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 scale1\u1eband a slow mean revertingprocess with scale \u3b4, and we perform the expansion for the associated charac-teristic function, at maturity time T > 0, in powers of 1a \u1eb and 1a \u3b4. 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
