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 r ͫ . 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(2 ͫ m³) 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.