基于t-Copula的沪深300指数数据分析

发布时间：2018-01-20 01:03

本文关键词： 连接函数回归沪深300指数风险价值风险价值分解　出处：《东北大学》2012年硕士论文　论文类型：学位论文

【摘要】：Copula(连接函数)是研究变量间联合分布的理论,近些年来受到了各界广泛的关注与研究.本文研究了基于Copula结构的回归模型,并将模型应用于VaR(风险价值)分解理论中,通过该模型对沪深300指数的数据进行了分析. 首先,本文介绍了Copula理论,叙述了Copula的概念、性质以及几种常用的Copula函数,简要介绍了Copula模型的构造以及评价方法.并在Copula理论的基础上研究了构造回归模型的方法,介绍了几种Copula结构下的回归模型,重点讨论了t-Copoula回归模型.通过模拟数据回归模型的效果检验,发现t-Copula模型回归效果对于边缘分布服从t分布的数据的拟合效果较好. 然后,介绍了风险价值理论及风险价值分解的内容,叙述了在正态假设下风险价值和风险价值分解的计算方法,并研究了在t分布的假设下求解风险价值的方法. 最后,将Copula回归与VaR分解理论相结合,研究了使用t-Copula回归模型对某一投资组合中各个资产边际VaR,成分VaR的求解,在t分布的假设下,使用t-Copula模型对沪深300指数数据进行了研究.
[Abstract]:Copula (join function) is a theory to study the joint distribution of variables, which has been widely concerned and studied in recent years. In this paper, the regression model based on Copula structure is studied. The model is applied to the decomposition theory of VaR (risk value), and the data of Shanghai and Shenzhen 300 index are analyzed by the model. First of all, this paper introduces the Copula theory, describes the concept, properties and several commonly used Copula functions of Copula. This paper briefly introduces the construction and evaluation method of Copula model, studies the method of constructing regression model on the basis of Copula theory, and introduces several regression models under Copula structure. The t-Copoula regression model is discussed in detail. It is found that the regression effect of t-Copula model is better for fitting the data of the edge distribution from t distribution. Then, it introduces the theory of risk value and the content of risk value decomposition, and describes the calculation method of risk value and risk value decomposition under normal assumption. The method of calculating the value of risk under the assumption of t distribution is also studied. Finally, combining Copula regression with VaR decomposition theory, this paper studies the solution of each asset marginal value and component VaR in a portfolio by using t-Copula regression model. Under the assumption of t distribution, t-Copula model is used to study the index data of Shanghai and Shenzhen 300.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.51;F224

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