An efficient radial basis function generated finite difference meshfree scheme to price multi-dimensional PDEs in financial options

Abstract

In this paper, the purpose is to focus on proposing a new solver for pricing financial option at the presence of several assets. Toward this goal, first we introduce the weighting coefficients of the radial basis function-finite difference (RBF-FD) procedure for approximating the derivatives of the functions under the inverse multi-quadric function (IMQ). The weights are employed on a nonuniform mesh of points when tackling multi-dimensional partial differential equations (PDEs). A new solver based on RBF-FD methodology is then constructed employing matrix notations for solving option pricing problems. The theoretical discussions will be confirmed via numerical experiments on several test problems consisting of four to five underlying assets.