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Fourier Transform Method with an Asymptotic Expansion Approach: an Application to Currency Options

Author

Listed:
  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Kohta Takehara

    (Graduate School of Economics, University of Tokyo)

Abstract

This paper develops a Fourier transform method with an asymptotic expansion approach for option pricing. The method is applied to European currency options with a libor market model of interest rates and jump-diffusion stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas of the characteristic functions of log-prices of the underlying assets and the prices of currency options based on a third order asymptotic expansion scheme; we use a jump-diffusion model with a mean-reverting stochastic variance process such as in Heston[1993]/Bates[1996] and log-normal market models for domestic and foreign interest rates. Finally, the validity of our method is confirmed through numerical examples.

Suggested Citation

  • Akihiko Takahashi & Kohta Takehara, 2007. "Fourier Transform Method with an Asymptotic Expansion Approach: an Application to Currency Options," CIRJE F-Series CIRJE-F-497, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2007cf497
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    Cited by:

    1. 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.

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