A Simple and Exact Simulation Approach to Heston Model

Abstract

In this paper we will propose a simple approach to simulating Heston model efficiently and accurately. All existing simulation schemes so far directly work with the mean-reverting square root process of the variance in Heston model, instead we transform the variance to an equivalent volatility which follows a mean-reverting Ornstein-Uhlenbeck process. We will show it is more convenient to simulate the transformed volatility process than the original variance process since the new Ornstein-Uhlenbeck process does not have any term of square root, and is not restricted to any parameter restriction. Based on the transformed volatility process, we suggest a simple and exact scheme for the simulation of Heston model. Numerical examples show that the new scheme and Andersen's QE scheme perform very closely, and outperform other schemes such as log-normal scheme. While QE scheme suffers from the problem of "leaking correlation", transformed volatility scheme does not, and therefore, provides a high-quality alternative to the existing simulation schemes for Heston model.

Keywords: Simulation, Stochastic volatility, Heston model, Mean-reverting squared root process, Mean-reverting Ornstein-Uhlenbeck process, Option prices

JEL Classification: G12, G13, C15