双斜率因子动态Nelson-Siegel利率期限结构模型及其应用

利率期限结构是利率产品定价的基础和核心,对利率市场化具有重要意义。根据我国债券市场的特点,本文对动态Nelson-Siegel模型进行扩展,引入第二个斜率因子,构造双斜率因子动态利率期限结构模型,增强收益率曲线近端的静态拟合和动态预测能力。本文提出的模型嵌套了动态Nelson-Siegel模型,是对动态Nelson-Siegel模型的实质性推广,极大似然比检验证明了第二个斜率因子引入的必要性。本文以状态空间模型的卡尔曼滤波构造样本似然函数,采用双折线优化算法计算模型参数的极大似然估计。基于我国银行间市场债券交易收益率数据的实证分析表明,双斜率因子模型能够显著改善动态Nelson-Siegel模型对收益率曲线近端的拟合能力,同时对短期预测能力也有改善。此外,第二个斜率因子反映出宏观经济活动对利率期限结构的滞后影响,扩展后的模型能捕捉我国利率期限结构更多的动态变化特征,给相关主体提供更具价值的参考信息。

Nelson-Siegel Dynamic Term Structure Model with Double Slope Factors and Its Applications

The four-factor dynamic term structure model is built up in this paper to improve substantially to widely used Nelson-Siegel model and tree-factor dynamic Nelson-Siege model. An additional slop factor is added to tree-factor dynamic model to make it more flexible in fitting and forecasting the short end of yield curve. Our model nests the three-factor dynamic Nelson-Siegel model as a special case and these two models can be compared directly by likelihood ratio. The model is formulated in state space form (6) and Kalman filtering is employed to construct likelihood. The empirical study is conducted using data from China interbank bond market and the conclusion shows that our double-slope-factor model can capture dynamics in short end of yield curve more accurately and then has a better fitting and forecasting performance than three-factor dynamic Nelson-Siegel model. The likelihood ratio test justifies the need of the additional slop factor. The model in the paper is an extension to those in the literature of term structure of interest rate and can be used in other empirical studies.