基于HJM框架的随机波动率短期利率模型

HJM-based short rate model with stochastic volatilities

在Heath-Jarrow-Morton(HJM)框架下,建立随机波动率短期利率模型(ECIR-SV),其中长期均值为时间函数.基于重度取样技巧,利用Laplace方法和P-样条方法给出了ECIR-SV模型的极大似然估计方法.实证结果表明对比一些嵌入模型,ECIR-SV模型描述时间序列数据效果是最优的;对于单因子模型,引入长期均值函数的模型稍微地改善了拟合效果;在随机波动率模型中,考虑长期均值函数模型更好地描述短期利率动态变化.此外,通过长期均值函数能够更好地说明资本流动的情况,为宏观政策的制定提供了一些可靠的依据.

This paper incorporates stochastic volatility and time-varying central tendency into the short-rate model（ECIR-SV） so that the Heath-Jarrow-Morton（HJM） model nests the ECIR-SV model.This paper also develops a maximum likelihood estimator for the ECIR-SV model by using the Laplace approximation and P-spline method based on importance sampling technique.The empirical results show that the ECIR-SV model is the best for the time series data comparison of the nested models.For the single-factor model with the time-varying mean,the model-fitting performance changes slightly.Incorporating into the time-varying central tendency,the stochastic volatility model can better characterize the short rate dynamics.Besides,the capital flows stated by the time-varying mean provides a reliable reference for macroeconomic policy.