IJPAM: Volume 93, No. 5 (2014)

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

Francesco Cordoni$^1$, Luca Di Persio$^2$
$^1$Mathematics Department
University of Trento
Via Sommarive, 14-38123, Trento, ITALY
$^2$Department of Coputer Science
University of Verona
Strada le Grazie, 14-37134, Verona, ITALY


Abstract. 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 $\frac{1}{\epsilon}$ and a slow mean reverting process with scale $\delta$, and we perform the expansion for the associated characteristic function, at maturity time $T>0$, in powers of $\sqrt{\epsilon}$ and $\sqrt{\delta}$. 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.

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
Year: 2014
Volume: 93
Issue: 5
Pages: 741 - 752

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).