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

F. Cordoni, L. Di Persio
2014 International Journal of Pure and Applied Mathematics  
The present work generalizes the results obtained in [3] to a d > 1 dimensional setting. In particular we give the first order asymptotic correction for the characteristic function of the log-return of a multidimensional asset price process whose volatility is driven by two diffusion processes on two different time scales. We consider a fast mean reverting process with reverting scale 1 ǫ and a slow mean reverting process with scale δ, and we perform the expansion for the associated
more » ... ociated 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 exploited to numerically analyze the fair price of a structured option written on d > 1 assets.
doi:10.12732/ijpam.v93i5.12 fatcat:jbfmoqeblbe5xcs2vxspipunle