Upcoming talks
Tuesday, August 27
Speaker: Christian Bayer (Weierstrass Institute, Berlin)
Title: A Reproducing Kernel Hilbert Space approach to singular local stochastic volatility McKean-Vlasov models
Abstract: Perfect calibration of stochastic local volatility models can be achieved by the particle method due to Guyon and Henry-Labordère. Starting from a back-bone stochastic volatility model, a local volatility factor is computed on the fly to perfectly fit market prices. Mathematically, the local volatility factor is given as a conditional expectation, which is approximated by a local regression procedure. While this procedure is quite popular among practitioners, there are substantial gaps in the theoretical understanding. Indeed, even well-posedness of the resulting singular McKean-Vlasov system is not known.
We develop a novel regularization approach based on the reproducing kernel Hilbert space technique (kernel ridge regression) and show that the regularized model is, in fact, well-posed. Furthermore, we prove propagation of chaos and provide error estimates for the numerical scheme. We demonstrate numerically that a thus regularized model is able to perfectly replicate option prices due to typical local volatility models, and demonstrate excellent performance. Our results are also applicable to more general McKean--Vlasov equations. (Joint work with Denis Belomestny, Oleg Butkovsky, and John Schoenmakers.)