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Asymptotic Expansion Approaches in Finance: Applications to Currency Options


  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Kohta Takehara

    (Graduate School of Economics, University of Tokyo)


This chapter presents a basic of the methodology so-called an asymptotic expansion approach, and applies this method to approximation of prices of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. The scheme enables us to derive closed-form approximation formulas for pricing currency options even with high flexibility of the underlying model; we do not model a foreign exchange rate's variance such as in Heston [27], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. At the end of this chapter some numerical examples are provided and the pricing formula is applied to the calibration of volatility surfaces in the JPY/USD option market.

Suggested Citation

  • 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.
  • Handle: RePEc:tky:fseres:2009cf654

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    References listed on IDEAS

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    6. Kaushik I. Amin & Robert A. Jarrow, 2008. "Pricing foreign currency options under stochastic interest rates," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 14, pages 307-326 World Scientific Publishing Co. Pte. Ltd..
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    11. Sakamoto, Yuji & Yoshida, Nakahiro, 1996. "Expansion of Perturbed Random Variables Based on Generalized Wiener Functionals," Journal of Multivariate Analysis, Elsevier, vol. 59(1), pages 34-59, October.
    12. Amin, Kaushik I & Bodurtha, James N, Jr, 1995. "Discrete-Time Valuation of American Options with Stochastic Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 193-234.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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