4hIl/PdNLb6bcSNMQkgoQt9dX0rqv2/AEkwqHz+1+s50qL8+O4ZjBo0sM9fMyvj9BksrevGmMSQsIV+WG4Gze0B6lu6XmKvL/30z+Ws2nmET05MY9bYrtd67W3Z6amnT4HQbssIGpMIErbQFztj6fu7n37d/jq+/dpObpo6lOsu6L8im5WRQkMXUyBYi94Y70vYQj8sBvPSH29u559fWM/wvAwe//glvTbFQTRyuuijDy0MbidjjfG6hG3Onbhoqp+GWKoq//rbTdQ0trL0wSv69ORrV7LSU2hs69xHHzgxPYIxxrsStkU/eGA6aclJ/XbR1LN/2csb2w/z8I2TuHRkXr+8ZqTsjNRTWvSqSlO732auNCYBJGyhT0oShuZm9MsQyw0Hj/OtV3cwb3IR9105us9fryvhVabCo4ya2wOo2vQHxiSChC30EOq+6etCX9/SwaLnP6QwO4Pv3N6//dGfDx4AAA6DSURBVPKRsjJS8AeV1o4gYPPcGJNIErzQZ/bpVMWqypeWbuJQfSv/fdf0bi3s3Vuyw9MgOP30jTZzpTEJI7ELfW4mhxpa8QeCffL8v3xvP69uPcQX50/gsgvy++Q1opWdfuoMltaiNyZxJHahz8skEFRqGtt6/bm3VNbzjT9s59qJhTxw1dhef/7zdWJOeqfQ+04UejsZa4zXJXShH+YMseztWSwbWzv47PMfUjAwje/ecSlJSbHpl4+UdVqLPnDK48YY70roQn/y6tje66dXVR7+3WYq6lr477umUzAwdv3ykcJ99D6nj966boxJHFEVehGZLyI7RaRMRB7uYnu6iPza2f6BiIx2Hh8tIi0issH5+nHvxu+ZvlhS8PnVB/jDpmoemjeej4wu6LXn7alw101Dp64ba9Eb433n/JSLSDLwNDAPqADWiMhyVd0Wsdv9QJ2qXiQidwLfAv7G2bZHVaf1cu5ekZWeQt6AVCrqmnvl+bZVNfC132/j6vFD+Mw1F/bKc/aW7IyuT8ZaoTfG+6Jp0c8EylS1XFXbgSXAgk77LAB+4dxeClwnsRowfp5G5GdSUdfzFr2vzc+i5z8kLzOVJz4RH/3ykcIF3RdR6EVgQJqdjDXG66JpzhUDByPuVwCzzrSPqvpFpB4Iz787RkTWAw3AV1T1z51fQEQWAgsBioqKKC0tPZ/v4RQ+n++8jk/3t7KzorFHr6mqPLOpjb1HA3xpZgZb1r4X1XHnm7Wn0pJhW1k5pSmV7NjTRnoSvP3221Ef3995e8JNWcFded2UFdyVt6+yRlPou2qadl6t40z7VAMXqOoxEZkBLBORi1W14ZQdVZ8BngEoKSnROXPmRBGra6WlpZzP8e80bWPLe/u55pprun3V6u8+rOC96o08NG88D143LurjzjdrT+W98wb5QwqZM+cSVhzdSG7dkfN6/f7O2xNuygruyuumrOCuvH2VNZqumwpgZMT9EUDVmfYRkRQgF6hV1TZVPQagquuAPcD4nobuTSPyB9DmD3LE1/2x9C9vqGLskIF8du5FvZis92U5891AeL1Y6583JhFEU+jXAONEZIyIpAF3Ass77bMcuNe5fTvwlqqqiAxxTuYiImOBcUB570TvHSMLQiNvetJPv+9YE5OG5ZAcZ/3ynWVnpJ6Y+sAWHTEmcZyz0KuqH1gEvAZsB36jqltF5DERucXZ7VlgkIiUAQ8B4SGYVwObRGQjoZO0D6pqbW9/Ez0xIn8A0P1C3+4PUlHXwtjBfb/ua09lp59cN7apzRYGNyZRRPVJV9UVwIpOjz0acbsVuKOL414EXuxhxj4VvmjqYG33hlgerGsmEFRG98MC3z2VnZHC4YbQxWG+Nv+JX3LGGG9L6CtjIXRl6KCBad1u0e872gTAaDe06CP76G3REWMSRsIXegiPpe9ei36vU+jd0HWTlZ4a0XUTICvDum6MSQRW6IERBQO63aLfe7SJ3MxU8uNkTpuzyc5Ioak9QCCo+Nr8NurGmARhhZ5Qi76yroVgsPPlAee271iTK7pt4OQ0CMeb22n3B8myk7HGJAQr9IRG3rQHgt2al37f0WZXdNvAyUJ/yDkhay16YxKDFXpgZH54LP359dO3dgSoPN7iihE3EOqjBzjkLJ9o4+iNSQxW6Dk5lv7geRb6/cdC+48e7I5hiuEWfXidXGvRG5MYrNAT6qMHqKg9/YRsIKisP1DX5XEnR9xk9V24XhQeZXP4RNeNDa80JhFYoQcyUpMZkp3e5cibl9ZXctsP32VrVf1p2/aeGEPvjhZ9TqcWvXXdGJMYrNA7RuRndtl1807ZUQDeLTt22rZ9R5sYnJV2Ypm+eBfOeci6boxJKFboHSPzTx9Lr6q8Xx4q8OF/I+091sQYl4y4gZMt+PCoG2vRG5MYrNA7RuRnUnW8hUDEWPqDtS1U17eSlZ7C6n21p2yDUNeNW0bcQGg1qSSxUTfGJBor9I6RBQPwB/VEaxdOtuI/fcVoGlv9bK8+uV6Kr83PkcY211wsBSAiZKWnnFgY3LpujEkMVugdJ0fenOynf3/vMQoGpvGp2ReE7kd03+xz0Rw3kcL99GnJSaSl2H+/MYnAPumOk2PpQ/30qsoH5bXMGlPAsNxMRg8awPvlJ6fS3+uiWSsjhcfS29BKYxKHFXrH8LwMRE5eHVtR10Ll8RZmjw2tcT577CBW7z12op/+xPTELuqjh8hCb902xiQKK/SO9JRkirIzOOhcNBXupgkX+lljC2ho9bPjUKiffu+xJoblZpCZ5q6Wcbjrxk7EGpM4rNBHGFlwcl7698tryR+QyrjC0FWvs8YMOvE4uG/ETVi4wFuL3pjEYYU+woiIsfQf7D3GrDGDSHIW/B6el8kFBQNOtPT3HXXP9MSRrOvGmMRjhT7CiPxMqutb2H+siYq6FmaPLThl++yxBazeW0tdUzt1zR2uG3EDJ+e7sWUEjUkcVugjjMwfQFBD89sAzHL658Nmjx1EfUsHf9xyCHDfiBuAHOujNybhWKGPEB5L/+KHFeQNSGVCUfYp28OF/9drDgAwxiWTmUWyPnpjEo8V+ggjC5yx9LUtzBxdcKJ/Pqw4L5ORBZlsrKgnSU7u7ybZJ7purNAbkyiiKvQiMl9EdopImYg83MX2dBH5tbP9AxEZHbHtEefxnSJyQ+9F731DczMI1/bZnbptwsKjb4rzM0lPcV8/t7XojUk85yz0IpIMPA3cCEwGPikikzvtdj9Qp6oXAd8HvuUcOxm4E7gYmA/80Hm+uJSanMSw3FD3zZkKffhxNw6thJPj6K3QG5M4omnRzwTKVLVcVduBJcCCTvssAH7h3F4KXCci4jy+RFXbVHUvUOY8X9wakZ9JbmYqE4dmd7l91pjQSBw3jriByK6buP19a4zpZdE064qBgxH3K4BZZ9pHVf0iUg8Mch5/v9Oxxd1O2w8evOZCapvaT+ufDxtZMIB/u2ECcycU9nOy3jFxaDYPXnMh14x3Z35jzPkTVT37DiJ3ADeo6gPO/XuAmar6TxH7bHX2qXDu7yHUcn8MeE9Vf+U8/iywQlVf7PQaC4GFAEVFRTOWLFnS7W/I5/ORleWONVzdlBXclddNWcFded2UFdyVtydZ586du05VS7raFk2LvgIYGXF/BFB1hn0qRCQFyAVqozwWVX0GeAagpKRE58yZE0WsrpWWltKT4/uTm7KCu/K6KSu4K6+bsoK78vZV1mj66NcA40RkjIikETq5urzTPsuBe53btwNvaehPheXAnc6onDHAOGB170Q3xhgTjXO26J0+90XAa0AysFhVt4rIY8BaVV0OPAv8j4iUEWrJ3+kcu1VEfgNsA/zAZ1U10EffizHGmC5ENcZOVVcAKzo99mjE7VbgjjMc+w3gGz3IaIwxpgfsylhjjPE4K/TGGONxVuiNMcbjrNAbY4zHnfOCqf4mIkeA/T14isHA0V6K09fclBXclddNWcFded2UFdyVtydZR6nqkK42xF2h7ykRWXumq8PijZuygrvyuikruCuvm7KCu/L2VVbrujHGGI+zQm+MMR7nxUL/TKwDnAc3ZQV35XVTVnBXXjdlBXfl7ZOsnuujN8YYcyovtuiNMcZEsEJvjDEe59pCLyKLRaRGRLZEPFYgIitFZLfzb34sM0YSkZEiskpEtovIVhH5nPN43GUWkQwRWS0iG52sX3MeH+Ms/r7bWQw+LdZZw0QkWUTWi8grzv14zrpPRDaLyAYRWes8FnfvgzARyRORpSKyw3n/Xh6PeUVkgvMzDX81iMjn4zErgIh8wfl8bRGRF5zPXZ+8b11b6IHnCC04Hulh4E1VHQe86dyPF37gX1R1EjAb+KyzeHo8Zm4DrlXVS4FpwHwRmU1o0ffvO1nrCC0KHy8+B2yPuB/PWQHmquq0iDHT8fg+CHsSeFVVJwKXEvo5x11eVd3p/EynATOAZuAl4jCriBQD/wyUqOoUQlPA30lfvW9V1bVfwGhgS8T9ncAw5/YwYGesM54l+8vAvHjPDAwAPiS0TvBRIMV5/HLgtVjnc7KMIPQBvhZ4BZB4zerk2QcM7vRYXL4PgBxgL87AjXjPG5Hvr4F34jUrJ9fZLiA0XfwrwA199b51c4u+K0WqWg3g/BuXK2CLyGhgOvABcZrZ6QrZANQAK4E9wHFV9Tu7xNNC7z8AvggEnfuDiN+sAAq8LiLrnPWSIU7fB8BY4Ajwc6dr7GciMpD4zRt2J/CCczvusqpqJfBd4ABQDdQD6+ij963XCn3cE5Es4EXg86raEOs8Z6KqAQ39CTyC0ELvk7rarX9TnU5EPgrUqOq6yIe72DXmWSNcqaqXATcS6sK7OtaBziIFuAz4kapOB5qIg66Ps3H6tW8BfhvrLGfinCdYAIwBhgMDCb0fOuuV963XCv1hERkG4PxbE+M8pxCRVEJF/n9V9XfOw3GdWVWPA6WEzivkOYu/wxkWeo+BK4FbRGQfsIRQ980PiM+sAKhqlfNvDaE+5JnE7/ugAqhQ1Q+c+0sJFf54zQuhgvmhqh527sdj1uuBvap6RFU7gN8BV9BH71uvFfrIRcrvJdQPHhdERAitrbtdVZ+I2BR3mUVkiIjkObczCb0ptwOrCC3+DnGSVVUfUdURqjqa0J/rb6nqp4jDrAAiMlBEssO3CfUlbyEO3wcAqnoIOCgiE5yHriO0BnRc5nV8kpPdNhCfWQ8As0VkgFMbwj/XvnnfxvqkRA9OZrxAqG+rg1Cr435CfbNvArudfwtinTMi71WE/gzbBGxwvm6Kx8zAJcB6J+sW4FHn8bHAaqCM0J/F6bHO2in3HOCVeM7q5NrofG0Fvuw8Hnfvg4jM04C1zvthGZAfr3kJDR44BuRGPBavWb8G7HA+Y/8DpPfV+9amQDDGGI/zWteNMcaYTqzQG2OMx1mhN8YYj7NCb4wxHmeF3hhjPM4KvTHGeJwVemOM8bj/D6LkmDKY3mzDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 548,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 555,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n",
      "multiple solutions for optimal implied volatility\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 564,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minError: 1.60867051404584e-05\n",
      "[110]\n",
      "0.2222\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 586,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minError: 1.60867051404584e-05\n",
      "Ind:  [2221]\n",
      "Sigma[Ind]:  [0.2222]\n",
      "implied_vol:  0.2222\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 588,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minError: 4.272955625990449e-05\n",
      "Ind:  [1517]\n",
      "Sigma[Ind]:  [0.1518]\n",
      "implied_vol:  0.15180000000000002\n"
     ]
    },
    {
     "data": {
      "image/png": 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zmP6zwVzYQ0cMhzMVukiQevvrbTw+Zy0J7Vvx2phkEtq38jqSeEyFLhJkSssreHJeDmlfbSOldwcm3zSAmOaRXseSAKBCFwkih48d564Z2XyRe4DU75/Nw5f3IUKniZMqKnSRIJG7t5Dx05ax83Axvxt5Htcnx3sdSQKMCl0kCMzfsJe7ZywnKrIJM1MvIKlbW68jSQBSoYsEMDPj9cVbePrDdfTuFMNrY5PpEtvC61gSoFToIgGqpKycX32whnez8rj8nE48f+P5tGymH1k5Ob07RALQ/sISbp+eRea2Q9zzw578/Ic9aaKdn1ILFbpIgMnZWcCEtEwOHC3hpZsHcNV5Z3odSYKECl0kgGTtKeP1z78kpnkk7068kHO7tvE6kgQRFbpIADAzpmTk8uLyEs6Pj+XV0Ul0jGnudSwJMip0EY8Vl5bzX7NX8deVOxnaOYI3U4fQPDIwTuAswUWFLuKh3fnFpE7PZPWOfB66vDd9bbvKXOpMX5gs4pEV2w/z45cWs2lvIa+OTubO4T10zk+pF62hi3hgzoodPDR7FR1aRzF93DB6d9Jp4qT+VOgijai8wnjuk/W8smAzg7u35U+3DKRddJTXsSREqNBFGklBcSn3zlxOxoZ93DrkLB6/+hydJk78SoUu0gg27ytkQlom2w4c46lrErl1SDevI0kIUqGLNLAFG/cxaUY2kRFNeGv8BQw5u53XkSREqdBFGkj1b0rsFdeaV8ckE9+2pdexJISp0EUaQHFpOY9+sJr3s3dwRWInfn+DvilRGp7eYSJ+tqegmNTpWazcfpj7LunF3Rf30DclSqNQoYv40Yrth0lNy6SwpIyXb03i8sROXkeSMKJCF/GT97PzeOT91cTFRJE27kL6dIrxOpKEGRW6SD2VVxjPfLSOVxdtYejZ7Zhyy0DatmrmdSwJQyp0kXrILyrlnpnLWbBxH2OGduPXV/XTh4XEM7W+85xzbzjn9jrn1pxkunPO/cE5l+ucW+WcG+j/mCKBJ3dvIddO+YIvcvfz9LXn8sSIRJW5eMqXd9+fgctPMf0KoGfVJRX4U/1jiQS2jPV7uXbKF+QXlTJjwhBuvuAsryOJ1F7oZrYQOHiKWUYAaVZpCRDrnOvsr4AigcTMeHnBJn42bRnxbVsyZ9IwBndv63UsEQCcmdU+k3MJwDwzS6xh2jzgGTNbXHX7H8DDZpZZw7ypVK7FExcXl5Senl6n0IWFhURHR9dp2WClMXvveLnx5poSvtpVzqBOEYxPjCKqqX+PLw+0MTcGjfn0pKSkZJlZck3T/LFTtKZ3dI2/JcxsKjAVIDk52YYPH16nJ5w/fz51XTZYacze2pVfxMTpWazadYwHL+vFXSkNczKKQBpzY9GY/ccfhZ4HxFe73RXY6YfHFQkI2d8eYuL0LI6VlDF1dBKXnaMPC0lg8scu+bnAmKqjXYYA+Wa2yw+PK+K5dzO3M+qVJbSIjOD9O4epzCWg1bqG7pybCQwH2jvn8oDHgUgAM3sZ+BC4EsgFjgG3NVRYkcZSWl7BU/NymPbVNi78Xjum3DyQM/RhIQlwtRa6md1Uy3QD7vJbIhGP7S8s4c63s1m65SDj/6M7j1zRh6Y6vlyCgD4pKlLN6rx8Jk7P5MDR47xw4/lcO6Cr15FEfKZCF6nywfI8HnlvNe1aNWP27Rdybtc2XkcSOS0qdAl7ZeUV/Paj9by+eAsXdG/LlFsG0j46yutYIqdNhS5h7eDR40yakc2Xmw7w0wsT+OWP+ur7WCRoqdAlbK3dmU9qWhb7Ckv43cjzuD45vvaFRAKYCl3C0tyVO3lo9kpiWzRj1sSh9I+P9TqSSL2p0CWslFcYz32ynlcWbGZQwhlMuWUgHVs39zqWiF+o0CVsHD52nLtnLmfRN/u5dchZPHbVOTRrqu3lEjpU6BIW1u8uIDUti135Rfz2unO5abC+v1xCjwpdQt6Hq3fx4LsriY5qSnrqUJK6neF1JJEGoUKXkFVeYTz/2QamZGxiwFmxvHxrEnEx2l4uoUuFLiEp/1gpP39nORkb9jFqUDz/PeIcoppGeB1LpEGp0CXkrNtVwMTpWew8XMST1yRy6wVnNcjJKEQCjQpdQsqcFTt4+L1VxDSP5J2JQ0jqpvN9SvhQoUtIKC2v4OkP1/HmF1sZnNCWl24ZoOPLJeyo0CXo7T1SzKS3l7N060FuG5bAo1fq+1gkPKnQJahlbTvIHW9lU1BcyuRR/RnRv4vXkUQ8o0KXoGRmvLVkG0/My+HM2BZM+9lg+naO8TqWiKdU6BJ0ikvLefSD1byfvYOL+3TkhRv606ZlpNexRDynQpegsv3gMSZOz2Ld7gLuu6QXd1/cgyZNdEiiCKjQJYgs2LiPe2Yux8x4Y+wgUvp09DqSSEBRoUvAq6gw/jg/l99/tpHeca15ZXQS3dq18jqWSMBRoUtAKygu5YFZK/ksZw/X9D+T3153Hi2a6SP8IjVRoUvA+ragnN+8uJi8Q0X85up+jL0wQR/hFzkFFboEpFmZ23lySTFto6NITx1CcoI+wi9SGxW6BJTi0nIem7OGWZl59GvXhLQ7LqJ9dJTXsUSCggpdAsbW/Ue54+1s1u0q4J6Le9A/cqfKXOQ06AsvJCB8vGY3V7+4mF35Rbx52yDuv6w3TbS9XOS0aA1dPFVaXsFzH6/n1UVbOD8+lj/eMpAusS28jiUSlFTo4pnd+cVMmpFN5rZDjBnajV/+qK/OKiRSDz5tcnHOXe6c2+Ccy3XOPVLD9J865/Y551ZUXcb7P6qEki9y93PVi4vI2VXA5FH9eWJEospcpJ5qXUN3zkUAU4BLgTxgmXNurpnlnDDrO2Y2qQEySgj556c+n/9sI2d3iCY9dSA9Orb2OpZISPBlk8tgINfMNgM459KBEcCJhS5ySgcKS7h/1koWbNzHiP5n8vS159IqSlv9RPzFl5+mLsD2arfzgAtqmO8nzrnvAxuB+8xsew3zSJhasvkA96Yv59CxUp66JpFbdOJmEb9zZnbqGZy7HvhPMxtfdXs0MNjM7q42Tzug0MxKnHO3AzeY2cU1PFYqkAoQFxeXlJ6eXqfQhYWFREdH12nZYBWsY64w46+bSvlLbilxLR139o/irBjftpUH65jrQ2MOD/UZc0pKSpaZJdc40cxOeQGGAp9Uu/0L4BenmD8CyK/tcZOSkqyuMjIy6rxssArGMe/JL7Kbpn5l3R6eZz9PX26FxaWntXwwjrm+NObwUJ8xA5l2kl71ZZPLMqCnc647sAMYBdxcfQbnXGcz21V188fAutP9rSOhZdE3+7jvnRUUlpTx3MjzuD6pqzaxiDSwWgvdzMqcc5OAT6hc+37DzNY6556g8jfFXOAe59yPgTLgIPDTBswsAaysvIIX/r6RP87fRM+O0cycMISecTqKRaQx+HSIgZl9CHx4wn2PVbv+Cyo3xUgY23m4iHvTl7Ns6yFGDYrn8avP0XeXizQiHTMmfvH5+j3cP2slpWUVTB7VnxH9u3gdSSTsqNClXopLy3nmo/X8+cut9Oscw0s3D+DsDuF1xIJIoFChS51t2H2Ee9OXs373EW4blsDDl/eheaQ2sYh4RYUup83MSPtqG//z4TpimjflzdsGkdK7o9exRMKeCl1Oy/7CEh6avYrP1+9leO8O/G7k+XRorZNQiAQCFbr4bMHGfTwwayUFxaU6abNIAFKhS61Kysp59qMNvPHFFnp2jGb6uMH07RzjdSwROYEKXU5p/e4C7ntnJet2FTBmaDcevbKvdnyKBCgVutSovMJ4bdFmfv/pRlo3b8prY5K5pF+c17FE5BRU6PId2w4c5cF3V7Js6yH+85w4/ufac2kfrR2fIoFOhS7/YmbMXLqdp/6WQ4RzPH/D+Vw7oIt2fIoECRW6ALCnoJiH31vF/A37GNajHb8beT5nxrbwOpaInAYVepgzM/66ahe//ssaSsrK+e8fn8PoId1o0kRr5SLBRoUexvYWFPPrOWv4ZO0e+sfH8vwN5+t7WESCmAo9DJkZs7PyeHJeDsVlFTxyRR/G/0d3mkY08TqaiNSDCj3M5B06xqMfrGHhxn0MSjiDZ39yntbKRUKECj1MVFQY05ds49mP1+OAJ0acw60XaFu5SChRoYeB3L1H+MX7q1m29RDf79WBp69NpOsZLb2OJSJ+pkIPYUXHy3nx8294ddFmWjZryv9efz4/GajjykVClQo9RP1j3R4en7uWvENF/GRgVx69sg/t9GlPkZCmQg8xOw4X8d9z1/Jpzh56dozmndQhXHB2O69jiUgjUKGHiJKyct5YvJUXP/+GCjMeurw34//jbJo11aGIIuFChR7kzIxP1u7m6Q/X8+3BY1zSN47Hr+5HfFvt9BQJNyr0IJazs4An5q1lyeaD9IqLJu1ng/l+rw5exxIRj6jQg9DeI8W88Nk3vLPsW9q0iOTJEedw0+Cz9ElPkTCnQg8i+UWlTF24iTcWb6W0vIKxFybw8x/2ok3LSK+jiUgAUKEHgaLj5fxt83HuXZBBflEpV59/Jvdf2ovu7Vt5HU1EAogKPYAVl5bzzrLtTMnIZe+RUob37sCDl/UmsUsbr6OJSABSoQegwpIy3lqyjdcWbWF/YQmDEs5gXF/HxOsGex1NRAJY0BX6l7n7eWpJES+u+xIHOAfOuf9/HVd1X/Xr1adXv+2q3XfCss7RIjKCmOaRtGkRSUyLpsS2jOTMNi04M7YFnds09/tOyINHj5P21Vbe/GIr+UWlXNSzPXelDOCC7m1ZsGCBX59LREJP0BV6kyaOqAhoHtkEMyovGGZQUQFGRdV9lcdoV/5beZuq2xVm1ZatnA9OeCwziksryC8qpbCk7Ls5HJwZ24I+nWLo27k1fTrFcF7XNnQ9o8Vpf1fKmh35TPtyK3NW7uR4WQWX9otjUkoPzo+Pref/loiEE58K3Tl3OTAZiABeM7NnTpgeBaQBScAB4EYz2+rfqJWGnN2O/xrUguHDhzTEw9eorLyCwpIyDhw9zs7DRew4VMSOw0Vs2X+UDbuPkLFhL+UVlb8UOsU0Z3D3tgzq3pYf9OzAWe1q/oBPcWk5n+bs4a2vtrF060FaREZwQ3JXxg5NoGdc60Ybm4iEjloL3TkXAUwBLgXygGXOublmllNttnHAITPr4ZwbBTwL3NgQgb3QNKIJsS2bEduyGd+r4WQQxaXl5O4tZPn2wyzdcpAlmw8wd+VOAHp2jObivh25pG8c/eNjWbMjn9lZefx15U4KisuIb9uCX/2oL9cnx9OmhQ4/FJG682UNfTCQa2abAZxz6cAIoHqhjwB+U3V9NvCSc87ZP7dlhLjmkREkdmlDYpc2jB7SDTNj64FjfL5+L5+v38Pri7bwyoLNNG3iKKswmkc24fJzOjEyKZ6h32tHhE4yISJ+4GrrXOfcSOByMxtfdXs0cIGZTao2z5qqefKqbm+qmmf/CY+VCqQCxMXFJaWnp9cpdGFhIdHRwXPatGOlxtoD5Ww6XEHnVo7BnZvSounplXiwjdkfNObwoDGfnpSUlCwzS65pmi9r6DU1z4m/BXyZBzObCkwFSE5OtuHDh/vw9N81f/586rqsV66s5/LBOOb60pjDg8bsP74cd5cHxFe73RXYebJ5nHNNgTbAQX8EFBER3/hS6MuAns657s65ZsAoYO4J88wFxlZdHwl8Hi7bz0VEAkWtm1zMrMw5Nwn4hMrDFt8ws7XOuSeATDObC7wOTHfO5VK5Zj6qIUOLiMh3+XQcupl9CHx4wn2PVbteDFzv32giInI69AXaIiIhQoUuIhIiVOgiIiFChS4iEiJq/aRogz2xc/uAbXVcvD2wv9a5QovGHB405vBQnzF3M7MazwbvWaHXh3Mu82QffQ1VGnN40JjDQ0ONWZtcRERChApdRCREBGuhT/U6gAc05vCgMYeHBhlzUG5DFxGR7wrWNXQRETmBCl1EJEQEdKE75y53zm1wzuU65x6pYXqUc+6dqulfO+cSGj+lf/kw5vudcznOuVXOuX8457p5kdOfahtztflGOufMORf0h7j5Mmbn3A1Vr/Va59yMxs7obz68t89yzmU455ZXvb/re14YTznn3nDO7a06o1tN051z7g9V/x+rnHMD67HuqC4AAALgSURBVP2kZhaQFyq/qncTcDbQDFgJ9DthnjuBl6uujwLe8Tp3I4w5BWhZdf2OcBhz1XytgYXAEiDZ69yN8Dr3BJYDZ1Td7uh17kYY81Tgjqrr/YCtXueu55i/DwwE1pxk+pXAR1Se8W0I8HV9nzOQ19D/dXJqMzsO/PPk1NWNAKZVXZ8N/NA5F8xnXK51zGaWYWbHqm4uofIMUsHMl9cZ4EngOaC4McM1EF/GPAGYYmaHAMxsbyNn9DdfxmxATNX1Nnz3zGhBxcwWcuozt40A0qzSEiDWOde5Ps8ZyIXeBdhe7XZe1X01zmNmZUA+0K5R0jUMX8Zc3Tgqf8MHs1rH7JwbAMSb2bzGDNaAfHmdewG9nHNfOOeWOOcub7R0DcOXMf8GuNU5l0fl+Rfubpxonjndn/da+XSCC4/47eTUQcTn8TjnbgWSgR80aKKGd8oxO+eaAC8AP22sQI3Al9e5KZWbXYZT+VfYIudcopkdbuBsDcWXMd8E/NnMfu+cG0rlWdASzayi4eN5wu/9Fchr6OF4cmpfxoxz7hLgl8CPzaykkbI1lNrG3BpIBOY757ZSua1xbpDvGPX1vT3HzErNbAuwgcqCD1a+jHkcMAvAzL4CmlP5JVahyqef99MRyIUejienrnXMVZsfXqGyzIN9uyrUMmYzyzez9maWYGYJVO43+LGZZXoT1y98eW//hcod4Djn2lO5CWZzo6b0L1/G/C3wQwDnXF8qC31fo6ZsXHOBMVVHuwwB8s1sV70e0es9wbXsJb4S2Ejl3vFfVt33BJU/0FD5gr8L5AJLgbO9ztwIY/47sAdYUXWZ63Xmhh7zCfPOJ8iPcvHxdXbA80AOsBoY5XXmRhhzP+ALKo+AWQFc5nXmeo53JrALKKVybXwccDtwe7XXeErV/8dqf7yv9dF/EZEQEcibXERE5DSo0EVEQoQKXUQkRKjQRURChApdRCREqNBFREKECl1EJET8HxgnoWT8MuYcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 589,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minError: 0.00012812650563531758\n",
      "Ind:  [1123]\n",
      "Sigma[Ind]:  [0.1124]\n",
      "implied_vol:  0.1124\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 583,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minError: 1.60867051404584e-05\n",
      "Ind:  [2221]\n",
      "implied_vol:  0.2222\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 592,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24\n",
      "minError: 1.60867051404584e-05\n",
      "Ind:  [2221]\n",
      "Sigma[Ind]:  [0.2222]\n",
      "implied_vol:  0.2222\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "volatility_smile(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 594,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minError: 1.60867051404584e-05\n",
      "Ind:  [2221]\n",
      "Sigma[Ind]:  [0.2222]\n",
      "implied_vol:  0.2222\n",
      "minError: 4.272955625990449e-05\n",
      "Ind:  [1517]\n",
      "Sigma[Ind]:  [0.1518]\n",
      "implied_vol:  0.15180000000000002\n",
      "minError: 0.00012812650563531758\n",
      "Ind:  [1123]\n",
      "Sigma[Ind]:  [0.1124]\n",
      "implied_vol:  0.1124\n",
      "minError: 0.00017235454207914502\n",
      "Ind:  [540]\n",
      "Sigma[Ind]:  [0.0541]\n",
      "implied_vol:  0.0541\n",
      "minError: 0.6499999999999981\n",
      "Ind:  [151, 157]\n",
      "Sigma[Ind]:  [0.0152 0.0158]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.0152\n",
      "minError: 1.2199999999999982\n",
      "Ind:  [263, 267, 279]\n",
      "Sigma[Ind]:  [0.0264 0.0268 0.028 ]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.0264\n",
      "minError: 1.7199999999999982\n",
      "Ind:  [384, 388]\n",
      "Sigma[Ind]:  [0.0385 0.0389]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.0385\n",
      "minError: 2.1699999999999964\n",
      "Ind:  [475]\n",
      "Sigma[Ind]:  [0.0476]\n",
      "implied_vol:  0.0476\n",
      "minError: 2.569999999999998\n",
      "Ind:  [559, 560, 561, 562, 563, 564, 572, 573, 577, 584, 587, 589, 593, 600]\n",
      "Sigma[Ind]:  [0.056  0.0561 0.0562 0.0563 0.0564 0.0565 0.0573 0.0574 0.0578 0.0585\n",
      " 0.0588 0.059  0.0594 0.0601]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.056\n",
      "minError: 2.8699999999999983\n",
      "Ind:  [648, 649, 650, 651, 652, 653, 654, 664, 665, 672, 673, 675, 683, 684, 693, 694, 699, 704]\n",
      "Sigma[Ind]:  [0.0649 0.065  0.0651 0.0652 0.0653 0.0654 0.0655 0.0665 0.0666 0.0673\n",
      " 0.0674 0.0676 0.0684 0.0685 0.0694 0.0695 0.07   0.0705]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.0649\n",
      "minError: 3.1099999999999985\n",
      "Ind:  [733, 734, 735, 736, 737, 738, 739, 751, 752, 760, 765, 769, 773, 778, 792]\n",
      "Sigma[Ind]:  [0.0734 0.0735 0.0736 0.0737 0.0738 0.0739 0.074  0.0752 0.0753 0.0761\n",
      " 0.0766 0.077  0.0774 0.0779 0.0793]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.0734\n",
      "minError: 3.669999999999998\n",
      "Ind:  [814, 815, 816, 817, 818, 819, 820, 834, 838, 839, 844, 846, 851, 855, 865, 868]\n",
      "Sigma[Ind]:  [0.0815 0.0816 0.0817 0.0818 0.0819 0.082  0.0821 0.0835 0.0839 0.084\n",
      " 0.0845 0.0847 0.0852 0.0856 0.0866 0.0869]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.0815\n",
      "minError: 4.5699999999999985\n",
      "Ind:  [891, 892, 893, 894, 895, 896, 897, 898, 913, 918, 929, 934, 937, 940]\n",
      "Sigma[Ind]:  [0.0892 0.0893 0.0894 0.0895 0.0896 0.0897 0.0898 0.0899 0.0914 0.0919\n",
      " 0.093  0.0935 0.0938 0.0941]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.0892\n",
      "minError: 4.869999999999998\n",
      "Ind:  [965, 966, 967, 968, 969, 970, 971, 998, 999, 1006, 1012, 1017, 1020, 1023, 1025, 1029, 1031, 1034]\n",
      "Sigma[Ind]:  [0.0966 0.0967 0.0968 0.0969 0.097  0.0971 0.0972 0.0999 0.1    0.1007\n",
      " 0.1013 0.1018 0.1021 0.1024 0.1026 0.103  0.1032 0.1035]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.0966\n",
      "minError: 4.349999999999996\n",
      "Ind:  [1053, 1054, 1055, 1083]\n",
      "Sigma[Ind]:  [0.1054 0.1055 0.1056 0.1084]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.10540000000000001\n",
      "minError: 4.399999999999997\n",
      "Ind:  [1122, 1123, 1124]\n",
      "Sigma[Ind]:  [0.1123 0.1124 0.1125]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.11230000000000001\n",
      "minError: 4.399999999999997\n",
      "Ind:  [1188, 1189, 1190, 1215, 1240]\n",
      "Sigma[Ind]:  [0.1189 0.119  0.1191 0.1216 0.1241]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.1189\n",
      "minError: 4.869999999999996\n",
      "Ind:  [1252, 1253, 1262, 1286, 1298]\n",
      "Sigma[Ind]:  [0.1253 0.1254 0.1263 0.1287 0.1299]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.1253\n",
      "minError: 4.969999999999997\n",
      "Ind:  [1314, 1331, 1332, 1367]\n",
      "Sigma[Ind]:  [0.1315 0.1332 0.1333 0.1368]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.1315\n",
      "minError: 5.069999999999995\n",
      "Ind:  [1373, 1391, 1396, 1422]\n",
      "Sigma[Ind]:  [0.1374 0.1392 0.1397 0.1423]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.1374\n",
      "minError: 4.769999999999994\n",
      "Ind:  [1449, 1459, 1467]\n",
      "Sigma[Ind]:  [0.145  0.146  0.1468]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.14500000000000002\n",
      "minError: 5.669999999999995\n",
      "Ind:  [1889, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1935, 1936, 1958, 1959, 1972, 1973, 1981, 1982, 1993]\n",
      "Sigma[Ind]:  [0.189  0.1891 0.1892 0.1893 0.1894 0.1895 0.1896 0.1897 0.1898 0.1899\n",
      " 0.19   0.1901 0.1902 0.1903 0.1904 0.1905 0.1906 0.1907 0.1908 0.1909\n",
      " 0.191  0.1911 0.1936 0.1937 0.1959 0.196  0.1973 0.1974 0.1982 0.1983\n",
      " 0.1994]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.189\n",
      "minError: 5.869999999999997\n",
      "Ind:  [2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2579, 2580, 2581, 2582, 2583, 2584, 2613, 2614, 2615, 2616, 2617, 2618, 2633, 2634, 2635, 2636, 2637, 2647, 2648, 2649, 2650, 2657, 2658, 2659, 2660, 2666, 2667, 2668, 2673, 2674, 2675, 2679, 2680, 2681]\n",
      "Sigma[Ind]:  [0.2571 0.2572 0.2573 0.2574 0.2575 0.2576 0.2577 0.2578 0.2579 0.258\n",
      " 0.2581 0.2582 0.2583 0.2584 0.2585 0.2614 0.2615 0.2616 0.2617 0.2618\n",
      " 0.2619 0.2634 0.2635 0.2636 0.2637 0.2638 0.2648 0.2649 0.265  0.2651\n",
      " 0.2658 0.2659 0.266  0.2661 0.2667 0.2668 0.2669 0.2674 0.2675 0.2676\n",
      " 0.268  0.2681 0.2682]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.2571\n",
      "minError: 6.36999999999999\n",
      "Ind:  [3056, 3057, 3058, 3059, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3131, 3132, 3170, 3171, 3192, 3193, 3208, 3209]\n",
      "Sigma[Ind]:  [0.3057 0.3058 0.3059 0.306  0.3061 0.3062 0.3063 0.3064 0.3065 0.3066\n",
      " 0.3067 0.3068 0.3069 0.307  0.3071 0.3072 0.3073 0.3074 0.3075 0.3076\n",
      " 0.3077 0.3078 0.3079 0.308  0.3081 0.3082 0.3083 0.3084 0.3085 0.3086\n",
      " 0.3087 0.3088 0.3089 0.3132 0.3133 0.3171 0.3172 0.3193 0.3194 0.3209\n",
      " 0.321 ]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.3057\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(24):\n",
    "    volatility_smile(df,i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 597,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minError: 2.5699999999999963\n",
      "Ind:  [19485, 19486, 19487, 19657, 19658, 19659, 19769, 19770, 19771]\n",
      "Sigma[Ind]:  [0.058458 0.058461 0.058464 0.058974 0.058977 0.05898  0.05931  0.059313\n",
      " 0.059316]\n",
      "multiple solutions for optimal implied volatility\n",
      "implied_vol:  0.058458\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "volatility_smile(df,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# how to minimize with scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 632,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " final_simplex: (array([[0.5       ],\n",
      "       [0.50009766]]), array([0.000000e+00, 9.765625e-05]))\n",
      "           fun: 0.0\n",
      "       message: 'Optimization terminated successfully.'\n",
      "          nfev: 18\n",
      "           nit: 9\n",
      "        status: 0\n",
      "       success: True\n",
      "             x: array([0.5])\n"
     ]
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "from scipy.optimize import minimize\n",
    "def f(x,y):\n",
    "    return norm.cdf(x)-y\n",
    "\n",
    "# célfüggvény\n",
    "def objective_function(x0, a):\n",
    "    \"\"\"objective function, to be solved.\"\"\"\n",
    "    return abs(f(a,x0))\n",
    "\n",
    "\n",
    "initial_guess = [0]  # initial guess can be anything\n",
    "result = optimize.minimize(objective_function, 0.5, initial_guess,method='nelder-mead')\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(x):\n",
    "    x1 = x[0]\n",
    "    x2 = x[1]\n",
    "    x3 = x[2]\n",
    "    x4 = x[3]   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 631,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 631,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.cdf(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 633,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 644,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9999999960566366"
      ]
     },
     "execution_count": 644,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def o(x):\n",
    "    return np.abs(x ** 2 - 4)\n",
    "def c1(x):\n",
    "    return x - 1\n",
    "def c2(x):\n",
    "    return 10 - x\n",
    "    \n",
    "x0 = 10 # initial guess\n",
    "\n",
    "o(x0)\n",
    "#b=(1,7)\n",
    "bound=(b)\n",
    "con1={'type': 'ineq', 'fun' : c1}\n",
    "con2={'type': 'ineq', 'fun' : c2}\n",
    "c=(con1,con2)\n",
    "# method=\"SLSQP\", bounds=bound)\n",
    "s = minimize(o, x0, constraints=c)\n",
    "x=s.x\n",
    "x=x[0]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 649,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7.4505805673858834e-09"
      ]
     },
     "execution_count": 649,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def o(x):\n",
    "    return np.abs(norm.cdf(x) - 1/2)\n",
    "    \n",
    "x0 = 1 # initial guess\n",
    "\n",
    "o(x0)\n",
    "#b=(1,7)\n",
    "#bound=(b)\n",
    "con1={'type': 'ineq', 'fun' : c1}\n",
    "con2={'type': 'ineq', 'fun' : c2}\n",
    "c=(con1,con2)\n",
    "# method=\"SLSQP\", bounds=bound)\n",
    "s = minimize(o, x0)\n",
    "x=s.x\n",
    "x=x[0]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 650,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:10: RuntimeWarning: invalid value encountered in true_divide\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The solution is tau = 1.021651\n",
      "at which the value of the expression is -0.000000\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import fsolve\n",
    "\n",
    "# Define the expression whose roots we want to find\n",
    "\n",
    "a = 0.5\n",
    "R = 1.6\n",
    "\n",
    "func = lambda tau : R - ((1.0 - np.exp(-tau))/(1.0 - np.exp(-a*tau))) \n",
    "\n",
    "# Plot it\n",
    "\n",
    "tau = np.linspace(-0.5, 1.5, 201)\n",
    "\n",
    "plt.plot(tau, func(tau))\n",
    "plt.xlabel(\"tau\")\n",
    "plt.ylabel(\"expression value\")\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# Use the numerical solver to find the roots\n",
    "\n",
    "tau_initial_guess = 0.5\n",
    "tau_solution = fsolve(func, tau_initial_guess)\n",
    "\n",
    "print(\"The solution is tau = %f\" % tau_solution)\n",
    "print(\"at which the value of the expression is %f\" % func(tau_solution))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 652,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      fun: 1.5808871493702169e-18\n",
      " hess_inv: array([[ 0.03898428, -0.01508996,  0.00433191],\n",
      "       [-0.01508996,  0.09405872,  0.10127539],\n",
      "       [ 0.00433191,  0.10127539,  0.56141594]])\n",
      "      jac: array([4.49424054e-08, 2.88924305e-08, 1.74158279e-08])\n",
      "  message: 'Optimization terminated successfully.'\n",
      "     nfev: 30\n",
      "      nit: 4\n",
      "     njev: 6\n",
      "   status: 0\n",
      "  success: True\n",
      "        x: array([ 0.24414812,  0.18485712, -0.88852078])\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "# find solutions of -0.7353 + 3.306 * abs(0.706 - x) + 1.247 * abs(0.721 - y) = 0.89072 - 1.4829 * x + 0.23239 * y - z\n",
    "f = lambda x: ((-0.7353 + 3.306 * (np.abs(0.706 - x[0])) + 1.247 * (np.abs(0.721 - x[1]))) - \\\n",
    "                (0.89072 - 1.4829 * x[0] + 0.23239 * x[1] - x[2]))**2\n",
    "x0 = [1, 1, 1]\n",
    "res = minimize(f, x0, tol=1e-6)\n",
    "x=res.x\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 660,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.24414812,  0.18485712, -0.88852078])"
      ]
     },
     "execution_count": 660,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "# find solutions of -0.7353 + 3.306 * abs(0.706 - x) + 1.247 * abs(0.721 - y) = 0.89072 - 1.4829 * x + 0.23239 * y - z\n",
    "f = lambda x: ((-0.7353 + 3.306 * (np.abs(0.706 - x[0])) + 1.247 * (np.abs(0.721 - x[1]))) - \\\n",
    "                (0.89072 - 1.4829 * x[0] + 0.23239 * x[1] - x[2]))**2\n",
    "x0 = [1, 1, 1]\n",
    "res = minimize(f, x0, tol=1e-10)\n",
    "x=res.x\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 655,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5808871493702169e-18"
      ]
     },
     "execution_count": 655,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 661,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = lambda x: -0.7353 + 3.306 * np.abs(0.706 - x[0]) + 1.247 * np.abs(0.721 - x[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 662,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4601524758465136"
      ]
     },
     "execution_count": 662,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 663,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = lambda x: 0.89072 - 1.4829 * x[0] + 0.23239 * x[1] - x[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 664,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4601524745891803"
      ]
     },
     "execution_count": 664,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 653,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5808871493702169e-18"
      ]
     },
     "execution_count": 653,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 665,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0232111212322122e+19"
      ]
     },
     "execution_count": 665,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10232111212322121212.21+10.23211121232212121221"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 667,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 667,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(2.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 669,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for -: 'function' and 'function'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-669-012ccc196445>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mnorm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcdf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mx0\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mminimize\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtol\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-10\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mres\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: unsupported operand type(s) for -: 'function' and 'function'"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "g = lambda x: 1/2\n",
    "# find solutions of -0.7353 + 3.306 * abs(0.706 - x) + 1.247 * abs(0.721 - y) = 0.89072 - 1.4829 * x + 0.23239 * y - z\n",
    "f = lambda x: norm.cdf(x)\n",
    "x0 = 1\n",
    "res = minimize(f-g, x0, tol=1e-10)\n",
    "x=res.x\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(speed, a, b, c, d):\n",
    "    ... # return stuff using a,b,c,d\n",
    "\n",
    "# define a0, b0, c0, d0 as convenient\n",
    "result = optimize.minimize(objective, x0, args=(a0,b0,c0,d0), method='nelder-mead')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 606,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.783263929997124"
      ]
     },
     "execution_count": 606,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.cdf(0.78326393)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 574,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      C\n",
       "313    P\n",
       "Name: Option Type, dtype: object"
      ]
     },
     "execution_count": 574,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Option Type\"].drop_duplicates()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 509,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-03-18 00:00:00\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Expiry Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>Option Type</th>\n",
       "      <th>Time to Expiry</th>\n",
       "      <th>Implied Price</th>\n",
       "      <th>Pricing Error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.10</td>\n",
       "      <td>265.14%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>3.558371</td>\n",
       "      <td>-4.541629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>11.0</td>\n",
       "      <td>7.10</td>\n",
       "      <td>232.23%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>2.970775</td>\n",
       "      <td>-4.129225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>12.0</td>\n",
       "      <td>6.20</td>\n",
       "      <td>205.66%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>2.466392</td>\n",
       "      <td>-3.733608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>13.0</td>\n",
       "      <td>5.40</td>\n",
       "      <td>183.50%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>2.038574</td>\n",
       "      <td>-3.361426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>14.0</td>\n",
       "      <td>4.62</td>\n",
       "      <td>168.12%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>1.679171</td>\n",
       "      <td>-2.940829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>28</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>15.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>156.54%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>1.379549</td>\n",
       "      <td>-2.620451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>34</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>16.0</td>\n",
       "      <td>3.60</td>\n",
       "      <td>92.82%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>1.131268</td>\n",
       "      <td>-2.468732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>44</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>17.0</td>\n",
       "      <td>3.10</td>\n",
       "      <td>140.92%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.926494</td>\n",
       "      <td>-2.173506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>51</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.75</td>\n",
       "      <td>137.21%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.758208</td>\n",
       "      <td>-1.991792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>57</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>19.0</td>\n",
       "      <td>2.45</td>\n",
       "      <td>132.91%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.620277</td>\n",
       "      <td>-1.829723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>67</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.15</td>\n",
       "      <td>129.64%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.507445</td>\n",
       "      <td>-1.642555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>79</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1.85</td>\n",
       "      <td>127.44%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.415263</td>\n",
       "      <td>-1.434737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>88</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1.70</td>\n",
       "      <td>125.49%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.340013</td>\n",
       "      <td>-1.359987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>95</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>23.0</td>\n",
       "      <td>1.53</td>\n",
       "      <td>123.88%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.278606</td>\n",
       "      <td>-1.251394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1.40</td>\n",
       "      <td>123.54%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.228497</td>\n",
       "      <td>-1.171503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>108</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>25.0</td>\n",
       "      <td>1.26</td>\n",
       "      <td>121.88%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.187597</td>\n",
       "      <td>-1.072403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>112</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>26.0</td>\n",
       "      <td>1.20</td>\n",
       "      <td>121.73%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.154197</td>\n",
       "      <td>-1.045803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>115</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>27.0</td>\n",
       "      <td>1.13</td>\n",
       "      <td>121.19%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.126901</td>\n",
       "      <td>-1.003099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>129</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.95</td>\n",
       "      <td>99.41%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.104575</td>\n",
       "      <td>-0.845425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>132</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.88</td>\n",
       "      <td>25.00%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.086295</td>\n",
       "      <td>-0.793705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>136</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0.81</td>\n",
       "      <td>100.68%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.071312</td>\n",
       "      <td>-0.738688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>149</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>32.5</td>\n",
       "      <td>0.65</td>\n",
       "      <td>119.04%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.044555</td>\n",
       "      <td>-0.605445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>160</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0.55</td>\n",
       "      <td>119.53%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.028100</td>\n",
       "      <td>-0.521900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>170</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>37.5</td>\n",
       "      <td>0.45</td>\n",
       "      <td>50.00%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.017891</td>\n",
       "      <td>-0.432109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>175</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>40.0</td>\n",
       "      <td>0.40</td>\n",
       "      <td>107.03%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.011499</td>\n",
       "      <td>-0.388501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>200</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>45.0</td>\n",
       "      <td>0.30</td>\n",
       "      <td>119.24%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.004883</td>\n",
       "      <td>-0.295117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>201</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>42.5</td>\n",
       "      <td>0.30</td>\n",
       "      <td>108.79%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.007460</td>\n",
       "      <td>-0.292540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>207</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>47.5</td>\n",
       "      <td>0.25</td>\n",
       "      <td>50.00%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.003225</td>\n",
       "      <td>-0.246775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>213</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.22</td>\n",
       "      <td>50.00%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.002148</td>\n",
       "      <td>-0.217852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>227</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>55.0</td>\n",
       "      <td>0.17</td>\n",
       "      <td>119.34%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.000976</td>\n",
       "      <td>-0.169024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>240</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>65.0</td>\n",
       "      <td>0.15</td>\n",
       "      <td>50.00%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.000221</td>\n",
       "      <td>-0.149779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>241</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0.15</td>\n",
       "      <td>112.89%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.000457</td>\n",
       "      <td>-0.149543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>247</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>75.0</td>\n",
       "      <td>0.13</td>\n",
       "      <td>125.00%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.000055</td>\n",
       "      <td>-0.129945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>267</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>70.0</td>\n",
       "      <td>0.09</td>\n",
       "      <td>126.17%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.000109</td>\n",
       "      <td>-0.089891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>275</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.07</td>\n",
       "      <td>50.00%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>-0.069971</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Expiry Date  Strike  Last Price Implied Volatility Option Type  \\\n",
       "0    2020-03-18    10.0        8.10            265.14%           C   \n",
       "4    2020-03-18    11.0        7.10            232.23%           C   \n",
       "8    2020-03-18    12.0        6.20            205.66%           C   \n",
       "12   2020-03-18    13.0        5.40            183.50%           C   \n",
       "22   2020-03-18    14.0        4.62            168.12%           C   \n",
       "28   2020-03-18    15.0        4.00            156.54%           C   \n",
       "34   2020-03-18    16.0        3.60             92.82%           C   \n",
       "44   2020-03-18    17.0        3.10            140.92%           C   \n",
       "51   2020-03-18    18.0        2.75            137.21%           C   \n",
       "57   2020-03-18    19.0        2.45            132.91%           C   \n",
       "67   2020-03-18    20.0        2.15            129.64%           C   \n",
       "79   2020-03-18    21.0        1.85            127.44%           C   \n",
       "88   2020-03-18    22.0        1.70            125.49%           C   \n",
       "95   2020-03-18    23.0        1.53            123.88%           C   \n",
       "99   2020-03-18    24.0        1.40            123.54%           C   \n",
       "108  2020-03-18    25.0        1.26            121.88%           C   \n",
       "112  2020-03-18    26.0        1.20            121.73%           C   \n",
       "115  2020-03-18    27.0        1.13            121.19%           C   \n",
       "129  2020-03-18    28.0        0.95             99.41%           C   \n",
       "132  2020-03-18    29.0        0.88             25.00%           C   \n",
       "136  2020-03-18    30.0        0.81            100.68%           C   \n",
       "149  2020-03-18    32.5        0.65            119.04%           C   \n",
       "160  2020-03-18    35.0        0.55            119.53%           C   \n",
       "170  2020-03-18    37.5        0.45             50.00%           C   \n",
       "175  2020-03-18    40.0        0.40            107.03%           C   \n",
       "200  2020-03-18    45.0        0.30            119.24%           C   \n",
       "201  2020-03-18    42.5        0.30            108.79%           C   \n",
       "207  2020-03-18    47.5        0.25             50.00%           C   \n",
       "213  2020-03-18    50.0        0.22             50.00%           C   \n",
       "227  2020-03-18    55.0        0.17            119.34%           C   \n",
       "240  2020-03-18    65.0        0.15             50.00%           C   \n",
       "241  2020-03-18    60.0        0.15            112.89%           C   \n",
       "247  2020-03-18    75.0        0.13            125.00%           C   \n",
       "267  2020-03-18    70.0        0.09            126.17%           C   \n",
       "275  2020-03-18    80.0        0.07             50.00%           C   \n",
       "\n",
       "     Time to Expiry  Implied Price  Pricing Error  \n",
       "0          0.535714       3.558371      -4.541629  \n",
       "4          0.535714       2.970775      -4.129225  \n",
       "8          0.535714       2.466392      -3.733608  \n",
       "12         0.535714       2.038574      -3.361426  \n",
       "22         0.535714       1.679171      -2.940829  \n",
       "28         0.535714       1.379549      -2.620451  \n",
       "34         0.535714       1.131268      -2.468732  \n",
       "44         0.535714       0.926494      -2.173506  \n",
       "51         0.535714       0.758208      -1.991792  \n",
       "57         0.535714       0.620277      -1.829723  \n",
       "67         0.535714       0.507445      -1.642555  \n",
       "79         0.535714       0.415263      -1.434737  \n",
       "88         0.535714       0.340013      -1.359987  \n",
       "95         0.535714       0.278606      -1.251394  \n",
       "99         0.535714       0.228497      -1.171503  \n",
       "108        0.535714       0.187597      -1.072403  \n",
       "112        0.535714       0.154197      -1.045803  \n",
       "115        0.535714       0.126901      -1.003099  \n",
       "129        0.535714       0.104575      -0.845425  \n",
       "132        0.535714       0.086295      -0.793705  \n",
       "136        0.535714       0.071312      -0.738688  \n",
       "149        0.535714       0.044555      -0.605445  \n",
       "160        0.535714       0.028100      -0.521900  \n",
       "170        0.535714       0.017891      -0.432109  \n",
       "175        0.535714       0.011499      -0.388501  \n",
       "200        0.535714       0.004883      -0.295117  \n",
       "201        0.535714       0.007460      -0.292540  \n",
       "207        0.535714       0.003225      -0.246775  \n",
       "213        0.535714       0.002148      -0.217852  \n",
       "227        0.535714       0.000976      -0.169024  \n",
       "240        0.535714       0.000221      -0.149779  \n",
       "241        0.535714       0.000457      -0.149543  \n",
       "247        0.535714       0.000055      -0.129945  \n",
       "267        0.535714       0.000109      -0.089891  \n",
       "275        0.535714       0.000029      -0.069971  "
      ]
     },
     "execution_count": 509,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "volatility_smile(df)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 503,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Expiry Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>Option Type</th>\n",
       "      <th>Time to Expiry</th>\n",
       "      <th>Implied Price</th>\n",
       "      <th>Pricing Error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.10</td>\n",
       "      <td>265.14%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>3.558371</td>\n",
       "      <td>-4.541629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2020-02-19</td>\n",
       "      <td>10.0</td>\n",
       "      <td>7.90</td>\n",
       "      <td>294.63%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.424603</td>\n",
       "      <td>3.382450</td>\n",
       "      <td>-4.517550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2020-04-15</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.20</td>\n",
       "      <td>250.88%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.646825</td>\n",
       "      <td>3.721204</td>\n",
       "      <td>-4.478796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>2020-02-19</td>\n",
       "      <td>11.0</td>\n",
       "      <td>6.97</td>\n",
       "      <td>255.66%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.424603</td>\n",
       "      <td>2.765039</td>\n",
       "      <td>-4.204961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>11.0</td>\n",
       "      <td>7.10</td>\n",
       "      <td>232.23%</td>\n",
       "      <td>C</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>2.970775</td>\n",
       "      <td>-4.129225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>552</td>\n",
       "      <td>2020-01-22</td>\n",
       "      <td>47.5</td>\n",
       "      <td>28.40</td>\n",
       "      <td>0.00%</td>\n",
       "      <td>P</td>\n",
       "      <td>0.313492</td>\n",
       "      <td>34.820058</td>\n",
       "      <td>6.420058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>553</td>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>80.0</td>\n",
       "      <td>60.80</td>\n",
       "      <td>0.00%</td>\n",
       "      <td>P</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>67.320029</td>\n",
       "      <td>6.520029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>554</td>\n",
       "      <td>2020-04-15</td>\n",
       "      <td>80.0</td>\n",
       "      <td>60.70</td>\n",
       "      <td>0.00%</td>\n",
       "      <td>P</td>\n",
       "      <td>0.646825</td>\n",
       "      <td>67.320177</td>\n",
       "      <td>6.620177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>555</td>\n",
       "      <td>2020-04-15</td>\n",
       "      <td>75.0</td>\n",
       "      <td>55.70</td>\n",
       "      <td>0.00%</td>\n",
       "      <td>P</td>\n",
       "      <td>0.646825</td>\n",
       "      <td>62.320305</td>\n",
       "      <td>6.620305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>556</td>\n",
       "      <td>2020-01-22</td>\n",
       "      <td>60.0</td>\n",
       "      <td>40.60</td>\n",
       "      <td>0.00%</td>\n",
       "      <td>P</td>\n",
       "      <td>0.313492</td>\n",
       "      <td>47.320002</td>\n",
       "      <td>6.720002</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>557 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Expiry Date  Strike  Last Price Implied Volatility Option Type  \\\n",
       "0    2020-03-18    10.0        8.10            265.14%           C   \n",
       "1    2020-02-19    10.0        7.90            294.63%           C   \n",
       "2    2020-04-15    10.0        8.20            250.88%           C   \n",
       "3    2020-02-19    11.0        6.97            255.66%           C   \n",
       "4    2020-03-18    11.0        7.10            232.23%           C   \n",
       "..          ...     ...         ...                ...         ...   \n",
       "552  2020-01-22    47.5       28.40              0.00%           P   \n",
       "553  2020-03-18    80.0       60.80              0.00%           P   \n",
       "554  2020-04-15    80.0       60.70              0.00%           P   \n",
       "555  2020-04-15    75.0       55.70              0.00%           P   \n",
       "556  2020-01-22    60.0       40.60              0.00%           P   \n",
       "\n",
       "     Time to Expiry  Implied Price  Pricing Error  \n",
       "0          0.535714       3.558371      -4.541629  \n",
       "1          0.424603       3.382450      -4.517550  \n",
       "2          0.646825       3.721204      -4.478796  \n",
       "3          0.424603       2.765039      -4.204961  \n",
       "4          0.535714       2.970775      -4.129225  \n",
       "..              ...            ...            ...  \n",
       "552        0.313492      34.820058       6.420058  \n",
       "553        0.535714      67.320029       6.520029  \n",
       "554        0.646825      67.320177       6.620177  \n",
       "555        0.646825      62.320305       6.620305  \n",
       "556        0.313492      47.320002       6.720002  \n",
       "\n",
       "[557 rows x 8 columns]"
      ]
     },
     "execution_count": 503,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 686,
   "metadata": {},
   "outputs": [],
   "source": [
    "def A(p):\n",
    "    return np.matrix([[np.sqrt(np.abs(p)),2],[3, 1/np.sqrt(np.abs(p))]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 676,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2. , 2. ],\n",
       "        [3. , 0.5]])"
      ]
     },
     "execution_count": 676,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 691,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.00e-06, -9.98e-07, -9.96e-07, ...,  9.96e-07,  9.98e-07,\n",
       "        1.00e-06])"
      ]
     },
     "execution_count": 691,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(-0.000001,0.000001,1001)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 692,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "y =np.array([np.linalg.det(A(p)) for p in x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 693,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aaab288d88>]"
      ]
     },
     "execution_count": 693,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 690,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5., -5., -5., ..., -5., -5., -5.])"
      ]
     },
     "execution_count": 690,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_volatility_smile(x,y):\n",
    "    plt.plot(x,y, label=\"RMS\")\n",
    "    plt.plot(x,y)\n",
    "    #plt.plot(x,z)\n",
    "    plt.title(\"Pricing errors\") \n",
    "    plt.xticks(rotation=45)\n",
    "    #plt.ylim(0, plt.ylim()[1]) #change only the first argument\n",
    "    plt.grid()\n",
    "    plt.legend(fontsize=8)\n",
    "    plt.ylabel(\"Pricing errors (RMS)\")\n",
    "    plt.xlabel(\"Implied Volatility\")\n",
    "    plt.tight_layout()\n",
    "    store=False\n",
    "    if store:\n",
    "        #p = os.path.join(platform_prefix(), ...)\n",
    "        plt.savefig(p,dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_pricing_errors(df):\n",
    "    df.sort_values(by=[\"Pricing Error\"],ascending=True,inplace=True)\n",
    "    df.reset_index(drop=True,inplace=True)\n",
    "    # plt.bar(df[\"Pricing Error\"], height=500, align='center')\n",
    "    plt.plot(df[\"Pricing Error\"], label=\"Pricing Errors\")\n",
    "    #plt.plot(x,y)\n",
    "    #plt.plot(x,z)\n",
    "    plt.title(\"Pricing Errors\") \n",
    "    plt.xticks(rotation=45)\n",
    "    #plt.ylim(0, plt.ylim()[1]) #change only the first argument\n",
    "    plt.grid()\n",
    "    plt.legend(fontsize=8)\n",
    "    plt.ylabel(\"Pricing errors\")\n",
    "    #plt.xlabel(\"Implied Volatility\")\n",
    "    plt.tight_layout()\n",
    "    store=False\n",
    "    if store:\n",
    "        #p = os.path.join(platform_prefix(), ...)\n",
    "        plt.savefig(p,dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Expiry Date</th>\n",
       "      <th>Contract Name</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Bid</th>\n",
       "      <th>Ask</th>\n",
       "      <th>Change</th>\n",
       "      <th>Change (%)</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Open Interest</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>Option Type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00010000</td>\n",
       "      <td>10.00</td>\n",
       "      <td>4.40</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.88</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>52</td>\n",
       "      <td>20</td>\n",
       "      <td>546.88%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00010500</td>\n",
       "      <td>10.50</td>\n",
       "      <td>3.20</td>\n",
       "      <td>2.70</td>\n",
       "      <td>3.40</td>\n",
       "      <td>-</td>\n",
       "      <td>-</td>\n",
       "      <td>4</td>\n",
       "      <td>-</td>\n",
       "      <td>496.09%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00011000</td>\n",
       "      <td>11.00</td>\n",
       "      <td>3.70</td>\n",
       "      <td>2.18</td>\n",
       "      <td>2.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>10</td>\n",
       "      <td>-</td>\n",
       "      <td>434.38%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00012000</td>\n",
       "      <td>12.00</td>\n",
       "      <td>1.70</td>\n",
       "      <td>1.40</td>\n",
       "      <td>1.70</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>-2.86%</td>\n",
       "      <td>21</td>\n",
       "      <td>17</td>\n",
       "      <td>318.75%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>2019-11-06</td>\n",
       "      <td>VIXW191106C00012500</td>\n",
       "      <td>12.50</td>\n",
       "      <td>1.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>74</td>\n",
       "      <td>80</td>\n",
       "      <td>6.25%</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Expiry Date        Contract Name Strike Last Price   Bid   Ask Change  \\\n",
       "0  2019-11-06  VIXW191106C00010000  10.00       4.40  3.15  3.88   0.00   \n",
       "1  2019-11-06  VIXW191106C00010500  10.50       3.20  2.70  3.40      -   \n",
       "2  2019-11-06  VIXW191106C00011000  11.00       3.70  2.18  2.90   0.00   \n",
       "3  2019-11-06  VIXW191106C00012000  12.00       1.70  1.40  1.70  -0.05   \n",
       "4  2019-11-06  VIXW191106C00012500  12.50       1.20  0.00  0.00   0.00   \n",
       "\n",
       "  Change (%) Volume Open Interest Implied Volatility Option Type  \n",
       "0          -     52            20            546.88%           C  \n",
       "1          -      4             -            496.09%           C  \n",
       "2          -     10             -            434.38%           C  \n",
       "3     -2.86%     21            17            318.75%           C  \n",
       "4          -     74            80              6.25%           C  "
      ]
     },
     "execution_count": 300,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ticker = \"^VIX\"\n",
    "opts = options(ticker)\n",
    "opts.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now, we have the table entries for the two options nearest to the money in HTML. \n",
    "# Let’s scrape the pricing data, volume, and implied volatility from the first call option:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['SPY191104C00325000', '2019-10-28 9:45AM EDT', '325.00', '0.01', '0.00', '0.01', '0.00', '-', '1', '0', '25.00%']\n"
     ]
    }
   ],
   "source": [
    "itm_call_data = [] \n",
    "for td in BeautifulSoup(str(itm_call), \"html.parser\").find_all(\"td\"):\n",
    "    itm_call_data.append(td.text)\n",
    "print(itm_call_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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