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

TL;DR

This paper introduces a new simulation scheme for the rough Heston model that achieves second order weak convergence with linear computational cost, improving efficiency over existing methods for option pricing.

Contribution

The authors develop a low-dimensional Markovian approximation scheme for the rough Heston model that is both accurate and computationally efficient, applicable in standard and hyper-rough regimes.

Findings

Second order weak convergence demonstrated through numerical experiments.

Computational cost increases linearly with the number of time steps.

Outperforms existing schemes with quadratic cost dependence.

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.