This article develops an efficient and accurate method for numerical evaluation of the integral equation which defines the American put option value function. Numerical integration using Gaussian quadrature and function approximation using Chebyshev polynomials are combined to evaluate recursive expectations and produce an approximation of the option value function in two dimensions, across stock prices and over time to maturity. A set of such solutions results in a multidimensional approximation that is extremely accurate and very quick to compute. The method is an effective alternative to finite difference methods, the binomial model, and various analytic approximations.

Journal Article Valuing American Put Options Using Gaussian Quadrature Get access Michael A. Sullivan Michael A. Sullivan Office of the Comptroller of the Currency Address correspondence to Michael A. Sullivan, Office of the Comptroller of the Currency, 250 E. St. SW, Washington, DC 20219, or e-mail:[email protected]. Search for other works by this author on: Oxford Academic Google Scholar The Review of Financial Studies, Volume 13, Issue 1, January 2000, Pages 75–94, https://doi.org/10.1093/rfs/13.1.75 Published: 15 June 2015