A generative adversarial network approach to calibration of local stochastic volatility models
This work addresses the problem of calibrating financial models for practitioners in quantitative finance, offering an incremental improvement by integrating neural SDEs and adversarial techniques to avoid ad hoc interpolation.
The authors tackled the calibration of local stochastic volatility models by proposing a data-driven approach that uses neural networks to parametrize the leverage function and adversarial networks to assess distances to market prices, achieving accurate and stable results as demonstrated in a statistical analysis on implied volatility smiles.
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, possibly 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 the calculation of 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 analysis on many samples of implied volatility smiles, showing the accuracy and stability of the method.