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

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  • 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, 2008. "Fourier Transform Method with an Asymptotic Expansion Approach: an Application to Currency Options," CIRJE F-Series CIRJE-F-538, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2008cf538
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    References listed on IDEAS

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    1. Takao Kobayashi & Akihiko Takahashi & Norio Tokioka, 2001. "Dynamic Optimality of Yield Curve Strategies," CIRJE F-Series CIRJE-F-141, CIRJE, Faculty of Economics, University of Tokyo.
    2. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    3. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    4. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
    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. Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), 2004. "Stochastic Processes and Applications to Mathematical Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5487.
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