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Pricing Currency Options with a Market Model of Interest Rates under Jump-Diffusion Stochastic Volatility Processes of Spot Exchange Rates

Author

Listed:
  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Kota Takehara

    (Graduate School of Economics, University of Tokyo)

  • Akira Yamazaki

    (Mizuho-DL Financial Technology Co., Ltd.)

Abstract

This paper proposes a pricing method of currency options with a market model of interest rates. Using a simple approximation and a Fourier transform method, we derive a formula of the option pricing under jump-diffusion stochastic volatility processes of spot exchange rates. As an application, we apply the formula to the calibration of volatility smiles in the JPY/USD currency option market. Moreover, using the approximate prices as a control variate, we achieve substantial variance reduction in Monte Carlo simulation.

Suggested Citation

  • Akihiko Takahashi & Kota Takehara & Akira Yamazaki, 2006. "Pricing Currency Options with a Market Model of Interest Rates under Jump-Diffusion Stochastic Volatility Processes of Spot Exchange Rates," CARF F-Series CARF-F-082, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf082
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    References listed on IDEAS

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    15. 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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    Cited by:

    1. 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.
    2. 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.
    3. Akihiko Takahashi & Kohta Takehara, 2007. "Fourier Transform Method with an Asymptotic Expansion Approach: an Application to Currency Options ( Revised in December 2008; subsequently published in "International Journal of Theoretical and ," CARF F-Series CARF-F-097, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. 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.
    5. Anatoliy Swishchuk & Maksym Tertychnyi & Robert Elliott, 2014. "Pricing Currency Derivatives with Markov-modulated Levy Dynamics," Papers 1402.1953, arXiv.org.
    6. Akihiko Takahashi & Kohta Takehara, 2008. "Fourier Transform Method With An Asymptotic Expansion Approach: An Application To Currency Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 381-401.
    7. Anatoliy Swishchuk & Maksym Tertychnyi & Winsor Hoang, 2014. "Currency Derivatives Pricing for Markov-modulated Merton Jump-diffusion Spot Forex Rate," Papers 1402.2273, arXiv.org.

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