Pricing American currency options in an exponential Lvi model,

In this article the problem of the American option valuation in a L´vy process setting is analyzed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps inthe call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying processat the exercise boundary (i.e. with positive jumps in the call case), original results are derived byrelying on first passage time and overshoot associated with a Levy process. For finite life American currency calls, the formula derived by Bates (1991) or Zhang (1995), in the context of a negative jump size, is tested. It is basically an extension of the one developed by Mac Millan (1987) and extended by Barone-Adesi and Whaley (1987). It is shown that Bates’ (1991) model generatespretty good results only when the process is continuous at the exercise boundary.