Error bounds for the perturbation solution of the transition density under a multi-factor CIR term structure model with weak mean-reversion effect. Issue 21 (1st November 2020)

• Record Type: Journal Article
• Authors: Wu, Cheng-Hsun; Chang, Kai-Jiun
• Is Part Of: Communications in statistics. Volume 49:Issue 21(2020)
• Page Start: 5294
• Page End: 5311
• Publication Date: 2020-11-01
• Subjects: Multi-factor CIR model -- term structure of interest rate -- perturbation theory -- Riccati equations -- transition density; 34E10 -- 60E10 -- 62E17 -- 65L70; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1617879
• Languages: English
• ISSNs: 0361-0926

Abstract

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.