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An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates

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Abstract

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for pricing currency options based on a third order asymptotic expansion scheme; we do not model a foreign exchange rate’s variance such as in Heston [(1993) The Review of Financial studies, 6, 327–343], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. Finally, numerical examples are provided and the pricing formula are applied to the calibration of volatility surfaces in the JPY/USD option market.

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Authors and Affiliations

  1. Graduate School of Economics, University of Tokyo, Bunkyo-ku, Hongo 7-3-1, Tokyo, 113-8654, Japan

    Akihiko Takahashi & Kohta Takehara

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  1. Akihiko Takahashi
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  2. Kohta Takehara
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Correspondence to Akihiko Takahashi.

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Takahashi, A., Takehara, K. An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates. Asia-Pacific Finan Markets 14, 69–121 (2007). https://doi.org/10.1007/s10690-007-9054-9

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