Improved numerical solution of multi-asset option pricing problem: A localized RBF-FD approach

Abstract The objective of this work is to present a novel procedure for tackling European multi-asset option problems, which are modeled mathematically in terms of time-dependent parabolic partial differential equations with variable coefficients. To use as low as possible of number computational grid points, a non-uniform grid is generated while a radial basis function-finite difference scheme with the Gaussian function is applied on such a grid to discretize the model as efficiently as possible. To reduce the burdensome for tackling the resulting set of ordinary differential equations, a Krylov method, which is due to the application of exponential matrix function on a vector, is taken into account. The combination of these techniques reduces the computational effort and the elapsed time. Several experiments are brought froward to illustrate the superiority of the new improved approach. In fact, the contributed procedure is capable to tackle even 6D PDEs on a normally-equipped computer quickly and efficiently.

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