基于多元混合Copula-GARCH模型的深圳股票市场中收益相关性分析与VaR风险度量
发布时间：2018-08-26 21:33
【摘要】：本文对深圳股票市场的收益与风险进行研究．选取深圳股票市场中具有代表性的六支股票作为研究对象，通过建立多元混合Copula-GARCH模型来分析股票收益的相关性以及对VaR进行计算．本文主要内容有： 第一章阐述了选题的背景和研究意义，并进行了相关的文献综述． 第二章对Copula函数概念、性质及分类进行了简要概述，为建立Copula函数模型提供概念上的准备． 第三章首先给出了Copula函数模型的一般构建方法，包括边际分布和Copula函数的选取、参数估计及其检验方法，其次给出几种重要的相关性测度，包括Copula函数的Kendall秩相关系数与尾部相关系数． 第四章是实证研究．选取深圳股票市场中2011年6月30日至2012年6月30日六支股票的收盘价格为指标变量，并对其数据进行预处理得到这六支股票收益率序列，在对数据进行基本统计分析的基础上，分别建立了这六支股票的GARCH-t模型来刻画相应的边际分布，为了分析六支股票两两间的相关关系，考虑到其中有15种不同组合的两两相关，为避免赘述，本文仅以深发展A与万科A为例对其Copula函数的建模进行详细的论证．具体过程如下：在同一个边际分布GARCH-t模型下分别选取四种不同的阿基米德Copula函数建立了多元Copula-GARCH模型并进行了参数估计与检验，根据χ2拟合优度检验的结果最终选择多元M-Copula-GARCH模型(4.9)来刻画这两支股票的相关性结构，据此模型不仅可以分别刻画这两支股票各自的运行规律，而且还可以得出以下相关性结论：深发展A股和万科A股收益率之间存在较强的正相关关系，两者的收益率之间存在显著的非对称的尾部相关关系，Kendall秩相关系数为0.7123，上尾部相关系数为0.5363，下尾相关系数为0.2757．而且由于模型给出了两支股票的联合分布，，从而可以掌握其协同运行规律．而对于其它14种股票组合的两两相关性讨论完全类似于深发展A与万科A的Copula函数模型的建模过程，为节省篇幅同时考虑到第五章的需要，本文仅列出了这些组合的秩相关系数的结果． 第五章根据第四章的建模方法与结果，利用一步向前预测法计算了单支股票收益率的1天持有期VaR，并进一步对六支股票的整体VaR进行计算，从而得到了深圳股票市场风险的一种度量．
[Abstract]:This paper studies the income and risk of Shenzhen stock market. Six representative stocks in Shenzhen stock market are selected as the research objects. The correlation of stock returns and the calculation of VaR are analyzed by establishing a multivariate mixed Copula-GARCH model. The main contents of this paper are as follows: the first chapter describes the background and significance of the topic. In the second chapter, the concept, properties and classification of Copula function are briefly summarized. In the third chapter, the general construction methods of Copula function model are given, including marginal distribution, selection of Copula function, parameter estimation and test method. Secondly, several important correlation measures are given. The Kendall rank correlation coefficient and tail correlation coefficient of Copula function are included. Chapter four is an empirical study. The closing prices of six stocks in Shenzhen Stock Market from June 30, 2011 to June 30, 2012 are selected as index variables. On the basis of the basic statistical analysis of the data, the GARCH-t model of the six stocks is established to depict the corresponding marginal distribution. In order to analyze the correlation between two and two stocks, and considering that there are 15 different combinations, in order to avoid repetition, In this paper, only the deep development A and Vanke A are taken as examples to demonstrate in detail the modeling of their Copula functions. The concrete process is as follows: four different Archimedes Copula functions are selected under the same marginal distribution GARCH-t model to establish the multivariate. The Copula-GARCH model is used to estimate and test the parameters. According to the results of 蠂 2 goodness of fit test, the multivariate M-Copula-GARCH model (4. 9) is chosen to describe the correlation structure of these two stocks. Furthermore, we can draw the following conclusions: there is a strong positive correlation between the returns of A shares and Vanke A shares. There is a significant asymmetric tail correlation between the two rates of return. The Kendall rank correlation coefficient is 0.7123, the upper tail correlation coefficient is 0.5363, and the lower tail correlation coefficient is 0.2757. Moreover, the joint distribution of the two stocks is given in the model. In order to save space and take into account the need of chapter 5, the discussion on the correlation of 14 other stock combinations is completely similar to the modeling process of the Copula function model of the further development of A and Vanke A. In this paper, only the results of rank correlation coefficients of these combinations are listed. The one-step forward prediction method is used to calculate the one-day holding period VaR, of a single stock return, and the overall VaR of six stocks is further calculated, thus a measure of the risk of Shenzhen stock market is obtained.
【学位授予单位】：南京财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51
本文编号：2206225
[Abstract]:This paper studies the income and risk of Shenzhen stock market. Six representative stocks in Shenzhen stock market are selected as the research objects. The correlation of stock returns and the calculation of VaR are analyzed by establishing a multivariate mixed Copula-GARCH model. The main contents of this paper are as follows: the first chapter describes the background and significance of the topic. In the second chapter, the concept, properties and classification of Copula function are briefly summarized. In the third chapter, the general construction methods of Copula function model are given, including marginal distribution, selection of Copula function, parameter estimation and test method. Secondly, several important correlation measures are given. The Kendall rank correlation coefficient and tail correlation coefficient of Copula function are included. Chapter four is an empirical study. The closing prices of six stocks in Shenzhen Stock Market from June 30, 2011 to June 30, 2012 are selected as index variables. On the basis of the basic statistical analysis of the data, the GARCH-t model of the six stocks is established to depict the corresponding marginal distribution. In order to analyze the correlation between two and two stocks, and considering that there are 15 different combinations, in order to avoid repetition, In this paper, only the deep development A and Vanke A are taken as examples to demonstrate in detail the modeling of their Copula functions. The concrete process is as follows: four different Archimedes Copula functions are selected under the same marginal distribution GARCH-t model to establish the multivariate. The Copula-GARCH model is used to estimate and test the parameters. According to the results of 蠂 2 goodness of fit test, the multivariate M-Copula-GARCH model (4. 9) is chosen to describe the correlation structure of these two stocks. Furthermore, we can draw the following conclusions: there is a strong positive correlation between the returns of A shares and Vanke A shares. There is a significant asymmetric tail correlation between the two rates of return. The Kendall rank correlation coefficient is 0.7123, the upper tail correlation coefficient is 0.5363, and the lower tail correlation coefficient is 0.2757. Moreover, the joint distribution of the two stocks is given in the model. In order to save space and take into account the need of chapter 5, the discussion on the correlation of 14 other stock combinations is completely similar to the modeling process of the Copula function model of the further development of A and Vanke A. In this paper, only the results of rank correlation coefficients of these combinations are listed. The one-step forward prediction method is used to calculate the one-day holding period VaR, of a single stock return, and the overall VaR of six stocks is further calculated, thus a measure of the risk of Shenzhen stock market is obtained.
【学位授予单位】：南京财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51
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