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Closed Forms for European Options in a Local Volatility Model

32 Pages Posted: 1 Oct 2008  

Eric Benhamou

Université Paris Est - Université Paris Est-Creteil

Emmanuel Gobet

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Mohammed Miri

Thomson Reuters

Date Written: September 30, 2008

Abstract

Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms.

Keywords: local volatility model, European options, asymptotic expansion, Malliavin calculus, small diffusion process, CEV model

JEL Classification: G13

Suggested Citation

Benhamou, Eric and Gobet, Emmanuel and Miri, Mohammed, Closed Forms for European Options in a Local Volatility Model (September 30, 2008). Available at SSRN: https://ssrn.com/abstract=1275872 or http://dx.doi.org/10.2139/ssrn.1275872

Eric Benhamou

Université Paris Est - Université Paris Est-Creteil ( email )

61 avenue du Général de Gaulle
Créteil, 940000
France

Emmanuel Gobet (Contact Author)

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )

Palaiseau Cedex, 91128
France

Mohammed Miri

Thomson Reuters ( email )

6 Bd Haussman
France, FL 75009
France

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