基于B样条函数的上交所利率期限结构估计

Estimating Shanghai Stock Exchange Term Structure of Interest Rates with B-Splines

本文结合上交所的市场背景，进行了合理的节点设置下，采用B样条函数表示贴现函数、零息票收益曲线和远期瞬时利率曲线等三种方式来估计上交所利率期限结构，并用上交所国债市场的日交易数据对估计进行了样本内和样本外的分组数据拟合优度检验。结果表明：上交所的利率期限结构估计在1～10年期限范围内能够获得可靠的估计，5～7年期限范围内的估计精度最高；在控制数据过拟的前提下，直接估计贴现函数的方式的最适合于上交所利率期限结构的估计。

Under the appropriate knot setting in the background of Shanghai Stock Exchange, this paper first uses B-spline to estimate Shanghai Stock Exchange term structure of interest rates, and then empirically tests the estimation in in-sample and out-of-sample grouping goodness of fit with daily market data. In the estimation, B-spline is used to directly express discount function, zero coupon yield curve and instantaneous forward rate curve. The empirical results show that the estimation is creditable in the maturities between 1 and 10 years, estimation in the maturities between 5 and 7 years have the highest precision, and that controlling for the influence of data over-fitting the method of direct estimating discount is the most appropriate for the estimation of the term structure of interest rates of Shanghai Stock Exchange.