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Effects Of Stochastic Interest Rates And Volatility On Contingent Claims

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  • NAOTO KUNITOMO
  • YONG‐JIN KIM

Abstract

We investigate the effects of stochastic interest rates and the volatility of the underlying asset price on contingent claim prices including futures and options prices. The futures price can be decomposed into the forward price and an additional term; the options price can be decomposed into the Black‐Scholes formula and several additional terms by applying the asymptotic expansion approach of the small disturbance asymptotics developed by Kunitomo and Takahashi (1995, 1998, 2001, 2003a, 2003b). The technical method is based on a new application of the Malliavin‐Watanabe Calculus or the Watanabe‐Yoshida Theory on Malliavin Calculus in stochastic analysis. We illustrate our new formulae and their numerical accuracy.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jecrev:v:58:y:2007:i:1:p:71-106
    DOI: 10.1111/j.1468-5876.2007.00345.x
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    Cited by:

    1. Akihiko Takahashi & Kohta Takehara, 2008. "A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options ( Revised in April 2008, January 2009 and April 2010; forthcoming in "International Journal of Theoretical and A," CARF F-Series CARF-F-116, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Akihiko Takahashi & Kohta Takehara, 2010. "A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options," CIRJE F-Series CIRJE-F-734, CIRJE, Faculty of Economics, University of Tokyo.
    3. Akihiko Takahashi & Kohta Takehara, 2009. "Asymptotic Expansion Approaches in Finance: Applications to Currency Options," CARF F-Series CARF-F-165, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Akihiko Takahashi & Kohta Takehara, 2007. "An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(1), pages 69-121, March.
    5. Akihiko Takahashi & Kohta Takehara, 2009. "Asymptotic Expansion Approaches in Finance: Applications to Currency Options," CIRJE F-Series CIRJE-F-654, CIRJE, Faculty of Economics, University of Tokyo.
    6. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    7. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CARF F-Series CARF-F-149, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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