On an improved computational solution for the 3D HCIR PDE in finance

Abstract

The aim of this work is to tackle the three-dimensional (3D) Heston-Cox-Ingersoll-Ross (HCIR) time-dependent partial differential equation (PDE) computationally by employing a non-uniform discretization and gathering the finite difference (FD) weighting coefficients into differentiation matrices. In fact, a non-uniform discretization of the 3D computational domain is employed to achieve the second-order of accuracy for all the spatial variables. It is contributed that under what conditions the proposed procedure is stable. This stability bound is novel in literature for solving this model. Several financial experiments are worked out along with computation of the hedging quantities Delta and Gamma.