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

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 the third order asymptotic expansion scheme; we do not model a foreign exchange rate's variance such as in Heston[1993], but its volatility that follows a general time-inhomogeneous Markovian process, and we allow the correlations among all the factors, that is domestic and foreign interest rates, a spot foreign exchange rate and its volatility. Finally, we provide numerical examples and apply the pricing formula to the calibration of volatility surfaces in the JPY/USD option market.Revised in August 2007 and January 2009; subsequently published in Asia-Pacific Financial Markets, vol.14, pp.69-121, 2007