Valuing American put options using Gaussian quadrature

This article develops an efficient and accurate method for numericalevaluation of the integral equation which defines the Americanput option value function. Numerical integration using Gaussianquadrature and function approximation using Chebyshev polynomialsare combined to evaluate recursive expectations and producean approximation of the option value function in two dimensions,across stock prices and over time to maturity. A set of suchsolutions results in a multidimensional approximation that isextremely accurate and very quick to compute. The method isan effective alternative to finite difference methods, the binomialmodel, and various analytic approximations.