基于不同核函数的非参数利率期限结构模型的估计

Estimation using a nonparametric term structure model of interest rates based on different kernel functions

给出了用非参数方法估计利率期限结构的过程,并以上海证券交易所的国债回购利率数据为样本,采用4种不同核函数:高斯核、抛物线核、四次方核和六次方核对利率期限结构模型进行估计。结果显示:当利率小于4%时,4种核函数估计结果相近;当利率大于4%时,高斯核和抛物线核的估计结果相近,四次方核和六次方核的估计结果相近;从利率均值回复的角度来说,后两者要优于前两者。所有结果表明:短期利率的密度函数是非正态的,扩散过程的漂移函数和扩散函数是非线性的,印证了非参数利率期限结构模型在刻画利率行为方面的优越性。

The estimation process using a nonparametric term structure model of, interest rates is described. Based on the repurchasing rate of government bonds in the Shanghai stock market, the nonparametric term structure model of interest rates has been estimated by using four different kernel functions： the Gauss kernel function, the Epanechnikov kernel function, a quartic kernel function and a six-power kernel funct.ion. The empirical results show that the results of estimations using the four kinds of kernel functions are all very similar when the interest rate was less than 4 %. When the interest rate was more than 4 %, the estimation results with the Gauss kernel function were also very similar to those using the Epanechnikov kernel function and the estimation results with the quartic kernel function and the six-power kernel function were also similar to each other. Based on the mean-reversion of interest rates, the former two functions are superior to the latter two. The results demonstrate that the density function of short interest rates is a non-normal distribution, and that the drift and diffusion function are nonlinear, and verify the superiority of a nonparametric term structure model of interest rates for describing the behavior of interest rates.