基于Zipf律的尾部特征分析及VaR计算

Tail Behavior Analysis and VaR Calculation Based on Zipf Law

分布的尾部特征分析在许多领域都非常重要,估计和分辨尾部服从幂律特征还是指数特征非常重要。在本文中,我们提出了在分析数据的Zipf幂律的基础上来分辨尾部特征的方法。通过实证分析,我们得出了上证指数收益率的确存在具有尺度不变性的Zipf幂律现象,然后分布的尾部特征就被确定,并得到了尾部指数的一种简单的估计方法,最后对该市场的在险价值(VaR)进行了计算和分析。

It is important to analyze the tail behavior of distributions in many areas, and there is a controversy about distinctions between exponential-type and power-type tails. In this paper, a new method to discriminate the tail behavior based on Zipf law is presented. By empirical analysis, the power law is found in Shanghai Composite. Then the tail behavior can be ensured. At last, the value of VaR is calculated and analyzed.