POT模型阈值的选取及应用

发布时间：2018-04-02 23:15

本文选题：极值理论　切入点：POT模型　出处：《吉林大学》2014年硕士论文

【摘要】：近年来,频繁的金融危机事件以及金融市场的波动,使得金融监管机构和投资者对金融资产价值大幅下滑的波动尤为敏感.尖峰、厚尾现象的金融资产收益率序列,也使得传统的正态分布假设受到严重质疑.极值理论是解决这类问题较实用的方法.极值理论包括BMM模型和POT模型,是研究随机过程的极值分布及其特征的模型技术.极值理论具有超越样本数据的能力,并能准确描述分布的尾部. 本文第一章对极值理论产生的背景进行介绍.第二章简单介绍了BMM模型的原理,包括广义极值函数的定义和Fisher Tippett定理,然后详细介绍了POT模型的构造,广义帕累托函数参数估计以及风险测量指标VaR和ES估计.第三章主要介绍了POT模型中阈值选取的若干方法,例如Hill图法,指数回归模型法和核拟合优度统计量法.第四章介绍了平均超额函数法，，并在其基础上提出拟合残差法，以提高阈值选取的稳定性.最后,我们使用上海证券交易所股票价格综合指数2006年1月1日至2007年1月1日的数据以及1968-2009年黄金每月价格来检验本文所述的POT模型中阈值选取方法的可行性.
[Abstract]:In recent years, frequent financial crises and financial market volatility, which is particularly sensitive to financial regulators and investors to the sharp decline in the value of financial assets. The fluctuation of financial assets return rate series of spikes, thick tail phenomenon, but also makes the traditional assumption of normal distribution has been seriously questioned. Extreme value theory is a method to solve this kind of problem more practical. The extreme value theory including BMM model and POT model, is a model of extreme value distribution and its characteristics of the technology of stochastic process. The extreme value theory has the ability to transcend the sample data, and can accurately describe the tail of the distribution.
This paper introduces the first chapter on the background of extreme value theory. The second chapter simply introduces the principle of BMM model, including the definition of generalized extreme value function and the Fisher Tippett theorem, and then introduces the structure of POT model, generalized Pareto function parameters estimation and risk measurement indexes of VaR and ES estimation. The third chapter mainly introduces several methods to choose the threshold POT model, such as Hill graph method, exponential regression model and kernel goodness of fit method. The fourth chapter introduces the mean excess function method, and puts forward the fitting residual error method on the basis of it, in order to improve the stability of the selected threshold. Finally, we use the Shanghai stock exchange stock price index from January 1, 2006 to January 1, 2007 the data and the 1968-2009 years of gold to test the feasibility of the monthly price threshold selection method of POT model this paper.

【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.9

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