Copula理论及其在股市相关性的应用

发布时间：2018-02-22 06:08

本文关键词： Copula函数金融市场相关性尾部相关　出处：《天津财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：随着世界各国之间对外贸易的不断加深以及对资本流动、技术转移和提供服务限制的逐渐放开,全球经济、金融市场由此形成了一个不可分割、相互影响的整体。全球金融市场之间的价格协同运动使得世界上任何国家金融市场的局部波动都会快速的波及、传染、放大到其他金融市场,产生巨大的蝴蝶效应。金融市场间的相关关系变得越来越复杂,多呈现非对称、非线性以及尾部相关的结构形式。而Sklar提出的Copula函数可以捕捉到随机变量间非线性的相关关系,同时Copula函数可以迅速有效地捕获到非正态、非对称分布的尾部相关信息,在运用Copula理论建立金融序列模型时,还可将随机变量的边缘分布与它们之间的相关结构分开来研究,其中它们的相关结构可由一个Copula函数来描述,这就大大简化了变量建模问题。因此,运用Copula理论研究金融市场间的相关性具有非常重要的理论意义和应用价值。文章研究的重点包括三个部分：第一,对Copula函数的性质及其函数族做了详细的讨论,在相关性的测度上引入了几种直观的图形检验方法,其中包括通过观测样本的秩数对,判断变量之间的相关关系以及在引入秩数对的基础上提出了Chi-plot和K-plot检验方法。第二,将半参数的估计方法与参数估价方法做了简要的对比,分析了二者的优劣势。同时,介绍了一种在半参数估计方法下检验模型拟合效果的方法,S。检验方法。第三,采用参数估计方法和半参数估计方法实证分析了沪深指数收益率序列间的相关关系,通过拟合优度检验对多种Copulas函数进行筛选,发现Gumbel Copula函数和t-Copula函数从整体上描述两者相关结构的能力较好,但为了更客观反映二者之间的关系又构造了M-Copula,结果表明其刻画沪深股市间尾部相关性的效果更好。研究内容的创新点主要表现在以下两个方面：第一,在相关性的测度上引入了几种直观的图形检验方法,使得应用更加便捷。第二,实证分析了沪深指数收益率序列的相关结构。
[Abstract]:With the deepening of foreign trade among countries in the world and the gradual liberalization of restrictions on capital flows, technology transfer and the provision of services, the global economy and financial markets have become inseparable. The price synergy between global financial markets makes the local volatility of financial markets in any country in the world quickly spread, spread, and magnify to other financial markets, The relationship between financial markets is becoming more and more complex, often in the form of asymmetric, nonlinear and tail dependent structure. Sklar's Copula function can capture the nonlinear correlation between random variables. At the same time, the Copula function can quickly and effectively capture the tail correlation information of non-normal and asymmetric distribution. When using Copula theory to establish the financial sequence model, the edge distribution of random variables and the correlation structure between them can be studied separately. Their related structures can be described by a Copula function, which greatly simplifies the problem of variable modeling. It is of great theoretical significance and practical value to use Copula theory to study the correlation between financial markets. The emphasis of this paper includes three parts: first, the properties of Copula functions and their families are discussed in detail. Several intuitionistic graphic test methods are introduced into the measure of correlation, including the rank pairs of observation samples, the correlation relationship between variables and the Chi-plot and K-plot test methods based on the introduction of rank number pairs. This paper makes a brief comparison between the semi-parameter estimation method and the parameter evaluation method, and analyzes their advantages and disadvantages. At the same time, a method to test the model fitting effect under the semi-parameter estimation method is introduced. By using parameter estimation method and semi-parameter estimation method, the correlation between Shanghai and Shenzhen index yield series is analyzed empirically, and various Copulas functions are screened by goodness of fit test. It is found that the Gumbel Copula function and the t-Copula function can describe the correlation structure of the two functions as a whole. But in order to reflect the relationship between the two more objectively and construct M-Copula, the result shows that it is better to depict the tail correlation between Shanghai and Shenzhen stock markets. The innovation of the research mainly shows in the following two aspects: first, Several intuitionistic graphic test methods are introduced to measure the correlation, which makes the application more convenient. Secondly, the correlation structure of the returns series of Shanghai and Shenzhen index is analyzed empirically.
【学位授予单位】：天津财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.91;F224

【参考文献】