A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models. (17th June 2015)

• Record Type: Journal Article
• Authors: Merino, Raúl; Vives, Josep
• Other Names: Yong Jiongmin Academic Editor.
• Is Part Of: International journal of stochastic analysis. Volume 2015(2015)
• Publication Date: 2015-06-17
• Subjects: Stochastic analysis -- Periodicals; Stochastic analysis; Periodicals; 519.22
• DOI: 10.1155/2015/103647
• Languages: English
• ISSNs: 2090-3332

Abstract

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.