Error bounds for the perturbation solution of the transition density under a multi-factor CIR term structure model with weak mean-reversion effect

Abstract

We consider a multi-factor Cox-Ingersoll-Ross (CIR) model of the term structure of interest rates with weak mean-reversion effect. We use perturbation theory to analyze its conditional characteristic function illustrated by a system of Riccati equations and derive the error bounds for the perturbation approximations. Using the Fourier inversion theorem, we clarify that the perturbation approximation of the conditional characteristic function can be applied to estimate the transition density and likelihood function. We provide their error bounds and accuracy orders. Finally, we discuss the performance of the perturbation approximation in estimating the transition density via simulation.

Keywords:

• Multi-factor CIR model
• term structure of interest rate
• perturbation theory
• Riccati equations
• transition density

Mathematics subject classifications:

• 34E10
• 60E10
• 62E17
• 65L70

Acknowledgments

The authors would like to thank Dr. Shuenn-Jyi Sheu for his constructive suggestions. We are also grateful to the editor and anonymous referee for their helpful comments that improved the presentation of this article.

Additional information

Funding

The work of the first author was supported by the grant MOST 104-2115-M-031-002 offered by Ministry of Science and Technology, Taiwan.