American Option Pricing by the Finite Difference Method

For the special, but important, case of American option pricing, practitioners often find that otherwise well-functioning finite difference methods yield results that are slower, less accurate, and less stable than expected. Perhaps, as a consequence, simpler special purpose methods (e.g., the binomial tree) are sometimes preferred for American options, despite various theoretical and practical drawbacks. In this paper, the authors show how to remedy this situation, through a range of minimally invasive "tips and tricks" that significantly improve the speed and stability of the popular theta-method finite difference scheme when applied to American option values and greeks.