This chapter presents a basic of the methodology so-called an asymptotic expansion
approach, and applies this method to approximation of prices of currency options with
a libor market model of interest rates and stochastic volatility models of spot exchange
rates. The scheme enables us to derive closed-form approximation formulas for pricing
currency options even with high flexibility of the underlying model; we do not model
a foreign exchange rate's variance such as in Heston [27], 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. At the end of this chapter some numerical examples are
provided and the pricing formula is applied to the calibration of volatility surfaces in
the JPY/USD option market.
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