Valuation of Option Pricing with Meshless Radial Basis Functions Approximation

Abstract

This work focuses on valuation scheme of European and American options of single asset with meshless radial basis approximations. The prices are governed by Black – Scholes equations. The option price is approximated with three infinitely smooth positive definite radial basis functions (RBFs), namely, Gaussian (GA), Multiquadrics (MQ), Inverse Multiquadrics (IMQ). The RBFs were used for discretizing the space variables while Runge-Kutta method was used as a time-stepping marching method to integrate the resulting systems of differential equations. Numerical examples are shown to illustrate the strength of the method developed. The findings show that the RBFs has proven to be adaptable interpolation method because it does not depend on the locations of the approximation nodes which have overcome frequently evolving problems in computational finance such as slow convergent numerical solutions. Thus, the results allow concluding that the RBF-FD-GA and RBF-FD-MQ methods are well suited for modeling and analyzing Black and Scholes equation.