基于P-样条方法的短期利率模型参数估计

P-spline Estimation for Short-term Interest Rate Model

由于在Hull-White短期利率模型中均值是时间的函数,因此本文将应用两阶段方法估计上述模型中的均值函数和其它常数参数值,其中对于均值函数使用P-样条方法,并给出了相应正则化参数选取的方法,而且也证明了两阶段估计方法的相容性和参数的渐进性性质.最后,基于零息债券数据,实证结果表明了引入均值函数模型对于债券价格的回归没有显著的区别,这一现象归因于债券价格对于短期利率不太敏感的性质.

Since the mean reverting is a function in the Hull-White model, this paper devel- ops the estimator and provides the estimation of the mean revering function, wl^ich will be estimated by using P-spline estimator and other constant parameters. In addition, we also present an alternative approach to select the regularization parameter. Furthermore, we prove the consistency of the two-stage method and its asymptotic normality of parameters. Finally, based on the zero coupon bond price data, empirical evidences show that there is a slightly less difference between the goodness-of-fit and the constant parameter estimates arising from the bond price less sensitive to short-term rate.