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