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Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment

Author

Listed:
  • Kyo Yamamoto

    (Graduate School of Economics, University of Tokyo)

  • Seisho Sato

    (Department of Prediction and Control, 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, 2009. "Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-625, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2009cf625
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2009/2009cf625.pdf
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Kyo Yamamoto & Akihiko Takahashi, 2009. "A Remark on a Singular Perturbation Method for Option Pricing Under a Stochastic Volatility Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(4), pages 333-345, December.

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