The purpose of this paper is to compare a variety of approximation techniques for valuing contingent contracts when analytic solutions do not exist. The comparison is made with respect to the differences in both the approximation theory and the efficiency of the com- putation algorithms. The focus of the computational comparison is upon binomial and finite difference methods applied to option valuation models with one stochastic variable. However, many ofthe results would generalize to pricing corporate securities, and also to certain aspects of problems involving multiple stochastic variables.