Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach

An increasingly popular and promising approach to solve option pricing models is the use of numerical methods based on radial basis functions (RBF). These techniques yield high levels of accuracy, but have the drawback of requiring the inversion of large full system matrices. In the present paper, by combining Gaussian radial basis functions with a suitable operator splitting scheme, a new RBF method is developed in which the inversion of large system matrices is avoided. The method proposed is applied to five different problems which concern the pricing of European and American options under both the Black-Scholes and the Heston models. The results obtained reveal that the novel RBF scheme is accurate and fast, and performs fairly better than the finite difference approach. Finally, the RBF method proposed is very versatile, and, just like finite difference schemes, can be used to solve an infinite variety of models and problems, not only in the finance area but also in other fields of science and engineering.