A Numerical Approach to American Currency Option Valuation

Abstract

Option theory has produced models of increasing richness that are capable of incorporating many sources of randomness (“stochastic state variables,” as theorists would say). For interest rate dependent instruments, the highly flexible Heath-Jarrow-Morton (HJM) family provides some of the most widely used models. However, implementation of HJM models typically runs into serious computational problems as the number of state variables increases. Pricing a currency option, for example, requires at least three state variables, one for each country's interest rate and one for the exchange rate. American exercise makes the problem harder still. In this article, Choi and Marcozzi describe a numerical technique based on approximating the option value with radial basis functions that offers considerable efficiency improvement. They illustrate its use on HJM-style currency options. One large advantage of this approach is that the approximating functions are analytic, so that the Greek letter risk exposures can be obtained directly using calculus rather than requiring multiple runs through a pricing lattice to approximate them.