基于Copula理论的上证指数与道琼斯指数相关性与投资组合风险度量研究-金融学专业论文.docxVIP

I I 摘 要 由于金融市场数据常常呈现非正态、非对称的特点，传统的相关性分析方 法在使用上受到限制。Copula 函数在刻画金融市场之间的相关性方面有独特的 优势，能够捕捉到随机变量之间非正态、非对称的相关结构，并通过分析尾部 相关性，为风险管理提供了一种有效的新途径。实证研究表明，Copula 方法可 以较好地描述上证指数与道琼斯指数之间的相关性结构。通过估计模型参数和 欧式平方距离检验，找到拟合程度最佳的 Copula 函数。接着用 Gumbel Copula 函数和 Clayton Copula 函数对股票市场之间的尾部相关程度进行刻画，表明在 整个数据样本观察期间，上证指数与道琼斯指数的上下尾相关关系都很弱；而 且从观察的前后两个阶段表明，上证指数与道琼斯指数的相关关系在后一个阶 段比前一个阶段还要弱。最后计算基于 Copula 函数计算的投资组合 VaR 优于传 统正态模拟计算的 VaR。通过股票市场的相关性分析，将有助于投资者进行跨 市场组合投资分析，从而分散风险。此外，有利于政府监管部门对于维持我国 证券市场的正常运行，抵御外来金融风险冲击，也对相关政策的制定具有一定 的参考价值。 关键词：Copula 函数，相关性，上证指数，道琼斯指数 II II Abstract Financial market data often appear non-normal, non-symmetrical features, the traditional correlation analysis method is in restricted use. Copula function has a unique advantage in portraying the correlation between the financial markets, to capture the random variables of non-normal, non-related structure symmetry. Through the analysis of the tail dependence, Copula theory provides a new and effective way for the risk management. Empirical study shows that the Copula method can be used to describe the correlation structure between Shanghai Composite Index and the Dow Jones index. By estimating the model parameters and the squared Euclidean distance test, we can find the best fitting degree of Copula function. We use the Gumbel Copula function and Clayton Copula function to describe the tail dependence degree on the stock market. It shows that the tail dependence between Shanghai Composite Index and the Dow Jones index is very weak in the entire data samples. It also presents that the correlation between the Shanghai Composite Index and the Dow Jones index in stage II is much less than the figure in the previous stage. Finally, the calculation of portfolio based on Copula function VaR is superior to the traditional normal simulation VaR. By the analysis of the correlation of stock market, it will help investors to analyze the financial market, thereby to disperse the risk. In addition, it is conducive to the supervision depar