Pricing American Options on Foreign Assets in a Stochastic Interest Rate Economy

This paper values American options on foreign assets in a stochastic interest rate economy using a two-point Geske and Johnson (1984) technique. The method requires the valuation of just two options: a European option and a twice-exercisable option. I first derive the risk-neutral distributions of asset prices under two forward risk-adjusted measures. Closed form solutions for European options on foreign assets are then obtained by applying these risk-neutral distributions. This article also provides analytic solutions for pricing twice exercisable options that are at most two-dimensional even though the valuation problem involves four risk factors at two exercise dates. I report the results of numerical evaluations of American option values using my method and show how they vary with the interest rate parameters. I also verify the accuracy of the proposed method by comparing with the benchmark values obtained from the least-square method of Longstaff and Schwartz (2001).