Perturbation solutions for bond-pricing equations under a multivariate CIR model with weak dependences

Abstract

In this article, we derive the explicit perturbation solutions for bond-pricing equations under a multivariate Cox–Ingersoll–Ross model whose factors have weak dependences between each other. The error bounds of the perturbation approximations are demonstrated for the Riccati equation and zero-coupon bond price. These results provide the accuracy order for the perturbation approximation. Since the perturbation approximations are constructed based on the exact solution of the Riccati equation, this computational approach can be applied to deal with the stiffness problem. Numerical results are presented to show that this computation approach is tractable and accurate for evaluating the bond price.