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Probability Distribution And Option Pricing For Drawdown In A Stochastic Volatility Environment

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Author Info

  • KYO YAMAMOTO

    ()
    (GCI Asset Management, Inc., 12F Chiyoda First Bldg, East, 3-8-1 Nishi Kanda, Chiyoda-ku, Tokyo 101-0065, Japan)

  • SEISHO SATO

    ()
    (Risk Analysis Research Center, Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan)

  • AKIHIKO TAKAHASHI

    (Graduate School of Economics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8654, Japan)

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    Abstract

    This paper studies the probability distribution and option pricing for drawdown in a stochastic volatility environment. Their analytical approximation formulas are derived by the application of a singular perturbation method (Fouque et al., 2000). The mathematical validity of the approximation is also proven. Then, numerical examples show that the instantaneous correlation between the asset value and the volatility state crucially affects the probability distribution and option prices for drawdown.

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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): 13 (2010)
    Issue (Month): 02 ()
    Pages: 335-354

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    Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:02:p:335-354

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    Related research

    Keywords: Drawdown; stochastic voaltility; singular perturbation;

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    Cited by:
    1. Akihiko Takahashi & Masashi Toda, 2012. "Note on an Extension of an Asymptotic Expansion Scheme," CIRJE F-Series CIRJE-F-860, CIRJE, Faculty of Economics, University of Tokyo.

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