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Applications of the Asymptotic Expansion Approach based on Malliavin-Watanabe Calculus in Financial Problems

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Listed:
  • Naoto Kunitomo

    (Faculty of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Graduate School of Mathematical Sciences and Economics, University of Tokyo)

Abstract

This paper reviews the asymptotic expansion approach based on Malliavin-Watanabe Calculus in Mathematical Finance. We give the basic formulation of the asymptotic expansion approach and discuss its power and usefulness to solve important problems arised in nance. As illustrations we use three major problems in nance and give some useful formulae and new results including numerical analyses.

Suggested Citation

  • Naoto Kunitomo & Akihiko Takahashi, 2003. "Applications of the Asymptotic Expansion Approach based on Malliavin-Watanabe Calculus in Financial Problems," CIRJE F-Series CIRJE-F-245, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2003cf245
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2003/2003cf245.pdf
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    References listed on IDEAS

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    1. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    2. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    3. Akihiko Takahashi & Nakahiro Yoshida, 2003. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-249, CIRJE, Faculty of Economics, University of Tokyo.
    4. Yong-Jin Kim & Naoto Kunitomo, 1999. "Pricing Options under Stochastic Interest Rates: A New Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 6(1), pages 49-70, January.
    5. Yoshifumi Muroi, 2005. "Pricing contingent claims with credit risk: Asymptotic expansion approach," Finance and Stochastics, Springer, vol. 9(3), pages 415-427, July.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Naoto Kunitomo & Akihiko Takahashi, 1998. "On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis," CIRJE F-Series 98-F-6, CIRJE, Faculty of Economics, University of Tokyo.
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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. Naoto Kunitomo & Yong‐Jin Kim, 2007. "Effects Of Stochastic Interest Rates And Volatility On Contingent Claims," The Japanese Economic Review, Japanese Economic Association, vol. 58(1), pages 71-106, March.
    3. Naoto Kunitomo & Yong-Jin Kim, 2001. "Effects of Stochastic Interest Rates and Volatility on Contingent Claims (Revised Version)," CIRJE F-Series CIRJE-F-129, CIRJE, Faculty of Economics, University of Tokyo.
    4. 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.

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