基于多项式样条函数的我国零息票收益率曲线构造

零息票收益率曲线是利率期限结构理论分析的基础,在金融估价和风险管理中发挥着重要作用。提出基于多项式样条函数构造零息票收益率曲线的过程及改进方法:考虑国债采样日位于付息日之间、年付息次数可变的情形,使分析更具一般性;针对多项式样条函数拟合时回归系数不显著的问题,采取剔除不显著变量的方法进行改进;讨论比较了两种样条值确定方法在我国的适用性,并研究了模型的稳定性。选取上交所国债进行的实证研究表明,在现阶段我国国债样本数据较少、结构不甚合理的情况下,采用剔除不显著变量的三段三次样条函数可以较好地构造我国的零息票收益率曲线。

Zero-Coupon Bond Yield Curve in China Based on Polynomial Spline Functions

Zero-coupon bond yield curve is the basis of term structure of interest rates. It plays an important role in financial pricing and risk management. Considering the frequency of interest payment and the situation of sampling date between interest payment dates, the general process of constructing the zero coupon bond yield curve is given based on polynomial spline functions. In response to the problem that the regression coefficients are not significant, a model excluding not-significant variables is given. The applicability of the two methods to determine the spline knots is discussed as well as the stability of the model. Using the bond data from Shanghai Stock Exchange, the empirical analysis shows that the cubic spline model with three knots excluding not-significant variables is more accurate and closer to the reality in China.