Asymptotic expansion for the characteristic function of a multiscale stochastic volatility model

Abstract: We give the first order asymptotic correction for the characteristicfunction of the log-return of an asset price process whose volatility is driven bytwo diffusion processes on two different time scales. In particular we considera fast mean reverting process with reverting scale1ǫand a slow mean revertingprocess with scale δ, and we perform the expansion for the associated charac-teristic function, at maturity time T > 0, in powers of√ ǫ and √ δ. The latterresult, according, e.g., to [2, 3, 8, 11], can be exploited to compute the fair pricefor an option written on the asset of interest.