基于有理插值函数的利率期限结构模型

本文基于重心权有理插值函数,提出了一种新的利率期限结构静态估计模型,并给出一整套建模过程(包括基函数的构造、参数估计、节点选择、模型预测等).与传统的样条方法相比,本文提出的模型具有以下四个方面的优势:拟合的利率曲线光滑性更好;模型计算复杂度较低;参数估计存在明确的经济意义;模型的预测精度更高.最后,将该模型应用于上海证券交易所交易的国债利率期限结构研究,结果显示:模型在结构分析、计算复杂度、预测能力及经济内涵等方面均优于传统模型,能够有效提高国债利率期限结构拟合与定价的准确性.

Modelling term structure of interest rates based on rational interpolation function

Based on the barycentric rational interpolation, we propose a new model to fit the term structure of interest rates, which include construction of basis function, parameter estimation, knot selection and model forecasting. Compared with the traditional models, the new model has at least four advantages. Firstly, it has higher smoothness in fitting interest curve. Secondly, it has lower computational complexity in estimating parameters. Thirdly, it has richer economic significance of estimation parameters. And lastly, it has higher prediction accuracy. Our empirical results are based on the term structure of treasury bills in Shanghai Stock Exchange, and the results show that the new model not only has better performance in structure analysis, computational complexity, prediction capability and economic significance, but also improve the fitting and pricing accuracy of bonds.