基于Realized GARCH模型的沪深300指数波动率研究

摘要

Based on Chinese Shanghai-Shenzhen 300 Index and use the 5 minutes high frequency data to calculate and take the realized range as the volatility estimated value.Establish the Realized GARCH model and assume the yield rate residual error respectively obey the normal distribution and generalized hyperbol-ic distribution.Empirical results show that no matter take realized variance or realized range as the realized measure,the fitting results of Realized GARCH model that obey the generalized hyperbolic distribution is always better than it of Realized GARCH model that obey the normal distribution.No matter the residual error obeys the normal distribution or generalized hyperbolic distribution,the fitting results of Realized GARCH model that take realized range as the realized measure is always better than it of Realized GARCH model that take realized variance as the realized measure.On the other hand,in the term of improvement of likelihood value,changing the volatility estimated value will bring out higher improvement of likelihood value than changing residual error distribution,it means that select a appropriate volatility estimated value has significant influence on the fitting results of Realized GARCH model.%基于中国沪深300指数，采用5 min 高频数据计算已实现极差作为波动率估计量。建立Realized GARCH 模型，并假设收益率残差分别服从正态分布和广义双曲线分布。实证结果表明：无论是选择已实现方差还是已实现极差作为已实现测度，服从广义双曲线分布的 Realized GARCH模型拟合效果都比服从正态分布的Realized GARCH 模型要好。无论残差服从广义双曲线分布还是正态分布，采用已实现极差作为已实现测度的Realized GARCH 模型的拟合效果都比采用已实现方差作为已实现测度的Realized GARCH 模型要好。另一方面，从似然值提高的程度来看，改变波动率估计量比改变残差分布带来更大的似然值提高，说明选择一个合适的波动率估计量对 Realized GARCH 模型拟合效果起着至关重要的作用。