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New approximations in local volatility models

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Author Info

  • Emmanuel Gobet

    ()
    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

  • Ali Suleiman

    (ENSIMAG - École nationale supérieure d'informatique et de mathématiques appliquées - Université Joseph Fourier - Grenoble I)

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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.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/52/33/69/PDF/GOBET_SULEIMAN_VolLocale_FinalVersion.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00523369.

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    Date of creation: 05 Oct 2010
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    Handle: RePEc:hal:wpaper:hal-00523369

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00523369/en/
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    Web page: http://hal.archives-ouvertes.fr/

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