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On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis

Author

Listed:
  • Naoto Kunitomo

    (Faculty of Economics, University of Tokyo.)

  • Akihiko Takahashi

Abstract

Kunitomo and Takahashi (1995), and Takahashi (1997) have proposed a new methodology, called Small Disturbance Asymptotics, for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Ito processes. It can be applicable to a wide range of valuation problems including complicated contingent claims associated with the Black-Scholes model and the term structure model of interest rates in the Heath-Jarrow-Morton framework. Our approach can be rigorously justified by an infinite dimensional analysis called the Watanabe-Yoshida theory on the Malliavin Calculus recently developed in stochastic analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:98f06
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Akihiko Takahashi & Nakahiro Yoshida, 2003. "An Asymptotic Expansion Scheme for the Optimal Investment Problems," CIRJE F-Series CIRJE-F-248, CIRJE, Faculty of Economics, University of Tokyo.
    4. 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.
    5. 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.
    6. Yoshida, Nakahiro, 2003. "Conditional expansions and their applications," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 53-81, September.

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