利率期限结构的三因子高斯动态模型及应用

Three-factor Gaussian Dynamic Model for Term Structure of Interest Rate:An Application to the SHIBOR Market

国内文献主要集中于仿射模型在我国利率期限结构中的应用,对高斯动态期限结构模型(Gaussian Dynamic Term Structure Model,简称GDTSM)的研究几乎是空白。基于JSZ规范化形式,本文首次构建了三因子高斯动态期限结构模型,并基于极大似然估计法给出了模型参数的估计过程。利用该模型对2008年1月4日至2012年4月28日上海银行间同业拆放利率(Shanghai Inter Bank Offered Rate,简称SHIBOR)的期限结构展开实证研究,同时对模型估计误差项进行多层次分解,重点探讨了利率期限结构的内在结构特征。研究结果显示:(1)三因子GDTSM模型能够很好地拟合和预测SHIBOR市场利率;(2)水平因子和斜率因子是短期利率期限结构的主要影响因素,曲度因子是长期利率期限结构的主要影响因素。作为利率期限结构实证研究的技术基础,三因子高斯动态期限结构模型为国债及其衍生品定价和风险管理提供一种新的技术支持。

Domestic literature mainly focus on the application of affine model to term structure of interest rate, and few attentions are paid to Gaussian Dynamic Term Structure Model （GDTSM）. Based on the JSZ normalization, a new three-factor GDTSM is proposed, and maximum likelihood estimator is used to estimate the parameters. Using the three-factor GDTSM, the term structure of Shanghai Inter Bank Offered Rate （SHIBOR） market from January 4, 2008 to April 28, 2012 is analyzed, and then its internal structure features is discussed by decomposing the corresponding error terms. The results show that. （1） the three-factor GDTSM fit and forecast the SHIBOR market very well; （2） the level and slope factors affect the short-term interest rates, and the curvature factor explains the long-term interest rate. As the basic tech- nology for empirical researches on rate term structure, the three-factor GDTSM could be applied in national debt and derivatives pricing and risk management.