A New Stable Local Radial Basis Function Approach for Option Pricing

In this paper, we develop a new local meshless approach based on radial basis functions (RBFs) to solve the Black–Scholes equation. The global RBF approximations derived from conventional global collocation method usually lead to ill-conditioned matrices. The new scheme employs the idea of the finite difference method to localize them. It removes the difficulty of ill-conditioning of the original method. The new proposed approach is unconditionally stable as it is shown by Von-Neumann stability analysis. As well as it is fast and it produces accurate results as shown in numerical experiments.