New approximations in local volatility models

Emmanuel Gobet () and Ali Suleiman
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Emmanuel Gobet: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Ali Suleiman: ENSIMAG - École nationale supérieure d'informatique et de mathématiques appliquées - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology

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Abstract: For general time-dependent local volatility models, we propose new approximation 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.

Date: 2013
New Economics Papers: this item is included in nep-ger
Note: View the original document on HAL open archive server: https://hal.science/hal-00523369v1
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Published in Y. Kabanov and M. Rutkowski and T. Zariphopoulou. Inspired by Finance. The Musiela Festschrift, Springer, pp.305--330, 2013

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