Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212120210501An effective algorithm to solve option pricing problems261271478210.22075/ijnaa.2021.4782ENMojtaba MoradipourDepartment of Mathematics, Lorestan University, Khorramabad, IranJournal Article20200818We 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.https://ijnaa.semnan.ac.ir/article_4782_59c7fd62925d15df4f6446ccf405aa46.pdf