In this repository, we presented the original codes for developing a new local meshless approach (RBF-FD) to solve the Black-Sholes equation in option pricing. The codes are developed in 2014, and we published the results in 2 articles as follows:
- A. Golbabai, E. Mohebianfar, A new method for evaluating options based on multiquadric RBF-FD method, Applied Mathematics and Computation, 308 (2017) 130-141.
- A. Golbabai, E. Mohebianfar, A New Stable Local Radial Basis Function Approach for Option Pricing, Computational Economics, 49 (2017) 271–288.
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 origi- nal 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.
Please refer to above articles for more information.
To use the codes for academic research, please cite via:
