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-Lipschtiz coefficient functions), or by an equivalent integrated variance formulation. Using weak convergence techniques, we prove that the limits of the discretetime 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.

Semimartingale and continuous-time Markov chain approximation for rough stochastic local volatility models

“…In particular, El generalized the classical Heston model to the rough Heston model and derive the characteristic function of the log asset price. See also Abi Jaber and El Euch (2019b); Richard et al (2021); Abi Jaber and El Euch (2019a) for extensions. Note that some numerical challenges still remain for solving the fractional Riccatti system in an efficient way, and see Callegaro et al (2021) for recent developments along that direction.…”