FOURIER TRANSFORM METHOD WITH AN ASYMPTOTIC EXPANSION APPROACH: AN APPLICATION TO CURRENCY OPTIONS

Akihiko Takahashi () and Kohta Takehara
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Akihiko Takahashi: Graduate School of Economics, The University of Tokyo, Bunkyo-ku, Hongo 7-3-1, Tokyo 113-8654, Japan
Kohta Takehara: Graduate School of Economics, The University of Tokyo, Bunkyo-ku, Hongo 7-3-1, Tokyo 113-8654, Japan

International Journal of Theoretical and Applied Finance (IJTAF), 2008, vol. 11, issue 04, 381-401

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 [7]/Bates [1] and log-normal market models for domestic and foreign interest rates. Finally, the validity of our method is confirmed through numerical examples.

Keywords: Currency option; libor market model; stochastic volatility; asymptotic expansion; Fourier transform (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (12)

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DOI: 10.1142/S0219024908004853

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