基于极值理论的Copula-GARCH模型及其在金融风险中的应用

发布时间：2018-04-25 09:38

本文选题：混合Copula + GARCH模型　；参考：《中央民族大学》2013年硕士论文

【摘要】：在过去的一段时间内,金融市场的相关关系被大量研究。由于Copula模型不仅考虑了金融时间序列间的相关程度,也将相关结构考虑其中,已经成为研究金融风险领域的重要工具。在实际应用中,想用一个单一的Copula函数全面刻画金融市场中的相关关系是很难的,所以需要构建一个更为灵活的Copula函数,以便可以更好的描述复杂的金融市场之间的相关关系。通过考虑不同Copula函数的特性,选取不同特征的Copula函数以不同的权重组合在一起,形成一个新的Copula函数——即混合Copula函数(M-Copula)。相对于某一特定的Copula函数来说,构建混合Copula函数的优势是混合Copula可以包含不同类型的Copula函数,即为混合Copula函数通过相关参数来度量变量之间的相关程度,而线性组合系数可以捕获相依结构之间的不同模式。而且,从经验来看,混合Copula函数可以通过自由选择不同的Copula函数来建立相关结构,与单一的Copula函数相比,能更好的描述真实相关结构。由于金融市场中的资产回报分布有明显的尖峰厚尾特性,所以假设正态分布会低估尾部的极端风险。极值理论可以针对数据的尾部建立模型,这种方法不需要假设金融资产收益的分布,而是运用数据直接拟合尾部的分布,通过这种方法可以很好地捕捉极端事件发生的概率,极值理论在度量高置信度风险方面能够显示出独特的优势。我们选取2002年1月4日至2012年12月31日上证工业指数、商业指数和公用指数三个行业指数序列的2666组数据进行实证分析。对于每一个指数序列分别拟合GARCH类模型来描述边缘分布,运用极值理论对数据尾部进行改进,选取阿基米德Copula函数中的Gumbel Copula、Clayton Copula和Frank Copula来构造M-Copula模型。从中可以看到：(1)利用极值理论中的POT模型改进了边缘分布,使得风险评估更加贴近真实。(2)结合混合Copula模型以及蒙特卡洛模拟来计算VAR是有效的,而某一个单一的Copula函数会低估了真实存在的风险值。这说明混合Copula函数能够更加真实的反应潜在的相关结构。
[Abstract]:Over the past period of time, the relationship between financial markets has been a lot of research. Because the Copula model not only considers the degree of correlation among financial time series, but also takes the correlation structure into account, it has become an important tool in the field of financial risk research. In practical application, it is difficult to describe the correlation relationship in financial market with a single Copula function, so it is necessary to construct a more flexible Copula function to describe the correlation relationship between complex financial markets better. By considering the characteristics of different Copula functions, Copula functions with different characteristics are selected and combined with different weights to form a new Copula function, that is, mixed Copula function (M-Copula). The advantage of building a hybrid Copula function over a particular Copula function is that the hybrid Copula can contain different types of Copula functions, that is, the hybrid Copula function measures the correlation between variables by correlation parameters. Linear combination coefficients can capture different patterns between dependent structures. Moreover, from the experience, the mixed Copula function can establish the correlation structure by choosing different Copula functions freely. Compared with the single Copula function, the hybrid Copula function can describe the real correlation structure better. Because the distribution of return on assets in financial markets has the characteristic of peak and thick tail, it is assumed that the normal distribution will underestimate the extreme risk of tail. The extreme value theory can build a model for the tail of the data. This method does not need to assume the distribution of the return on the financial assets, but uses the data to fit the distribution of the tail directly. By this method, the probability of extreme events can be captured very well. Extreme value theory can show unique advantages in measuring the risk of high confidence. From January 4, 2002 to December 31, 2012, we choose 2666 sets of data from Shanghai Stock Exchange Industrial Index, Business Index and Public Index to carry out empirical analysis. For each exponential sequence, the GARCH class model is fitted to describe the edge distribution, and the extreme value theory is used to improve the tail of the data. The Gumbel Copula Clayton Copula and Frank Copula in the Archimedes Copula function are selected to construct the M-Copula model. We can see that: 1) using the POT model in extreme value theory to improve the edge distribution, make the risk assessment more close to the reality.) it is effective to combine the mixed Copula model and Monte Carlo simulation to calculate the VAR. A single Copula function underestimates the real risk. This shows that the mixed Copula function can reflect the potential correlation structure more realistically.
【学位授予单位】：中央民族大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.91;O211.4

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