On the Short-Time Behavior of the Implied Volatility for Jump-Diffusion Models With Stochastic Volatility

22 Pages Posted: 24 Jul 2007

See all articles by Elisa Alos

Elisa Alos

University of Pompeu Fabra - Department of Economics

Jorge A. Leon

Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV-IPN)

Josep Vives

University of Barcelona

Date Written: June 2006

Abstract

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

Keywords: Black-Scholes formula, derivative operator, Itô's formula for the Skorohod integral, jump-diffusion stochastic volatility model

JEL Classification: G12, G13

Suggested Citation

Alos, Elisa and Leon, Jorge A. and Vives, Josep, On the Short-Time Behavior of the Implied Volatility for Jump-Diffusion Models With Stochastic Volatility (June 2006). Available at SSRN: https://ssrn.com/abstract=1002308 or http://dx.doi.org/10.2139/ssrn.1002308

Elisa Alos (Contact Author)

University of Pompeu Fabra - Department of Economics ( email )

c/o Ramon Trias Fargas 25-27
08005 Barcelona
Spain
34 93 542 19 25 (Phone)
34 93 542 17 46 (Fax)

Jorge A. Leon

Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV-IPN) ( email )

07360 Mexico, D.F.
Mexico

Josep Vives

University of Barcelona ( email )

Gran Via de les Corts Catalanes, 585
Barcelona, 08007
Spain

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