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Asymptotic and Non Asymptotic Approximations for Option Valuation

Computational finance, Thomas Gerstner and Peter Kloeden (Ed.) (2012)

80 Pages Posted: 25 Jul 2012  

Romain Bompis

Ecole Polytechnique, Paris

Emmanuel Gobet

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Date Written: July 25, 2012

Abstract

We give a broad overview of approximation methods to derive analytical formulas for accurate and quick evaluation of option prices. We compare different approaches, from the theoretical point of view regarding the tools they require, and also from the numerical point of view regarding their performances. In the case of local volatility models with general time-dependency, we derive new formulas using the local volatility function at the mid-point between strike and spot: in general, our approximations outperform previous ones by Hagan and Henry - Labordère. We also provide approximations of the option delta.

Suggested Citation

Bompis, Romain and Gobet, Emmanuel, Asymptotic and Non Asymptotic Approximations for Option Valuation (July 25, 2012). Computational finance, Thomas Gerstner and Peter Kloeden (Ed.) (2012). Available at SSRN: https://ssrn.com/abstract=2117080

Romain Bompis

Ecole Polytechnique, Paris ( email )

1 rue Descartes
Paris, 75005
France

Emmanuel Gobet (Contact Author)

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

Palaiseau Cedex, 91128
France

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