Option valuation by using discrete singular convolution

This paper explores the utility of a discrete singular convolution (DSC) algorithm for solving the Black-Scholes equation. Both European and American style options, which include all nontrivial plain option pricing problems, are considered to test the accuracy and to examine the efficiency of the present algorithm. Adaptive meshes are constructed to enhance the performance of the DSC algorithm. All the present results are validated either by the analytical solution or by the standard binomial tree method. Extensive comparisons are carried out with two standard finite difference schemes and two binomial models of high speed convergence. Numerical experiments reveal that the present approach is accurate, efficient and reliable for financial derivative valuations.