On the numerical performance of the weak multilevel Monte-Carlo method for the Heston Model

In this article, we discuss the numerical implementation of the Multilevel Monte-Carlo (MLMC) scheme for option pricing within the Heston asset model. The Heston model is a stochastic volatility model that captures the dynamics of the underlying asset price and its volatility. The MLMC method is a variance reduction technique that exploits the difference between two consecutive levels of discretization to estimate the expected value of a quantity of interest. We begin by providing an overview of the MLMC method, followed by an introduction to the weak methods used to approximate the Heston model. Weak methods are numerical schemes that preserve the distributional properties of the solution, rather than its pathwise behavior. Subsequently, we present the results of some numerical experiments conducted to evaluate the performance of the approach. Two different cases are surveyed.