POT模型中GPD“厚尾”性及金融风险测度

Tail Thickness of GPD in POT Model and Finance Risk Measurement

极端值模型是准确估计"厚尾"分布金融资产回报市场风险的有力工具。在越槛高峰(POT)模型中,本文对超阈值近似服从的广义Pareto分布的形状参数与"厚尾"性关系及其在金融风险测度中的应用进行了分析。结果表明,当0<ε≤1,y>2β/(1-ε)时,分布为"厚尾"分布且尾部随着形状参数的增加而变厚,此时最适合于金融资产时间序列"厚尾"分布风险测度和参数的极大似然估计。国内外大量的实证研究验证了上述理论并得出我国沪深股市风险特征的一些新结论。

Extreme value model is a powerful tool to accurately estimate market risk of ＂fat tail＂ distribution of return on financial assets. In this article, we analyze the relation between the shape parameter and the thickness of the GPD tail of the POT model and its application in risk measurement. The results show that at the time 0〈ε≤1,y〉2β/（1-ε） the thickness of the distribution tail is ＂fat tail＂ and with the increase of shape parameters thickening. At this time it is most suitable for modeling to ＂fat tail＂ distribution of the financial assets time series and its parameter＇s MLE. Many empirical studies improve the theory and draw some new conclusions about risk feature in stock market of China.