Valuing American put options using Gaussian quadrature

This article develops an efficient and accurate method for numerical evalua tion of the integral equation which defines the American put option value f unction. Numerical integration using Gaussian quadrature and function appro ximation using Chebyshev polynomials are combined to evaluate recursive exp ectations and produce an approximation of the option value function in two dimensions, across stock prices and over time to maturity. A set of such so lutions results in a multidimensional approximation that is extremely accur ate and very quick to compute. The method is an effective alternative to fi nite difference methods, the binomial model, and various analytic approxima tions.