  We propose two localized Radial Basis Function (RBF) methods, the Radial
Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis
Function generated Finite Differences method (RBF-FD), for solving financial
derivative pricing problems arising from market models with multiple stochastic
factors. We demonstrate the useful features of the proposed methods, such as
high accuracy, sparsity of the differentiation matrices, mesh-free nature and
multi-dimensional extendability, and show how to apply these methods for
solving time-dependent higher-dimensional PDEs in finance. We test these
methods on several problems that incorporate stochastic asset, volatility, and
interest rate dynamics by conducting numerical experiments. The results
illustrate the capability of both methods to solve the problems to a sufficient
accuracy within reasonable time. Both methods exhibit similar orders of
convergence, which can be further improved by a more elaborate choice of the
method parameters. Finally, we discuss the parallelization potentials of the
proposed methods and report the speedup on the example of RBF-FD.
