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In this paper, we study the benefits of using polyharmonic splines and nodelayouts with smoothly varying density for developing robust and efficientradial basis function generated finite difference (RBF-FD) methods for pricingof financial derivatives. We present a significantly improved RBF-FD scheme andsuccessfully apply it to two types of multidimensional partial differentialequations in finance: a two-asset European call basket option under theBlack--Scholes--Merton model, and a European call option under the Hestonmodel. We also show that the performance of the improved method is equally highwhen it comes to pricing American options. By studying convergence,computational performance, and conditioning of the discrete systems, we showthe superiority of the introduced approaches over previously used versions ofthe RBF-FD method in financial applications.

Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts