兰州大学机构库 >数学与统计学院
Copula理论及其在金融分析中的应用
Alternative TitleCopula Theory and Its Application In Financial Analysis
高阳
Thesis Advisor焦桂梅
2016-05-17
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name学士
Keyword金融资产 Copula理论 秩相关系数 沪深综指
Abstract作者基于前人的理论成果,对Copula理论进行了解与学习,并对已有的Copula理论进行了综述。文献[1,5,6,8,16]详细介绍了Copula函数的概念、基本性质和相关定理,对Copula函数进行分类介绍,即阿基米德Copula和椭圆Copula。文献[5,6]对常用的Copula函数在描述相关性结构方面的特点作了具体分析;通过查阅资料我们发现,不同的Copula函数对捕捉尾部相关性不同的金融市场间的相关关系的敏感度不同。文献[5,7,8,10]对Copula函数的参数估计方法进行了介绍,主要有参数估计法和非参数估计法,认为非参数估计法由于不存在边缘分布的假定,对边缘分布的厚尾情形更加实用;而当样本容量较大时,参数估计法则更好。除此之外,文献[5]对Copula函数的拟合检验进行了部分介绍,可根据具体的需要具体选择。最后作者利用前述Copula理论在金融分析中进行应用,利用Kendall秩相关系数和Spearman秩相关系数对沪深综指的相关性进行实证分析。对沪深综指分别确定各自的边际分布和进行联合分布的拟合,通过各自的边际分布以及自相关性检验发现,两指的联合分布密度分布图具有对称性;通过查阅文献以及前述Copula函数关于描述相关性结构特点的理论,发现学生t-Copula函数能够对两指的联合分布进行较好的拟合,并进行实证。结果表明,沪深综指具有很强的相关性,收益率走势趋于相同,并且联合分布的拟合结果很好。
Other AbstractBased on previous theoretical results, author understand and learn, and existing Copula theory is reviewed.In [1,5,6,8,16], the concept, basic properties and related theorems of Copula function are introduced in detail in. The classifications of Copula function are introduced in this paper,namely Archimedes Copula and elliptical Copula.Commonly used herein and in the description of the characteristics of the Copula function correlation structure make specific analysis in [5,6]; during the documents, we find that different Copula functions are sensitive to the correlation between different financial markets with different tail dependence.In [5,7,8,10], parameter estimation methods of Copula functions are summarized, mainly including parameter estimation method and non-parametric estimation, and think that the non parametric estimation method is more practical for the edge distribution of the thick tail due to the assumption that there is no marginal distribution;and when the sample size bigger, parameter estimation is better.In addition to,in [5], fitting tests of Copula functions are part of the presentation, may be specifically selected according to specific needs. Finally, the author using the preceding Copula theory uses in the financial analysis, using Kendall's rank correlation coefficient and Spearman rank correlation coefficient of correlation between the empirical analysis of Shanghai and Shenzhen Composite Index.Shanghai and Shenzhen Composite Index are determined marginal distributions and fitting joint distribution,by marginal distributions and autocorrelation test,we find that two-finger joint distribution density distribution is symmetry;with a review of the literature and Copula functions theoretical description of the relevant characteristics of the structure,we find that students t-Copula function of the joint distribution of two fingers can be a good fit, and empirical.The result shows that the Shanghai and Shenzhen Composite Index have a strong correlation, and the trend tends to yield the same results of the joint distribution and fitting well.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225725
Collection数学与统计学院
Recommended Citation
GB/T 7714
高阳. Copula理论及其在金融分析中的应用[D]. 兰州. 兰州大学,2016.
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