Inverse multi-quadric RBF for computing the weights of FD method: Application to American options

Abstract

In this paper, we derive new exact formulas for the weights of the first and second derivatives using the radial basis function (RBF) generated by finite difference (FD) method. The considered radial function is the inverse multi-quadric (IMQ) function. Using these formulas, we compute Taylor expansions for the errors and also to construct stable approximations for fast implementations. The application of the new formulas is given in the framework of an RBF-FD method for pricing American option which has no exact solution. The discussed results are corroborated by computational experiments.