利率期限结构模型改进极大似然估计效率研究

Efficiency Research on the Improved Maximum Likelihood Estimation of Models of Term Structure of Interest Rates

考虑一种改进的极大似然估计算法估计一维利率期限结构模型的未知参数,该方法首先利用Crank-Nicolson差分法求解与该扩散模型相关联的偏微分方程(PDE),获得累积分布函数,然后利用数值微分得到转移密度函数的近似值。数值模拟实验结果表明,当取较小空间步长时,该改进估计法比Euler法具有更高的效率,并考察该改进估计法在中国银行间同业拆借利率的实证分析,实证结果表明,在所考虑的样本区间内,中国利率的长期水平值是0.025 1,且中国货币市场利率粘性系数的值接近于0.5。

Considering an improved maximum likelihood estimation algorithm for estimating unknown parameter of one dimensional term structure of interest rates models. Crank--Nicolson difference scheme is provided to obtain the numerical solution of the corresponding Kolmogorov PDEs, from which the transitional cumulative distribution function （CDF） is obtained. Numerical differentiation of the transitional CDF follows the transitional probability density function （PDF）. The estimation results of numerical test show that the improved estimation algorithm perform better than Euler method under small spatial step. Meanwhile, the improved estimation method is used to estimate the model of the Chinese interbank offer rate data, the results show that the long term of mean--reverting value is 0. 0251 and the viscosity coefficient is about 0. 5.