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

  • 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)

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    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.

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    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-625.

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    Length: 23 pages
    Date of creation: Jun 2009
    Date of revision:
    Handle: RePEc:tky:fseres:2009cf625
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    1. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276.
    2. 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.
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