An effective algorithm to solve option pricing problems

We are aimed to develop a fast and direct algorithm to solve linear complementarity problems (LCP's) arising from option pricing problems. We discretize the free boundary problem of American options in temporal direction and obtain a sequence of linear complementarity problems (LCP's) in the finite dimensional Euclidian space Rm. We develop a fast and direct algorithm based on the active set strategy to solve the LCP's. The active set strategy in general needs O(2mm3) operations to solve m dimensional LCP's. Using Thomas algorithm, we develop an algorithm with order of complexity O(m) which can extremely speed up the computations.