Variance reduction for Monte Carlo simulation in a stochastic volatility environment

We propose a variance reduction method for Monte Carlo computation of option prices in the context of stochastic volatility. This method is based on importance sampling using an approximation of the option price obtained by a fast mean-reversion expansion introduced in Fouque et al (2000 Derivatives in Financial Markets with Stochastic Volatility (Cambridge: Cambridge University Press)). We compare this with the small noise expansion method proposed in Fournie et al (1997 Asymptotic Anal. 14 361-76) and demonstrate numerically the efficiency of our method, in particular in the presence of a skew.