A generative adversarial network approach to calibration of local stochastic volatility models

We propose a fully data driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface. To achieve this, we parametrize the leverage function by a family of feed forward neural networks and learn their parameters directly from the available market option prices. This should be seen in the context of neural SDEs and (causal) generative adversarial networks: we generate volatility surfaces by specific neural SDEs, whose quality is assessed by quantifying, in an adversarial manner, distances to market prices. The minimization of the calibration functional relies strongly on a variance reduction technique based on hedging and deep hedging, which is interesting in its own right: it allows to calculate model prices and model implied volatilities in an accurate way using only small sets of sample paths. For numerical illustration we implement a SABR-type LSV model and conduct a thorough statistical performance analyis on many samples of implied volatility smiles, showing the accuracy and stability of the method.