基于SGT分布的ES估计、后验分析及在沪深股市中应用

The Estimating and Backtesting of Expected Shortfall Based on SGT Distribution with Application to Chinese Stock Markets

由于VaR可能低估尾部风险,巴塞尔委员会在第三次巴塞尔协议[1]中建议将ES取代VaR作为主要的风险度量工具,因此,有必要提出更精确且稳健的ES估计模型。鉴于股票收益率序列通常同时呈现出尖峰、厚尾、偏斜等特征,为更全面地刻画这些特征,本文采用具有三个形状参数的广义偏t分布(Skewed Generalized T Distribution,SGT)刻画收益率序列的分布形状,该分布囊括了多种常见的主流分布,通过结合能够刻画收益率序列杠杆性的EGARCH模型来估计收益率序列的ES,然后使用Du和Escanciano[2]最近提出的ES后验分析方法对其稳健性进行评估。在实证研究中,本文将该模型用于估计我国上证综指和深圳成指的日ES,结果表明,本文提出的EGARCH-SGT模型相比常见的基于偏t分布和学生t分布的EGARCH模型明显呈现出对收益率序列更好的拟合效果,且基于该模型估计的ES顺利通过了后验分析,表现出较好的稳健性。

Since traditional VaR might underestimate the tail risk,Basel Committee on Banking Supervision(BIS)recommend using Expected Shortfall(ES)as the main tool for measuring market risk instead of VaR in the third Basel Accord[1].Therefore,it is necessary to propose more accurate and robust method for estimating ES.It is known that stock return usually exhibits the characteristics of sharp peak,heavy tail and asymmetric distribution.To describe these characteristics comprehensively,this paper employs the Skewed Generalized T distribution that has three shape parameters combined with EGARCH model which can characterize the leverage of the return series to estimate stock return’s ES,and then use the backtesting method recently proposed by Du and Escanciano[2]to evaluate its accuracy.In the empirical study,we use our model to estimate the daily ES of Shanghai composite index and Shenzhen component index.The results indicate that,compared with the performance of EG ARCH models based on the common-used Skewed t distribution and Student’s t distribution,the EGARCH-SGT model obviously exhibit better performance.Moreover,this model passed the backtesting successfully,indicating that it is robust.