利用GARCH-M类模型和极值理论对上证综指的研究

To Analyse for the Research on Shangzheng Index Based on GARCH-M Models and Extreme Value Theory

金融时间序列具有分布的厚尾性、波动的集聚性等特征,传统的方法难以准确的度量其风险。文中运用一种新的估计VaR和ES的方法,即采取两阶段法。首先用GARCH-M类模型(GARCH-M、EGARCH-M和TGARCH-M)拟和原始收益率数据,得到残差序列;第二步用极值分析的方法分析的尾部,最后得到收益率序列的动态VaR和ES。最后对三个模型的计算结果进行比较。

Financial time series have the characteristic of fat tail and violation assembly,so it is difficult to measure the VaR （value at risk）accurately by conventional methods.We propose a new method for estimating VaR and ES （Expected shortfall）callod two-stage approach.Firstly,GARCH-M.EGARCH-M and TGARCH-M models are used to simulated the original return rate series; then extreme value theory is used to model the tail of residuals;finally we can obtain the dynamic VaR and ES of the return rate series.At last the results of the three models are compared.