  This paper proposes a numerical method for pricing foreign exchange (FX)
options in a model which deals with stochastic interest rates and stochastic
volatility of the FX rate. The model considers four stochastic drivers, each
represented by an It\^{o}'s diffusion with time--dependent drift, and with a
full matrix of correlations. It is known that prices of FX options in this
model can be found by solving an associated backward partial differential
equation (PDE). However, it contains non--affine terms, which makes its
difficult to solve it analytically. Also, a standard approach of solving it
numerically by using traditional finite--difference (FD) or finite elements
(FE) methods suffers from the high computational burden. Therefore, in this
paper a flavor of a localized radial basis functions (RBFs) method, RBF--FD, is
developed which allows for a good accuracy at a relatively low computational
cost. Results of numerical simulations are presented which demonstrate
efficiency of such an approach in terms of both performance and accuracy for
pricing FX options and computation of the associated Greeks.
