基于Vine-copula的金融市场波动关联性影响分析

发布时间：2017-12-30 18:33

本文关键词：基于Vine-copula的金融市场波动关联性影响分析　出处：《西南交通大学》2014年硕士论文　论文类型：学位论文

【摘要】：近年来Copula理论研究领域中,出现了一种新的研究方法：基于Vine结构的Vine-copula分解模型。将其运用在对多元随机变量数据建模中,即在图形建模工具Vine的结构基础上运用系列Vine-copula模块。而在通常情况下,利用它来描述多元联合分布和分析多元变量间的相依结构,为高维情况下的数据分析提供了理论基础。与直接利用多元Copula函数来描述多元联合分布相比,Vine-copula分解模型是将多元联合分布分解成系列两两变量间的Vine-copula模块,用Vine结构连接起来。其中每对Vine-copula模块是根据AIC值的大小来选择恰当的二元Copula函数予以拟合的,这使得建模的灵活性得以凸显,多元分布中变量间的相关差异性能够较好得以捕获。第一章本文在对研究背景及研究意义的简要叙述的基础上,对文章的相关理论知识点的国内外近期研究现状予以了相应的介绍,阐述了论文的主要贡献和论文的结构。第二章本文对Vine-copula的相关基础知识点进行了一定的介绍,其中包括Copula函数的定义、Copula函数的基本性质、几种常用的Copula函数、Vine的定义、Regular Vine的定义等等。第三章本文引入了构建完整的Vine-copula模型用于多元金融市场相关结构的建模步骤,以及两种用于参数估计的非线性算法(梯度法和序列二次规划算法),并利用拟合仿真对两种算法的优劣性予以比较,以分析算法的选择是否会对拟合结果的有效性产生影响。第四章本文选取美国次贷危机时期这个特殊的时间段作为研究的时间点,结合Vine-copula模型对四个金融市场(中国大陆股票市场、中国香港股票市场、日本股票市场、美国股票市场)之间的波动影响进行实证分析研究,探讨美国次贷危机对其它金融市场是否会造成一定程度的影响。
[Abstract]:The field of theoretical research on Copula in recent years, the emergence of a new research method: Vine structure model based on Vine-copula decomposition. The use of multivariate random variables in data modeling, using a series of Vine-copula module in the structure based graphical modeling tool Vine. Normally, use it to describe the multi joint distribution and analysis of multivariate dependence structure between variables and provides a theoretical basis for the analysis of the case of high dimensional data. With the direct use of multiple Copula function to describe the multivariate joint distribution compared to Vine-copula decomposition model is the multivariate joint distribution into Vine-copula module series between 22 variables, together with Vine Vine-copula of each structure. The Copula function module is two yuan according to the magnitude of AIC to choose the right to be fit, which makes the modeling flexibility to highlight multivariate distribution The correlation difference between variables can be better captured.
In the first chapter, based on the brief description of the research background and research significance, this paper introduces the recent research status of the related theoretical knowledge points both at home and abroad, and expounds the main contributions and the structure of the thesis.
The second chapter introduces the basic knowledge points of Vine-copula, including the definition of Copula function, the basic properties of Copula function, several commonly used Copula functions, the definition of Vine, the definition of Regular Vine, and so on.
The third chapter of this paper introduces the Vine-copula model to build a complete model for multiple steps of the relevant structure of financial market, and two for nonlinear parameter estimation algorithm (two planning algorithm of gradient method and sequence), and by fitting the advantages and disadvantages of two types of algorithms to compare, to analyze the choice of algorithm will have an impact the effectiveness of the fitting results.
The fourth chapter selects the United States subprime mortgage crisis in this special period of time as the time point, combined with the Vine-copula model of the four financial markets (Chinese, China stock market, Hongkong stock market, the Japanese stock market, the U.S. stock market) the empirical analysis between the volatility of the U.S. subprime mortgage crisis, the other financial market will cause a certain degree of influence.

【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F831.51

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