基于GARCH-GPD-COPULA函数的资产组合风险研究

发布时间：2019-06-04 21:10

【摘要】：随着金融市场的不断变化,金融资产之间的相关关系越来越复杂,呈现出非线性、非对称性和尾部相关的特性,基于线性相关关系的分析方法有的时候不能准确反映金融市场的相关关系,同时现实中金融资产收益率存在尖峰厚尾的特征,明显具有非正态特性与非线性相关,因此有时候采用传统VaR计算方法不尽合理,这时有必要采用合理的方法描述收益率的实际分布与相关性。而运用COPULA函数方法可以构造灵活的多元分布函数,很好的描述金融资产收益率的真实分布与相关关系,从而可以建立起更为有效的风险度量模型,所以运用COPULA函数研究金融资产风险价值具有重要的理论价值与运用意义。论文首先介绍了GARCH模型族,并且对GARCH模型残差的分布进行了研究,引入了两种厚尾分布t分布与GED分布；然后给出了广义帕累托分布(GPD)的定义和阀值的选择方法；接着本文详细的介绍了COPULA函数的定义、性质以及常用的五种COPULA函数,并且给出了COPULA函数的估计方法,以及最优COPULA函数的选择方法。在此基础上,引入了GARCH-COPULA、GPD-COPULA和GARCH-GPD-COPULA三种计算风险价值的VaR模型。在实证部分首先运用历史模拟法与分析法计算出资产组合在不同分位数下的风险价值(VaR)。然后,运用蒙特卡洛模拟法计算出三种模型GARCH-COPULA、GPD-COPULA、GARCH-GPD-COPUL对应的风险价值(VaR)。最后,对五种结果在1%,2%,3%,4%,5%,10%分位数下的VaR运用失败频率法加以检验,并且进行比较,实证结果表明基于GARCH-GPD-COPULA方法计算的VaR在样本内失败率是最低的,说明它估计的风险价值最接近真实风险价值。本文的创新主要体现在以下几个方面：(1)系统全面的总结了COPULA函数的定义,分类以及估计方法。(2)在运用GARCH模型对边缘分布进行拟合时,考虑了残差在正态分布,t分布与广义误差分布(GED)的不同情况,最后选择出最优的GARCH模型。(3)在前人对COPULA函数研究的基础上,将CARCH-COPULA和GPD-COPULA进行结合,提出了GARCH-GPD-COPULA函数,并进行了相应的实证分析。
[Abstract]:With the continuous change of financial markets, the correlation between financial assets is becoming more and more complex, showing nonlinear, asymmetric and tail-related characteristics. The analysis method based on linear correlation sometimes can not accurately reflect the correlation of financial market. At the same time, in reality, the rate of return on financial assets has the characteristics of sharp peak and thick tail, which obviously has non-normal characteristics and nonlinear correlation. Therefore, sometimes it is unreasonable to use the traditional VaR calculation method, so it is necessary to use a reasonable method to describe the actual distribution and correlation of the rate of return. By using the COPULA function method, a flexible multivariate distribution function can be constructed to describe the real distribution and correlation of the rate of return on financial assets, so that a more effective risk measurement model can be established. Therefore, it is of great theoretical value and application significance to use COPULA function to study the risk value of financial assets. In this paper, the GARCH model family is introduced, and the residual distribution of GARCH model is studied, and two kinds of thick tail distribution t distribution and GED distribution are introduced, and then the definition of generalized Pareto distribution (GPD) and the selection method of threshold value are given. Then, the definition and properties of COPULA function and five kinds of COPULA functions are introduced in detail, and the estimation method of COPULA function and the selection method of optimal COPULA function are given. On this basis, three VaR models, GARCH-COPULA,GPD-COPULA and GARCH-GPD-COPULA, are introduced to calculate the risk value. In the empirical part, the risk value (VaR). Of asset portfolio under different quartile is calculated by using historical simulation method and analysis method. Then, the risk value (VaR). Corresponding to GARCH-COPULA,GPD-COPULA,GARCH-GPD-COPUL of three models is calculated by Monte Carlo simulation method. Finally, the failure frequency method was used to test and compare the five kinds of results in 1%, 2%, 3%, 4%, 5%, 10% of the quartile, and the failure frequency method was used to test and compare the five kinds of results at 1%, 2%, 3%, 4% and 5%, respectively. The empirical results show that the failure rate of VaR calculated by GARCH-GPD-COPULA method is the lowest in the sample, which indicates that the estimated risk value is the closest to the real risk value. The innovation of this paper is mainly reflected in the following aspects: (1) the definition, classification and estimation method of COPULA function are summarized systematically and comprehensively. (2) when the GARCH model is used to fit the edge distribution, the residual error in the normal distribution is considered. According to the difference between t distribution and generalized error distribution (GED), the optimal GARCH model is selected. (3) on the basis of previous research on COPULA function, CARCH-COPULA and GPD-COPULA are combined to propose GARCH-GPD-COPULA function. And the corresponding empirical analysis is carried out.
【学位授予单位】：天津财经大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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