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New approximations in local volatility models

Author

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  • Emmanuel Gobet

    () (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Ali Suleiman

    (ENSIMAG - École nationale supérieure d'informatique et de mathématiques appliquées - UJF - Université Joseph Fourier - Grenoble 1)

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.

Suggested Citation

  • Emmanuel Gobet & Ali Suleiman, 2013. "New approximations in local volatility models," Post-Print hal-00523369, HAL.
  • Handle: RePEc:hal:journl:hal-00523369
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00523369
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    File URL: https://hal.archives-ouvertes.fr/hal-00523369/document
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    References listed on IDEAS

    as
    1. Eric Benhamou & Emmanuel Gobet & Mohammed Miri, 2010. "Expansion formulas for European options in a local volatility model," Post-Print hal-00325939, HAL.
    2. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480.
    3. Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
    4. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-219, March.
    5. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
    6. Eric Benhamou & Emmanuel Gobet & Mohammed Miri, 2009. "Smart expansion and fast calibration for jump diffusion," Post-Print hal-00200395, HAL.
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