基于极值理论的VaR和ES度量——以中兴通讯数据为例

Computing VaR and ES Based on the Extreme Value Theory:A Case Study of ZTE Data

风险价值(VaR)是市场风险的重要度量工具。以具有厚尾的中兴通讯股票收益率数据为例,分别运用极值理论中的分块样本极大值模型(BMM)和超阈值模型(POT)对VaR进行计算,并给出相应的预期损失(ES),同时提出了一种差异度量的方法对POT模型的阈值进行选取。结果表明,使用极值理论度量风险可以更好地捕捉尾部数据信息,得到更合理且符合实际需求的VaR和ES估计值,且POT模型比BMM模型所得计算结果更加稳定。

Value at Risk （VaR）is an important measurement tool for market risk. The Block Maxima Model （BMM）and the Peak Over Threshold （POT）model are employed to compute the VaR and Expected Shortfall （ES）for ZTE return data with heavy tails respectively. A discrepancy measure is proposed to select the threshold for the POT model. The data analysis shows that applying the extreme value theory in risk measurement can fully capture information from the tail of data and obtain reasonable VaR and ES to satisfy actual needs, and the results from the POT model are more stable than the ones from BMM.