WIAS Preprint No. 3045, (2023)

Efficient option pricing in the rough Heston model using weak simulation schemes


Authors

  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Breneis, Simon

2020 Mathematics Subject Classification

  • 91G60 91G20

Keywords

  • Rough Heston model, Markovian approximations, simulation, weak error, Bermudan options

DOI

10.20347/WIAS.PREPRINT.3045

Abstract

We provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$). The scheme is based on low-dimensional Markovian approximations of the rough Heston process derived in [Bayer and Breneis, arXiv:2309.07023], and provides weak approximation to the rough Heston process. Numerical experiments show that the new scheme exhibits second order weak convergence, while the computational cost increases linear with respect to the number of time steps. In comparison, existing schemes based on discretization of the underlying stochastic Volterra integrals such as Gatheral's HQE scheme show a quadratic dependence of the computational cost. Extensive numerical tests for standard and path-dependent European options and Bermudan options show the method's accuracy and efficiency.

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