Efficient simulation of a multi-factor stochastic volatility model

Abstract

Empirical phenomenon in financial markets such as volatility smiles and term structure of implied volatilities made stochastic volatility models more attractive. In this paper, we consider a two-factor stochastic volatility model with slow and fast mean reverting factors for which a first order asymptotic approximation formula in terms of the homogenized Black–Scholes solution is given by Fouque et al. (2004) [1]. We compare the simulation efficiency of importance sampling estimators derived from the zeroth and first order terms in the asymptotic expansion formula with the benchmark crude Monte Carlo estimator. We implement the zeroth order importance sampling estimators for the barrier option pricing by the use of the discrete barrier option pricing formula with the continuity correction. Results show that using the importance sampling estimator based on the zeroth order term together with some of the well known randomized quasi-Monte Carlo sequences is computationally the most efficient method for pricing the European and barrier options considered.