FIRST ORDER CORRECTION FOR THE CHARACTERISTIC FUNCTION OF A MULTIDIMENSIONAL AND MULTISCALE STOCHASTIC VOLATILITY MODEL

Abstract: The present work generalizes the results obtained in [3] to a d > 1dimensional setting. In particular we give the first order asymptotic correctionfor the characteristic function of the log-return of a multidimensional asset priceprocess whose volatility is driven by two diffusion processes on two different timescales. We consider a fast mean reverting process with reverting scale 1ǫ anda slow mean reverting process with scale δ, and we perform the expansion forthe associated characteristic function, at maturity time T > 0, in powers of√ǫ and √δ. Latter result, according, e.g., to [2, 4, 9, 12], can be exploitedto numerically analyze the fair price of a structured option written on d > 1assets.