Collocation Methods for Pricing American Strangle Options

The aim of this paper is to develop high-order collocation methods for pricing American strangle options. The major difficulty in pricing American strangles is to determine the optimal exercise boundaries. Chiarella and Ziogas (2005) derived that the optimal exercise boundaries satisfy a system of integral equations. Since the analytical solutions of the integral equation system cannot be found, it relies on numerical methods to solve the integral equation system. In the literature, there are no efficient and reliable numerical methods for solving the integral equation system. This paper develops a high-order collocation method to solve the integral equation system. Numerical example is carried out to show that the collocation methods are much more reliable and efficient.