Evaluating American-Style Call Option Prices Based on Constrained Least-Squares

Computing the current value of an American call option requires solving the BlackScholes PDE. The asset may be exercised at any time before its expiration date. The numerical computation involves solving this free boundary problem. A finite difference approximation leads to a linear complementarity problem with a tridiagonal matrix. What is new in this paper is an efficient technique for solving a related quadratic programming problem. This development is based on a non-negative constrained least-squares (NNLS) algorithm. Three examples are given, including graphics illustrating the solutions. Introduction We are interested in the pricing of an American call option. Generalizing what is given in [1, p. 121], the parabolic differential equation (Black-Scholes) for the value of a call option is given by c s c r D sc rc t ss s + + − − =