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New Approximations in Local Volatility Models

23 Pages Posted: 7 Oct 2010  

Emmanuel Gobet

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Ali Suleiman

affiliation not provided to SSRN

Date Written: October 5, 2010

Abstract

For general time-dependent local volatility models, we propose new ap- proximation formulas for the price of call options. This extends previous results of [BGM10b] where stochastic expansions combined with Malliavin calculus were performed to obtain approximation formulas based on the local volatility At The Money. Here, we derive alternative expansions involving the local volatility at strike. Averaging both expansions give even more accurate results. Approximations of the implied volatility are provided as well.

Keywords: Local volatility model, European option, asymptotic expansion, CEV model

Suggested Citation

Gobet, Emmanuel and Suleiman, Ali, New Approximations in Local Volatility Models (October 5, 2010). Available at SSRN: https://ssrn.com/abstract=1687583 or http://dx.doi.org/10.2139/ssrn.1687583

Emmanuel Gobet (Contact Author)

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

Palaiseau Cedex, 91128
France

Ali Suleiman

affiliation not provided to SSRN ( email )

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