Option pricing for stochastic volatility models : Vol-of-Vol expansion

In this article, we propose an analytical approximation for the pricing of European op- tions for some lognormal stochastic volatility models. This approximation is a second-order Taylor series expansion of the Fourier transform with respect to the "volatility of volatility". We give, using these formulas, a new method of variance reduction for the Monte-Carlo simulation of the trajectories of the underlying.