A fourth-order RBF-FD scheme based on integral representations of the multiquadric for high-dimensional Black–Scholes PDEs

The valuation of multi-asset European options poses major challenges due to the curse of dimensionality. We present a fourth-order meshless radial basis function-produced finite difference (RBF-FD) approach based on a modified multiquadric kernel and its integral representations. This construction yields analytical differentiation weights on specific five-point stencils and enables efficient spatial discretization. Numerical experiments confirm the method’s stability, efficiency and convergence.