A novel local meshless scheme based on the radial basis function for pricing multi-asset options

Abstract

‎A novel local meshless scheme based on the radial basis function (RBF) is introduced in this article for price multi-asset options of even European and American types based on the Black-Scholes model‎. ‎The proposed approach is obtained by using operator splitting and repeating the schemes of Richardson extrapolation in the time direction and coupling the RBF technology with a finite-difference (FD) method that leads to extremely sparse matrices in the spatial direction‎. ‎Therefore‎, ‎it is free of the ill-conditioned difficulties that are typical of the standard RBF approximation‎. ‎We have used a strong iterative idea named the stabilized Bi-conjugate gradient process (BiCGSTAB) to solve highly sparse systems raised by the new approach‎. ‎Moreover‎, ‎based on a review performed in the current study‎, ‎the presented scheme is unconditionally stable in the case of independent assets when spatial discretization nodes are equispaced‎. ‎As seen in numerical experiments‎, ‎it has a low computational cost and generates higher accuracy‎. ‎Finally‎, ‎the proposed local RBF scheme is very versatile so that it can be used easily for Solving numerous models and obstacles not just in the finance sector‎, ‎as well as in other fields of engineering and science‎. ‎Finally‎, ‎we conclude that the proposed local RBF scheme is very versatile so that it can be used easily for Solving numerous models and obstacles not just in the finance sector‎, ‎as well as in other fields of engineering and science‎.