1. The opposite of the American option is the European-style option.

2. Turning its back in the face of such challenges is no longer a viable American option.

3. This article is an outgrowth of an earlier article titled “Bounds and Approximations for American Option Values.” It has been presented at CERCA (Center for Research on Computation and its Applications), the Workshop on Mathematical Finance at Columbia University, the Financial Mathematics Program at the University of Cambridge, and the 1995 Western Finance Association meetings.