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

Cheng-Hsun Wu and Kai-Jiun Chang

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 21, 5294-5311

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.

Date: 2020
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DOI: 10.1080/03610926.2019.1617879

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