A Simple and Accurate Simulation Approach to the
Heston Model

Abstract

Models with stochastic volatility often require Monte Carlo simulation. One of the most popular volatility processes is the mean-reverting square root diffusion, as proposed by Heston. The theoretical model as developed in continuous time has the virtue that it does not allow volatility to become negative. But when the model is adapted to discrete non-infinitesimal time steps in a simulation, negative variance values can be encountered. Several ways to deal with this problem have been proposed, but they can come with inconvenient side effects, such as slow or erratic convergence or the failure to preserve correlation properties with other stochastic variables in the model. Zhu shows how building the model in terms of volatility rather than variance can produce more-accurate and more-efficient simulations within a Heston-type model