Weak Markovian Approximations of Rough Heston

TL;DR

This paper develops new Markovian approximation methods for the rough Heston model, providing bounds on weak errors, demonstrating super-polynomial convergence, and showing improved numerical performance in option pricing.

Contribution

It extends error analysis to weak errors using $L^1$-error bounds and introduces super-polynomial converging Markovian approximations for the rough Heston model.

Findings

Weak error bounds using $L^1$-error in kernel approximation.

Super-polynomial convergence of certain Markovian approximations.

Numerical superiority in option pricing compared to previous methods.

Abstract

The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice. A way to resolve this problem is to use Markovian approximations of the model. Several previous works have shown that these approximations can be very accurate even when the number of additional factors is very low. Existing error analysis is largely based on the strong error, corresponding to the $L^2$ distance between the kernels. Extending earlier results by [Abi Jaber and El Euch, SIAM Journal on Financial Mathematics 10(2):309--349, 2019], we show that the weak error of the Markovian approximations can be bounded using the $L^1$-error in the kernel approximation for general classes of payoff functions for European style options. Moreover, we give specific Markovian approximations which converge super-polynomially in the number of dimensions, and illustrate their numerical superiority in option pricing compared to previously existing approximations. The new approximations also work for the hyper-rough case $H > -1/2$.