基于时变t-Copula的沪深股指组合的风险度量

发布时间：2018-03-01 12:31

本文关键词： Copula VaR 时变Copula 蒙特卡洛模拟　出处：《西南交通大学》2013年硕士论文　论文类型：学位论文

【摘要】：当前的金融市场,随着金融改革的深入化,金融市场的联系日益紧密,投资组合、金融风险管理更是成为学者们关注的热点问题。投资组合风险的研究,首先就是要研究金融变量之间的相关性关系。对于研究投资组合的相关关系,传统投资组合一般都是以正态分布为假设前提的,但实际金融市场的数据并不都是服从正态分布。同时,相关性分析的常用方法就是线性相关系数的分析,线性相关系数要求变量之间的关系是线性的,而金融资产组合之间的关系并不都是线性相关关系,也有很多资产组合之间存在非线性关系,此时也就无法用线性相关系数来准确地描述金融资产之间的相关性。所以,在正态分布假设下,仅使用线性相关来分析资产组合之间的相关性,进而计算其投资组合的风险价值往往与实际的风险价值是存在差异的。因此本文引入Copula函数,作为分析变量之间相关性的工具,无论是变量之间的线性关系还是非线性关系,Copula函数都能够很好地处理并且较好地描述。此外,目前采用Copula函数研究的相关关系大都假定是不变的,但在实际的金融市场中,国家政策变动、金融事件的发生,都会引起经济市场中各种变量之间各种关系的变动,其中变量之间的相关性就不会静止不变,而是会会随着时间变化而变化,所以,本文在利用Copula函数的基础上又进一步利用时变Copula函数来研究资产组合的相关关系。本文首先是介绍本文的研究背景以及意义,通过回顾国内外研究现状,指出传统关于相关性研究方法的不足之处,并指出Copula理论在分析变量之间相关关系的必要性,同时对已有研究文献进行了评述；然后详尽地介绍Copula函数理论,包括Copula函数的性质、定理、类型,然后介绍了Copula模型的构建方法以及参数估计方法、模型评价和检验方法,最后着重介绍时变t-Copula模型；同时对于VaR也作了全面的阐述,其中介绍了其产生、影响因素以及VaR的三种计算方法,并且举例说明了VaR的计算方法。在介绍了Copula和VaR理论的基础上,将时变Copula函数理论应用到风险管理中的实证分析,通过选择沪深股票市场下的投资组合,先用历史数据确定边缘分布,然后选择几种不同的Copula函数和时变Copula来描述资产之间的相关性,进而度量出相应投资组合风险,并进行比较和评价,发现在时变Copula能够更好地估算资产组合的VaR。
[Abstract]:The current financial market, with the deepening of financial reform, the financial market is increasingly closely linked, portfolio, financial risk management has become a hot issue of concern to scholars. The first is to study the correlation between financial variables. For the study of portfolio correlation, the traditional portfolio is generally based on the assumption of normal distribution. At the same time, the commonly used method of correlation analysis is the analysis of linear correlation coefficient, the linear correlation coefficient requires that the relationship between variables is linear. But the relationship between the financial asset portfolio is not all linear correlation, and there are many nonlinear relationships between the portfolio, so the linear correlation coefficient can not be used to accurately describe the correlation between the financial assets. Under the assumption of normal distribution, only linear correlation is used to analyze the correlation between asset portfolios, and then the risk value of the portfolio is often different from the actual risk value. Therefore, the Copula function is introduced in this paper. As a tool for analyzing the correlation between variables, the Copula function, whether linear or nonlinear, can be well handled and well described. At present, most of the related relations studied by Copula function are assumed to be invariant, but in the actual financial market, the change of national policy and the occurrence of financial events will cause the changes of the relations between various variables in the economic market. The correlation between variables is not static, but will change with time. Therefore, based on the Copula function, we further use the time-varying Copula function to study the correlation of asset combinations. This paper first introduces the research background and significance of this paper, points out the shortcomings of the traditional methods of correlation research, and points out the necessity of Copula theory in analyzing the correlation relationship between variables by reviewing the current research situation at home and abroad. Then the theory of Copula function is introduced in detail, including the properties, theorems, types of Copula function, and then the construction method of Copula model, the method of parameter estimation, the method of model evaluation and test are introduced. Finally, the time-varying t-Copula model is introduced, and the VaR is also described, including its generation, influencing factors and three calculation methods of VaR. Based on the introduction of Copula and VaR theory, the time-varying Copula function theory is applied to the empirical analysis of risk management. Firstly, the edge distribution is determined by historical data, then several different Copula functions and time-varying Copula are selected to describe the correlation between assets, and then the corresponding portfolio risk is measured and compared and evaluated. It is found that in time-varying Copula, it can better estimate the value of portfolio.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F832.51

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