A Numerically Efficient Valuation Method for American Currency Options with Stochastic Interest Rates

Abstract

This paper extends Ho, Stapleton, and Subrahmanyam's (1997a) generalized Geske-Johnson (1984) technique to price American currency options in a stochastic interest rate economy. We derive closed form solutions for European currency options and analytical form solutions for twice-exercisable currency options assuming that the volatility functions determining the term structure are deterministic. The two-point Geske and Johnson (1984) approximation formula is then applied to estimate American option prices. Numerical evaluations and comparative statics are presented to show the effect of stochastic interest rates. Although the model in this article is a special case of Amin and Bodurtha's (1995) general model, our numerical results are similar to theirs yet our method is numerically efficient.