A new method for evaluating options based on multiquadric RBF-FD method

In this paper, a new local meshless approach based on radial basis functions (RBFs) is presented to price the options under the Black-Scholes model. The global RBF approximations derived from the conventional global collocation method usually lead to ill-conditioned matrices. Employing the idea of local approximants of the finite difference (FD) method and combining it with the radial basis function (RBF) method can result in a local meshless approach such as RBF-FD. It removes the difficulty of ill-conditionness of the original method. The new proposed approach is unconditionally stable as it is shown by Von-Neumann stability analysis. It is fast and produces high accurate results as shown in numerical experiments. Moreover, we took into account the variation of shape parameter and analyzed numerically the behavior of the RBF-FD method.