On the discrete-time simulation of the rough Heston model

TL;DR

This paper analyzes the convergence of Euler-type discrete-time schemes for the rough Heston model, a stochastic volatility model described by Volterra equations, and provides numerical results for option pricing.

Contribution

It proves the convergence of discrete schemes to the solution of the rough Heston model using weak convergence techniques and modified Volterra equations.

Findings

Discrete schemes converge to the model's solution.

Modified Volterra equations share the same unique solution as the original.

Numerical examples evaluate derivative option prices under the model.

Abstract

We study Euler-type discrete-time schemes for the rough Heston model, which can be described by a stochastic Volterra equation (with non-Lipschtiz coefficient functions), or by an equivalent integrated variance formulation. Using weak convergence techniques, we prove that the limits of the discrete-time schemes are solution to some modified Volterra equations. Such modified equations are then proved to share the same unique solution as the initial equations, which implies the convergence of the discrete-time schemes. Numerical examples are also provided in order to evaluate different derivative options prices under the rough Heston model.