A greedy algorithm for partition of unity collocation method in pricing American options

Abstract

A greedy algorithm in combination with radial basis functions partition of unity collocation (GRBF-PUC) scheme is used as a locally meshless method for American option pricing. The radial basis function partition of unity method (RBF-PUM) is a localization technique. Because of having interpolation matrices with large condition numbers, global approximants and some local ones suffer from instability. To overcome this, a greedy algorithm is added to RBF-PUM. The greedy algorithm furnishes a subset of best nodes among the points X. Such nodes are then used as points of trial in a locally supported RBF approximant for each partition. Using of greedy selected points leads to decreasing the condition number of interpolation matrices and reducing the burdensome in pricing American options.