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 coe cients 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.

中文翻译：

---

关于金融中 3D HCIR PDE 的改进计算解决方案

摘要 这项工作的目的是通过采用非均匀离散化和收集有限差分 (FD) 来计算三维 (3D) Heston-Cox-Ingersoll-Ross (HCIR) 时间相关偏微分方程 (PDE) ) 将系数加权到微分矩阵中。事实上，采用 3D 计算域的非均匀离散化来实现所有空间变量的二阶精度。所提出的程序在什么条件下是稳定的。这个稳定性界限在解决这个模型的文献中是新颖的。与对冲量 Delta 和 Gamma 的计算一起制定了几个金融实验。