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

Pricing Derivatives under Multiple Stochastic Factors by Localized Radial Basis Function Methods