使用GARCH-EVT和藤式Copula进行极端值依赖性建模和在险价值估计

发布时间：2018-07-03 12:50

本文选题：Vine + Copula极端值理论依赖性GARCH　；参考：《西南财经大学》2014年博士论文

【摘要】：依赖性建模和VaR估计是金融风险管理中的重要概念。但是,必须注意VaR高度依赖我们要研究的金融收益的分布假设的合理性和精度。因此,这篇论文使用GARCH-EVT和藤式Copula对极端值依赖性建模,并且进行了VaR和期望损失估计。在这两项任务中,首先要做的就是在极端值分析之前对收益率使用GARCH类模型进行过滤。关于VaR(在险价值,Value at Risk)的估计,分析中使用了边缘分布函数推断(IMF)方法。在此,估计被分为两个阶段。第一步是边缘分布函数的建模。这一步是使用了半参数方法,其中超阈值峰值法(peak-over threshold,POT)用于对每一个残差序列尾部的分布进行建模(参数建模部分),而每一个序列的主体部分则通过核函数光滑进行实证建模(非参数建模部分)。IFM的第二步是依赖性建模。这一步是通过建立藤状copula实现,其中任意两个时间序列之间的配对copula作为构建藤状copula的基础。为了进行对照,我们也给出了使用其它方法对VaR的估计。我们建议的方法和其它方法对比的有效性评价基于VaR和尾部期望的后向检验结果性能。关于使用藤状copula对极端值的依赖性建模,超阈值峰值法用于挑选出资产组合中每一类资产的极端收益数据集合和极端损失数据集合。在本论文的依赖性建模中我们考虑了3种资产。为此我们的依赖性建模中总共使用了6个数据集合。在C类和D类藤状copula模型之间进行选择的时候,选择最佳依赖性模型的基础是看它们在统计检验中的表现。关于VaR的估计,基于后向检验结果的实证证据表明：使用半参数边缘分布,GARCH-EVT结合混合D类藤状copula模型的方法比其它方法的效果都要好一些,因为在1%和5%的显著性水平情况下,以最少的VaR越界数量通过了条件和非条件覆盖检验。关于依赖性建模,基于数据的实证证据表明,C类藤状copula模型更适用于构建极端值之间的依赖性关系。高端尾部和低端尾部的依赖性模型的有关参数显著不等于0。这些依赖性参数的大多数为负数,这表明资产组合中资产尾巴对的依赖性关系显著存在,这有助于有关人员进行资产管理规划。
[Abstract]:Dependency modeling and VaR estimation are important concepts in financial risk management. However, we must pay attention to the rationality and accuracy of the distribution hypothesis of financial returns that VaR is highly dependent on. Therefore, this paper uses GARCH-EVT and rattan copula to model the extreme value dependence, and estimates VaR and expected loss. In these two tasks, the first task is to filter the rate of return using the GARCH model before extreme value analysis. For the estimation of VaR (value at risk), the edge distribution function inference (IMF) method is used in the analysis. Here, estimates are divided into two stages. The first step is to model the edge distribution function. This step uses the semi-parametric method, The peak-over threshold peak method is used to model the tail distribution of each residual sequence (parametric modeling part), while the main part of each sequence is modeled empirically by kernel function smoothing (non-parametric modeling part). The second step of IFM is dependency modeling. This step is based on the establishment of a rattan copula, in which the paired copula between any two time series is used as the basis for the construction of a rattan copula. For comparison, we also give the estimation of VaR using other methods. The effectiveness of the proposed method compared with other methods is evaluated based on VaR and tail expected backward test results. For modeling the dependence of extreme values by using rattan copula, the super-threshold peak value method is used to select the extreme return data set and the extreme loss data set for each asset class in the portfolio. In this paper, we consider three kinds of assets in dependency modeling. For this purpose, we used a total of six data sets in our dependency modeling. When choosing between class C and class D rattan copula models, the basis of selecting the best dependency model is to see their performance in the statistical test. With regard to the estimation of VaR, empirical evidence based on backward test results shows that the use of semi-parametric edge distribution GARCH-EVT combined with mixed D-rattan copula model is more effective than other methods, because at a significant level of 1% and 5%, The conditional and non conditional coverage tests are passed with the minimum VaR number. With regard to dependency modeling, empirical evidence based on data shows that class C rattan copula model is more suitable for constructing dependency relationships between extreme values. The parameters of the high end tail dependent model and the low end tail dependency model are significantly different from 0. Most of these dependent parameters are negative, which indicates that there is a significant dependency relationship between the tail pair of assets in the asset portfolio, which is helpful for the personnel concerned to carry out the asset management planning.
【学位授予单位】：西南财经大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F224;F830.91

【共引文献】