基于EGARCH和Cornish-Fisher展开的VaR度量方法

VaR Measurement Method Based on EGARCH and Cornish Fisher Expansion

针对度量收益率风险价值VaR时,GARCH模型不能体现正负收益率的非对称效应,研究了基于EGARCH模型和Cornish-Fisher展开度量VaR的一般方法。该方法结合了EGARCH模型和Cornish-Fisher展开,将EGARCH模型的偏度和峰度代入Cornish-Fisher展开中对收益率VaR进行度量。实证分析选取标普500指数日收益率作为样本数据,度量该收益率的风险价值VaR;该收益率具有非对称性,建立了能够体现非对称性的EGARCH(1,1)模型,运用新的VaR的方法与经典的基于极值理论的VaR度量方法,和基于Bootstrap方法的VaR度量方法对收益率VaR进行了度量,在不同的置信水平下比较了3种方法VaR度量结果失败率的大小;结果显示:新的VaR方法对收益率VaR的度量效果优于其他两种方法,对于具有非对称效应的收益率,可考虑此方法度量收益率的VaR。

In view of the fact that GARCH model can not reflect the asymmetric effect of positive and negative returns when measuring the VaR of return at risk,this paper studies the general method of VaR measurement based on EGARCH model and Cornish Fisher expansion.This method combines EGARCH model and Cornish Fisher expansion,and substitutes skewness and kurtosis of EGARCH model into Cornish Fisher expansion to measure the yield VaR.Empirical analysis selects the daily return rate of S&P 500 index as sample data to measure the VaR of the return rate.The return is asymmetric.EGARCH(1,1)model which can reflect the asymmetry is established.The new VaR method,the classical VaR measurement method based on extreme value theory and the VaR measurement method based on bootstrap method are used to measure the yield VaR,and the failure rates of the three methods are compared under different confidence levels.The results show that the new VaR method is better than the other two methods in measuring the return VaR.For the return with asymmetric effect,we can consider this method to measure the VaR of return.