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 Applied Finance", Vol.11-4,pp.381-401. )

Akihiko Takahashi and Kohta Takehara
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Akihiko Takahashi: Faculty of Economics, University of Tokyo
Kohta Takehara: Graduate School of Economics, University of Tokyo

No CARF-F-097, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The 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.

Pages: 32 pages
Date: 2007-05
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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf097

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