A Simple Iterative Method for the Valuation of American Options
Forthcoming, Quantitative Finance
Posted: 28 Apr 2006 Last revised: 22 May 2012
Date Written: January 15, 2012
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 (2000) idea, 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, while conventional methods do not. Extensive numerical results indicate that our method is computationally more efficient than the methods currently available, particularly when finding hedge ratios.
Keywords: American option, iteration, exercise boundary, early exercise premium, numerical method
JEL Classification: C63, G13
Suggested Citation: Suggested Citation