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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Kyo Yamamoto & Seisho Sato & Akihiko Takahashi, 2010. "Probability Distribution And Option Pricing For Drawdown In A Stochastic Volatility Environment," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 335-354.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:02:n:s0219024910005796
    DOI: 10.1142/S0219024910005796
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    Citations

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    Cited by:

    1. Akihiko Takahashi & Masashi Toda, 2013. "Note on an Extension of an Asymptotic Expansion Scheme," CARF F-Series CARF-F-312, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    3. Akihiko Takahashi & Yukihiro Tsuzuki, 2013. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CIRJE F-Series CIRJE-F-874, CIRJE, Faculty of Economics, University of Tokyo.
    4. Akihiko Takahashi & Masashi Toda, 2012. "Note on an Extension of an Asymptotic Expansion Scheme," CARF F-Series CARF-F-286, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Dec 2012.
    5. Akihiko Takahashi & Yukihiro Tsuzuki, 2013. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-305, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. 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.
    7. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.

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