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 \mathbb{R}^m‎. ‎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(۲^m m^۳) 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.

کلیدواژه ها:

‎American options‎ ، ‎variational inequalities‎ ، ‎linear complementarity problems‎