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The Heat-Kernel Most-Likely-Path Approximation

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Author Info

  • JIM GATHERAL

    ()
    (Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA)

  • TAI-HO WANG

    ()
    (Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA)

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    Abstract

    In this article, we derive a new most-likely-path (MLP) approximation for implied volatility in terms of local volatility, based on time-integration of the lowest order term in the heat-kernel expansion. This new approximation formula turns out to be a natural extension of the well-known formula of Berestycki, Busca and Florent. Various other MLP approximations have been suggested in the literature involving different choices of most-likely-path; our work fixes a natural definition of the most-likely-path. We confirm the improved performance of our new approximation relative to existing approximations in an explicit computation using a realistic S&P500 local volatility function.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 15 (2012)
    Issue (Month): 01 ()
    Pages: 1250001-1-1250001-18

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    Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:01:p:1250001-1-1250001-18

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    Related research

    Keywords: Most-likely-path; heat kernel expansion; implied volatility; local volatility model; asymptotic expansion;

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    Cited by:
    1. Stefano De Marco & Peter Friz, 2013. "Varadhan's formula, conditioned diffusions, and local volatilities," Science & Finance (CFM) working paper archive 1311.1545, Science & Finance, Capital Fund Management.

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