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International Journal of Stochastic Analysis
Volume 2015 (2015), Article ID 103647, 11 pages
http://dx.doi.org/10.1155/2015/103647
Research Article

A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models

1Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
2VidaCaixa S.A., Investment Control Department, Juan Gris, 20-26, 08014 Barcelona, Spain

Received 27 March 2015; Accepted 30 May 2015

Academic Editor: Jiongmin Yong

Copyright © 2015 Raúl Merino and Josep Vives. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model, extending a previous decomposition formula for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used for this purpose are nonanticipative. In particular, we also see that equivalent results can be obtained by using Functional Itô Calculus. Using the same generalizing ideas, we also extend to nonexponential models the alternative call option price decomposition formula written in terms of the Malliavin derivative of the volatility process. Finally, we give a general expression for the derivative of the implied volatility under both the anticipative and the nonanticipative cases.