Calibration of Local Stochastic Volatility Models in Options Pricing

The problem of stochastic models calibration to the observable market prices has been widely studied during the past few years. This is a matter of not only theoretical interest but also of vast practical importance. As time goes by, the new - more accurate pricing models for financial derivatives being developed, or the old ones extended. It’s been a great step towards more realistic and accurate prices of the instruments, but also all of these induced in more time needed for calibration of these models. That is why nowadays there’s always a matter of the dispute in the trading floors - which model to choose for pricing: the less accurate one, but which can provide all the risk sensitivities faster, or the one, that would deliver more accurate prices. Usually, the first option wins this challenge. So, the speed of the model calibration process has great practical importance when choosing the model. Otherwise, the model can become impractical to use, even though it could be really valuable in terms of its accuracy. In several recent articles, a new approach to model calibration has been proposed. An application of Neural Networks to calibration process allows to divide the calculations by separate processes, one of which can be performed offline in a convenient time, and then provide the parameters in a rather short amount of time, comparing to other approaches. In this thesis, I’m going to introduce the recent researches made in the area of Local Stochastic Volatility (LSV) model calibration. Then, detail how Neural Networks (NNs) can be used in calibration. After that, I’m going to apply this methodology to the calibration of the Heston LSV model and provide a detailed analysis of the results.