WIAS Preprint No. 2921, (2022)

RKHS regularization of singular local stochastic volatility McKean--Vlasov models


Authors

  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Belomestny, Denis
  • Butkovsky, Oleg
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266

2020 Mathematics Subject Classification

  • 91G20 65C30 46E22

Keywords

  • Stochastic volatility models, singular McKean--Vlasov equations, reproducing kernel Hilbert spaces

DOI

10.20347/WIAS.PREPRINT.2921

Abstract

Motivated by the challenges related to the calibration of financial models, we consider the problem of solving numerically a singular McKean-Vlasov equation, which represents a singular local stochastic volatility model. Whilst such models are quite popular among practitioners, unfortunately, its well-posedness has not been fully understood yet and, in general, is possibly not guaranteed at all. We develop a novel regularization approach based on the reproducing kernel Hilbert space (RKHS) technique and show that the regularized model is well-posed. Furthermore, we prove propagation of chaos. We demonstrate numerically that a thus regularized model is able to perfectly replicate option prices due to typical local volatility models. Our results are also applicable to more general McKean--Vlasov equations.

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