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Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment ( Revised in May 2009; Electronic version of an article will be published in "International Journal of Theoretical and Applied Finance". [copyright world Scientific Publishing Company][http://www.worldscinet.com/ijtaf/] )

Author

Listed:
  • Kyo Yamamoto

    (Graduate School of Economics, University of Tokyo)

  • Seisho Sato

    (Institute of Statistical Mathematics)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

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. [7]). 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.

Suggested Citation

  • Kyo Yamamoto & Seisho Sato & Akihiko Takahashi, 2008. "Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment ( Revised in May 2009; Electronic version of an article will be published in "International Journal," CARF F-Series CARF-F-138, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf138
    as

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    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/143.pdf
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    References listed on IDEAS

    as
    1. Alexei Chekhlov & Stanislav Uryasev & Michael Zabarankin, 2005. "Drawdown Measure In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 13-58.
    2. Raphaël Douady & A.N. Shiryaev & Marc Yor, 2000. "On Probability Characteristics of "Downfalls" in a Standard Brownian Motion," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01477104, HAL.
    3. Kyo Yamamoto & Akihiko Takahashi, 2008. "A Remark on a Singular Perturbation Method for Option Pricing under a Stochastic Volatility," CIRJE F-Series CIRJE-F-597, CIRJE, Faculty of Economics, University of Tokyo.
    4. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    Full references (including those not matched with items on IDEAS)

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