IJPAM: Volume 93, No. 5 (2014)
FUNCTION OF A MULTIDIMENSIONAL AND
MULTISCALE STOCHASTIC VOLATILITY MODEL
University of Trento
Via Sommarive, 14-38123, Trento, ITALY
Department of Coputer Science
University of Verona
Strada le Grazie, 14-37134, Verona, ITALY
Abstract. The present work generalizes the results obtained in  to a 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 and a slow mean reverting process with scale , and we perform the expansion for the associated characteristic function, at maturity time , in powers of and . 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 assets.
Received: April 16, 2014
AMS Subject Classification: 635Q80, 60E10, 60F99, 91B70, 91G80
Key Words and Phrases: stochastic differential equations, stochastic volatility, fast mean-reversion, asymptotic expansion
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DOI: 10.12732/ijpam.v93i5.12 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 741 - 752
This work is licensed under the Creative Commons Attribution International License (CC BY).