Solving multi-dimensional European option pricing problems by integrals of the inverse quadratic radial basis function on non-uniform meshes

Abstract

This paper explores multi-asset options as a means to diversify portfolios, mitigating risk across various assets. We present a numerical method using radial basis function-generated finite difference solvers via integrals of the inverse quadratic kernel. Our method introduces new weights for the task we are dealing with. We derive and compute analytical solutions to approximate function derivatives on three-node stencils with non-uniform and uniform distances. Our findings highlight the convergence order of the proposed analytical weights. Numerical examples illustrate the theory.