American Options

Abstract

Chapter 5 is concerned with the pricing of American options. We present the characterization of the optimal exercise boundary associated with the American option models. In particular, we examine the behavior of the exercise boundary before and after a discrete dividend payment, and immediately prior to expiry. The two common pricing formulations of the American options, the linear complementarity formulation and the optimal stopping formulation, are discussed. We show how to express the early exercise premium in terms of the exercise boundary in the form of an integral representation. Since analytic price formulas are in general not available for American options, we present several analytic approximation methods for pricing American options. We also consider the pricing models for the American barrier options, the Russian option and the reset-strike options.