Analysis of an affine version of the Heston–Hull–White option pricing partial differential equation

For European plain vanilla options, we investigate the difference between solutions obtained by the full-scale and an approximate Heston–Hull–White (HHW) model. Based on the corresponding two option pricing PDEs, we analyze the quality of the approximation. To confirm the accuracy of the analysis, we solve the HHW PDE, its approximating PDE as well as the PDE for the error, numerically, via a semi-discretization in space by a finite difference scheme on nonuniform spatial grids, and the Alternating Direction Implicit (ADI) scheme in time direction. Test cases with different parameter settings are considered. The effect of the financial parameters on the errors is discussed in detail.