A Simple Iterative Method for the Valuation of American Options

Abstract

We introduce a simple iterative method to determine the optimal exercise boundary for American options, allowing us to compute the values of American options and their Greeks quickly and accurately. Following Little, Pant and Hou's idea (2000), we derive a new equation for the optimal exercise boundary containing a single integral. The proposed method is an iterative numerical method for finding its solution. Using it, we can calculate the entire optimal exercise boundary in a non-time-recursive way, in contrast to conventional methods. Extensive numerical results indicate that our method is computationally more efficient than the methods currently available, particularly for hedge ratios.