Efficient procedures for the valuation and hedging of American currency options with stochastic interest rates

Abstract

We develop a discrete time model to value currency options in which domestic interest rate risk, foreign interest rate risk, and currency risk are important. This model extends the Geske-Johnson (Geske, R., Johnson, 1984. ‘The American put valued analytically’, J. Finance, 39, December, 1511–1542) approach to a stochastic interest rate economy. We implement our method using only the values of once and twice exercisable options and report the results of the stochastic interest rate effects on the option values. Hence, our method provides an efficient procedure to value currency options with stochastic interest rates. In particular, it can be used to compute the values of the currency option with long-term maturity to a high degree of accuracy. Further, we also develop a simple forward hedging strategy, which can be implemented to hedge the risk from writing both the European and American currency options with stochastic interest rates. From the simulation results, we show that the interest rate risks have significant effects on the values of American currency options with long-term maturity. We also show that the hedging performance of our forward hedging strategy is significantly better than the other hedging strategy without hedging interest rate risks.