IDEAS home Printed from
   My bibliography  Save this paper

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)


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

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276.
    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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2009cf625. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.