基于幂律型分布的动态VaR模型及实证研究

Dynamic VaR Model Based on Power Law Distribution and Empirical Research

针对金融资产回报时间序列的尖峰厚尾性和波动集聚性,提出了基于AR(1)-GARCH(1,1)模型与幂律型分布相结合计算VaR的方法。用GARCH模型对时间序列建模刻画波动集聚性,用基于幂律型分布的扩展形式拟合GARCH模型的残差分布尾部,刻画回报时间序列的厚尾特征,两者结合更好地描述回报时序的动态波动现象。对上证综指进行实证分析,结果表明,文中提出的方法比基于正态分布的GARCH模型和静态幂律尾法更精确。

Aiming at the characteristics of peaks and fat tail and clustering flunctuation of financial asset return time series, an approach evaluating VaR based on AR（1）-GARCH（1,1） model and power law distribution is developed. Our approach combines GARCH model which describes clustering flunctuation and power law distribution for fitting the tail of residual which describes the nature of fat tail to depict phenomenon of dynamic volatility. Then an empirical analysis is done on Shangzheng index. The conclusion indicates that the approach is more precise than static power law tail approach and the approach based on GARCH model which is assumed normal distribution.