IJAM, Volume 27, No. 3 (2014)

Abstract. We give the first order asymptotic correction for the characteristic function of the log-return of an asset price process whose volatility is driven by two diffusion processes on two different time scales. In particular we consider a fast mean reverting process with reverting scale 1/ε and a slow mean reverting process with scale δ, and we perform the expansion for the associated characteristic function, at maturity time T>0, in powers of ε^1/2 and δ^1/2. The latter result, according, e.g., to [2, 3, 8, 11], can be exploited to compute the fair price for an option written on the asset of interest.