上交所债券利率期限结构与两因子Vasicek模型

Modeling the Term-structure of Yields in the SSE with Two-factor Vasicek Model

以上交所债券价格隐含的利率期限结构数据作为分析对象,利用主成份分析法分析发现,至少需要两个状态变量,利率模型才可能反映利率期限结构的变化,因此利用Kalman滤波法及极大似然估计法,估计了连续时间的两因子Vasicek模型.发现此利率模型可以很好解释1年期、2年期、3年期利率的相对变化,模型下的利率变化与实际利率的变化一致.但对4年期、5年期利率的拟合有一定的误差,主要表现在1998年利率变化幅度较大时.这种差别可能有两个方面原因.一种可能是1998年左右一段时间,市场没有准确预期利率将来的下降走势,导致4年期、5年期利率的市场观测值过高;另一种可能是模型不是一个异方差模型,并且模型下的风险金是常数,不能反映风险金的变化.而在1998年左右,市场利率波动较大,投资者承受的市场风险也较大,投资者对长期债券可能要求更高的风险金,从而导致长期债券的收益率较高.

With the data of term structures in the Shanghai Stock Exchange from January, 1991 to April, 2002, making use of principal component analysis approach, it is found at least two factors are needed to model the term structure changes in the SSE. With Kalman filter and maximum likelihood estimation approaches, twofactor continuoustime Vasicek model is estimated to model the term structures. It is found that twofactor Vasicek model can model the relative changes of oneyear, twoyear, threeyear interest rates quite well, but there exist some errors to model the 4year, 5year interest rates, especially in 1998. One possible explanation is that the market did not expect the decline of short interest rate accurately in 1998, and so market 4year and 5year rates are higher than modelimplied rates. Another explanation is that the Vasicek model can not model the change of risk premiums of bond returns, and perhaps the risk premium changes cause such modeling errors.