金融数据的极端风险度量及应用

发布时间：2018-02-14 07:43

本文关键词： VaR ES 广义极值分布广义Pareto分布 Poisson-GP复合超阈值分布　出处：《重庆大学》2014年硕士论文　论文类型：学位论文

【摘要】：在金融风险管理领域中，学者们已经得到许多基于正态分布假设的研究方法以及资产配置技术和套利策略等。极端的金融风险鲜有发生，但一旦出现极值事件，就会给人类的生产和生活带来难以承担的恶劣影响。特别是1970年以后，金融市场出现了极大波动，金融资产暴涨、暴跌变得尤为常见。传统的基于高斯正态分布假定的理论研究受到广大学者的严重质疑。对金融资产收益率序列尾部特征的研究正是基于此产生的，它是近几十年来发展起来的，是金融市场极端风险度量的重要内容之一。怎样使金融资产收益率序列的尾部特征得以有效描述，得到其近似分布函数，进而准确得到各类风险度量模型的参数估计和其置信区间，在理论研究和实际应用中都具有非常重要的意义和价值。本论文围绕基于极值理论和复合极值模型的风险度量方法展开深入的学习和研究。主要研究内容如下：系统地阐述和分析了BMM模型和POT模型的思想、原理和方法，并对这两种极值模型的优缺点进行了比较；针对被广泛应用的广义极值分布，本文介绍了其概念以及具体的三种类型，分别讨论了他们的最大值吸引场；给出了广义Pareto分布的原理，分析了其参数估计和计算金融资产收益率的VaR和ES值的方法，研究了POT模型中阈值的选取标准，，详细介绍了确定阈值的三种方法；对Poisson-Gumbel复合极值模型作简单介绍，在此基础上，结合Poisson分布与广义Pareto分布，赋予变量新的意义，得到新的分布——Poisson-GP复合超阈值分布，讨论并比较了该分布的三种参数估计方法——极大似然法、概率权矩法以及复合矩法，其估计效果显示，极大似然法最佳；最后采用广义Pareto分布和Poisson-GP复合超阈值分布，对上证指数1996-2013年间的日收益率序列进行了实证分析，利用POT模型来计算风险价值VaR和ES，对相应参数进行了估计，最终获得该金融数据的极端风险度量，结果显示了两个模型对金融资产收益率的拟合效果好、精度较高、能反映数据厚尾特征的优良性质；最后，总结本论文的不足之处并提出进一步的研究方向。
[Abstract]:In the field of financial risk management, scholars have obtained many research methods based on normal distribution hypothesis, asset allocation technology and arbitrage strategy, etc. Extreme financial risks rarely occur, but once extreme events occur, It will have an unbearable adverse impact on human production and life. Especially after 1970, financial markets have experienced great fluctuations and financial assets have soared. The traditional theoretical research based on Gao Si's normal distribution hypothesis has been seriously questioned by many scholars. It has been developed in recent decades and is one of the important contents of extreme risk measurement in financial market. How to describe the tail feature of financial asset return series effectively and obtain its approximate distribution function, Then the parameter estimation and confidence interval of various risk measurement models are obtained accurately. This paper focuses on the risk measurement method based on extreme value theory and compound extreme model. The main research contents are as follows:. The ideas, principles and methods of BMM model and POT model are systematically expounded and analyzed, and the advantages and disadvantages of these two extreme value models are compared. In this paper, the concept and three specific types are introduced, their maximum attraction fields are discussed, the principle of generalized Pareto distribution is given, and the methods of estimating its parameters and calculating the VaR and es values of financial asset returns are analyzed. In this paper, the criteria of threshold selection in POT model are studied, three methods of determining threshold are introduced in detail, and the Poisson-Gumbel compound extreme value model is simply introduced. On this basis, combining the Poisson distribution with the generalized Pareto distribution, the variables are given new significance. A new distribution Poisson-GP composite over-threshold distribution is obtained. Three parameter estimation methods, maximum likelihood method, probabilistic weight moment method and compound moment method, are discussed and compared. The results show that the maximum likelihood method is the best. Finally, by using generalized Pareto distribution and Poisson-GP composite over-threshold distribution, the daily yield series of Shanghai stock index from 1996 to 2013 are empirically analyzed. The POT model is used to calculate the risk value VaR and ESS, and the corresponding parameters are estimated. Finally, the extreme risk measurement of the financial data is obtained. The results show that the two models have good fitting effect on the return rate of financial assets, and the accuracy is high, which can reflect the excellent properties of the data with thick tail. Summarize the deficiency of this paper and put forward the further research direction.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.9;O211.3

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