On the Discrete-Time Simulation of the Rough Heston 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-Lipschitz coefficient functions) or by an equivalent integrated variance formulation. Using weak convergence techniques, we prove that the limits of the discrete-time schemes are a 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.