Differential quadrature method for pricing American options

In this article, differential quadrature method (DQM), a highly accurate and efficient numerical method for solving nonlinear problems, is used to overcome the difficulty in determining the optimal exercise boundary of American option. The following three parts of the problem in pricing American options are solved. The first part is how to treat the uncertainty of the early exercise boundary, or free boundary in the language of the PDE treatment of the American option, because American options can be exercised before the date of expiration. The second part is how to solve the nonlinear problem, because the problem of pricing American options is nonlinear. And the third part is how to treat the initial value condition with the singularity and the boundary conditions in the DQM. Numerical results for the free boundary of American option obtained by both DQM and finite difference method (FDM) are given and from which it can be seen the computational efficiency is greatly improved by DQM. (C) 2002 Wiley Periodicals, Inc.