Properties of the Integral Equation Arising in the Valuation of American Options

Abstract

Kim (1990), Jacka (1991), and Carr, Jarrow, and Myneni (1992) showed that American option price is equal to the corresponding European option price plus an integral representing the early exercise premium. While the American option price has an explicit representation, the optimal exercise boundary is implicitly defined by a nonlinear integral equation. This article studies the properties of integral equations arising in the valuation of American options. Based on the properties of integral equations, this article also presents a series of closed form upper bounds for the optimal exercise boundary.