A Concise Approximation for the Early Exercise Boundary of American Options (Financial Modeling and Analysis)

Abstract

This paper provides a concise approximation for the early exercise boundary (EEB) of an American option written on dividend-paying assets. Although a vast majority of traded options are of American-style optimally exercised before maturity, there are no explicit formulas for their prices as well as EEBs even in the standard model called vanilla. A closed-form EEB approximation is especially important in decision-making on optimal early exercise. Following a simple but indefinite idea of Carr et al. (1992) based on van Moerbeke (1976), we focus on a class of interpolation approximations with a square-root exponential weight. The unsettled problem there was how to determine the exponential decay rate. Applying the Laplace-Carson transform approach to this problem, we derive an explicit decay rate of the exponential weight to develop a pair of new EEB approximations for vanilla put/call options, both of which are consistent with the principal boundary features.