基于GARCH族模型的沪深300股指VaR度量

本文在修正了沪深300股票指数收益率序列的非平稳性和自身相关性之后,把ARMA模型与GARCH模型、GJR模型、IGARCH模型、FIGARCH模型、FIEGARCH模型、FIAPARCH模型、HYGARCH模型相结合,然后依次假设残差分布服从正态分布、t分布和偏t分布,来描述沪深300股票指数日对数收益率序列的尖峰厚尾性、杠杆效应和长记忆特性,利用上述模型分别计算沪深300股票指数的VaR值.在空头和多头投资者情况下,不同的波动性模型和不同残差分布的VaR预测有效性差距很大.比较得知,在不同的置信水平下,沪深300股票指数收益率序列空头和多头的VaR预测成功概率比较高的模型有HYGARCH和FIEGARCH这两类具有长记忆性的模型.

Value at Risk Measure of the HS 300 Stock Indexes Based on GARCH Models

In this paper we firstly try to characterize the sharp peak and fat tail phenomena, leverage effects and long memory features of the logarithmic returns of the Shanghai and Shenzhen 300 （ HS 300） stock indexes by using the ARMA model to describe the means and the 7 models ： the GARCH model, the GJR model, the IGARCH model, the FIGARCH model, the FIEGARCH model, the FIAPARCH model and the HYGARCH model, to respectively fit the residual sequences which are assumed sequently to follow a normal distribution, a t distribution or a skewed t distribu- tion, and then use those models to forecast the VaR of the HS 300 stock indexes. The empirical results show that the forecasts of the VaR with different models of volatilities and residual distributions in short and long cases differ greatly, and it is concluded by comparison that, at different confidence levels, the HYGARCH and the FIEGARCH models which are more suitable for characterizing long memory features have more accuracy for forecasting the VaR of the HS 300 stock indexes.