Calibration of local stochastic volatility in a conic finance setting using neural networks

In this thesis, we study the calibration of Local Stochastic Volatility (LSV) models using artificial neural networks, building upon prior work by C. Cuchiero, W. Khosrawi, and J. Teichmann. “A generative adversarial network approach to calibration of local stochastic volatility models”. In: Risks 8.4 (2020), p. 101. The proposed method approximates the map between market prices and model parameters by using a feed-forward neural network to approximate the local volatility component. The method allows us to circumvent the computation of Dupire's formula and avoid the interpolation of the volatility surface. Prior work is extended from the one-price setting to the two-price setting, using the conic finance framework. This allows us to consider only the information available in the market and derive calibrated bid and ask prices. Our method is evaluated through a numerical analysis that involves calibrating it with real market data and comparing the results against a benchmark model and method.