%0 Journal Article
%T An effective algorithm to solve option pricing problems
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Moradipour, Mojtaba
%D 2021
%\ 05/01/2021
%V 12
%N 1
%P 261-271
%! An effective algorithm to solve option pricing problems
%K American options
%K variational inequalities
%K linear complementarity problems
%R 10.22075/ijnaa.2021.4782
%X 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 $O(2^m m^3)$ 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.
%U https://ijnaa.semnan.ac.ir/article_4782_59c7fd62925d15df4f6446ccf405aa46.pdf