An Improved Singularity Separating Method For American Option Pricing

Closed form solutions for pricing American options are difficult to obtain and the design of an efficient and accurate numerical pricing algorithm remains a topic of considerable interest among researchers. The Amercian option pricing problem can be posed as a free boundary value problem. The formulations has led to a number of different methodogies for solving American optionsIn this paper, we describe a finite difference algorithm for the American options problem. Some researcher used a singularity separating method which computes the difference between an Amercian option and a European option. Since both options satisfy the linear Balck-Scholes equation, the difference will also satisfy the transformed heat equation and with the American and European payoffs being similar, the initial condition for the difference will be zero. At the same time, because the common practisce is to choose the computational domain large enough that the error introduced by applying far fidld boundary conditions at extremity isnegligible. This results in quantities of useless computations since many of the grid points are not of interest. And a method for locating the free boundary based on some properties of the Black-Scholes PDE has be found.Our proposed finite difference algorithm for pricing American options will combine these two approches. Computational results show that our algorithm is more accurate than both of the original methods.To assess the accuracy of all methods, we use the binomial method with large steps for the option prices.