Evaluation of Financial Options Using Radial Basis Functions in Mathematica

In the academic literature there are two common approaches for the evaluation of financial options. These are stochastic calculus and partial differential equations. The former is the method of choice for statisticians and theoreticians, while the latter is the principal tool of physicists and computer scientists because it lends itself to practical implementation schemes. Occasionally small modifications such as linear regression and binomial trees are used, but these are usually treated within either of the two previously mentioned fields. Rarely do the practitioners of these fields compare and contrast methodologies, let alone admit completely different approaches. While Radial Basis Function (RBF) methodology has previously been applied to solving some differential equations, there are very few papers considering its applicability to financial mathematics. The purpose of this article is to show not only that RBF can solve many of the evaluation problems for financial options, but that with Mathematica it can do so with accuracy and speed.