A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

15 Pages Posted: 24 Apr 2008

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)

Monique Pontier

Institut Mathématiques de Toulouse, Paul Sabatier University

Josep Vives

University of Barcelona

Date Written: January 4, 2008

Abstract

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Keywords: Hull and White formula, Malliavin calculus, Ito's formula for the Skorohod integral, jumpdiffusion stochastic volatility models

JEL Classification: G12, G13

Suggested Citation

Alos, Elisa and Leon, Jorge A. and Pontier, Monique and Vives, Josep, A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility (January 4, 2008). Available at SSRN: https://ssrn.com/abstract=1124823 or http://dx.doi.org/10.2139/ssrn.1124823

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

Monique Pontier

Institut Mathématiques de Toulouse, Paul Sabatier University ( email )

118 Route de Narbonne - Building 1R3
Toulouse Cedex 9, 31062
France

Josep Vives

University of Barcelona ( email )

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

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