Cox-Ingersoll-Ross模型的统计推断

Statistical Inference of Cox-Ingersoll-Ross Model

该文在离散样本观察下,研究了Cox-Ingersoll-Ross模型的统计推问题,给出了CIR过程的平稳均值m与平稳方差υ的矩估计,并用m和υ给出了CIR过程中尺度参数α与β波动率之间的关系,基于CIR过程的平方变差,得到参数β的平方变差估计和参数α的估计。通过数值模拟的方法对平方变差估计与条件矩估计([9])方法作了比较,并选择1997-2006年的R007数据对这两种方法进行了实证分析。

In this paper,the problem of estimating coefficients in the CIR model is studied under discretely sampled observations. The moment estimates of the equilibrium mean and the equilibrium variance of the CIR process is given. By assuming the parameters and the ' known' , the relation between the scale-parameter and the volatility is obtained. The quadratic variation estimation and estimation of parameter based on the quadratic variation for CIR process are gotten. The comparison between the quadratic variation estimation and the conditional moment estimate ( [9]) approach is made by simulation, and choice of data R007 has been tried in the two approaches from 1997 to 2006.