In this chapter, we deal with derivative securities related to at least two economies (a domestic market and a foreign market, say). Any such security will be referred to as a cross-currency derivative. In contrast to the model examined in Chap. 4, all interest rates and exchange rates are assumed to be random. It seems natural to expect that the fluctuations of interest rates and exchange rates will be highly correlated. This feature should be reflected in the valuation and hedging of foreign and cross-currency derivative securities in the domestic market. Feiger and Jacquillat (1979) (see also Grabbe (1983)) were probably the first to study, in a systematic way, the valuation of currency options within the framework of stochastic interest rates (they do not provide a closed-form solution for the price, however). More recently, Amin and Jarrow (1991) extended the HJM approach by incorporating foreign economies. Frachot (1995) examined a special case of the HJM model with stochastic volatilities, in which the bond price and the exchange rate are assumed to be deterministic functions of a single state variable.
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