Copula-MCMC理论在投资组合风险管理上的应用

发布时间：2018-01-13 20:09

本文关键词：Copula-MCMC理论在投资组合风险管理上的应用　出处：《湖南师范大学》2013年硕士论文　论文类型：学位论文

更多相关文章： 投资组合 Copula MCMC 风险值

【摘要】：本文对国内外关于投资组合及其风险值的研究进行了综述,虽然投资组合理论现已形成了完整的体系,但仍有不足的地方,主要体现在计算组合VaR值基于线性假设和确定最优投资组合的实际操作比较繁琐,而用MCMC方法操作起来比较简单,所以尝试将Copula理论和MCMC方法结合运用到投资组合分析中,并与传统的方法进行了比较,得出的结论是Copula-MCMC方法在资产配置和风险度量方面具有一定的改善效果。全文主要分为三个部分：第一部分,对Copula理论和MCMC方法的相关理论知识进行了阐述,有选择性地介绍了常用的Copula函数,如多元正态Copula函数、多元t-Copula函数和阿基米德Copula函数,并且介绍了M-H算法实施的具体步骤。第二部分,建立Copula模型和对计算VaR的方法进行改进,根据金融资产的波动性特征,用GARCH(1,1)模型来描述其特性,再结合Copula函数建立Copula-GARCH(1,1)模型,采用两阶段极大似然法对模型参数进行估计,然后用对数似然值和AIC值评价模型的拟合优度。传统方法计算VaR值用到的相关系数是线性的,而Copula模型中的相关系数能够很好地刻画金融资产的非线性相关关系,因此用Copula模型中的相关系数代替线性相关系数计算VaR更加符合实际。再根据样本数据的先验概率通过MCMC方法确定投资组合资产比例,用该比例和Copula模型相关系数计算VaR的值。第三部分,用建立的模型进行实证分析,本文选择欧盟排放权配额期货合约和华夏全球精选基金作为数据样本,对数据用Q-Q图检验发现样本数据的分布近似服从正态分布,所以选择用多元正态Copula函数作为连接函数。然后再用样本数据估计GARCH(1,1)模型参数,进而估计Copula-GARCH(1,1)模型的相关系数。最后分别用改进后的方法和传统方法计算了VaR的值,经比较后发现改进后的方法计算出来的VaR稍微比传统的要高一些,说明传统方法低估了风险,改进后的方法更加符合实际情况。
[Abstract]:This paper summarizes the research on portfolio and its risk value at home and abroad. Although portfolio theory has formed a complete system, but there are still shortcomings. The main manifestation is that the calculation of portfolio VaR value based on linear assumptions and the determination of the optimal portfolio of the actual operation is more cumbersome, but using the MCMC method to operate is relatively simple. So we try to apply Copula theory and MCMC method to portfolio analysis, and compare with traditional methods. The conclusion is that the Copula-MCMC method has a certain improvement effect in asset allocation and risk measurement. In the first part, the related theoretical knowledge of Copula theory and MCMC method is expounded, and the commonly used Copula functions, such as multivariate normal Copula functions, are introduced selectively. The multivariate t-Copula function and Archimedes Copula function are introduced, and the steps of M-H algorithm implementation are introduced. In the second part, the Copula model is established and the method of calculating VaR is improved. According to the volatility characteristics of financial assets, it is described by the Garch 1 / 1) model. Then the Copula-GARCH1) model is established with the Copula function, and the parameters of the model are estimated by using the two-stage maximum likelihood method. Then the logarithmic likelihood value and AIC value are used to evaluate the goodness of fit of the model. The correlation coefficient used in the traditional method to calculate the VaR value is linear. The correlation coefficient in Copula model can well describe the nonlinear correlation of financial assets. Therefore, using correlation coefficient in Copula model instead of linear correlation coefficient to calculate VaR is more practical. Then according to the prior probability of sample data, the ratio of portfolio assets is determined by MCMC method. The ratio and the correlation coefficient of Copula model are used to calculate the value of VaR. In the third part, using the established model for empirical analysis, this paper selects the European Union emissions quota futures contract and the Huaxia Global selection Fund as data samples. The Q-Q graph test shows that the distribution of the sample data is similar to the normal distribution, so the multivariate normal Copula function is chosen as the connection function, and then the sample data is used to estimate the GARCH(1. 1) the parameters of the model and the correlation coefficient of the Copula-GARCH1) model are estimated. Finally, the values of VaR are calculated by the improved method and the traditional method. After comparison, it is found that the VaR calculated by the improved method is slightly higher than that of the traditional one, which indicates that the traditional method underestimates the risk, and the improved method is more in line with the actual situation.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.48;F224

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