Copula函数在投资组合风险价值度量中的研究和应用

发布时间：2019-05-13 17:25

【摘要】：金融市场充满风险，，投资者面临两个重要的问题：一是当某一金融市场出现巨大波动时，其他金融市场会不会受影响？二是当持有某个投资组合时，投资者所面临的风险有多大，如何度量投资组合的在险价值VaR？考虑到Copula函数能更有效地捕捉金融资产之间的相关信息，其在金融市场之间的尾部相关性分析和投资组合的VaR计量上具有独特的优势，本文采用Copula函数分别对这两个问题进行研究，包括两个部分的实证分析。要解决的第一个问题，便是基于Copula函数导出两个金融市场之间的尾部相关性，以沪深300指数和香港恒生指数的日收益率序列为研究对象，分析二者之间的相关结构变动，从秩相关性和平方欧氏距离两个评价指标得出在五个Copula函数族模型中哪一个能更好地拟合观测数据。其次，要解决的第二个问题，是将Copula技术应用到投资组合的VaR度量中，并和传统的方法进行了比较。所选取的Copula函数族包括正态Copula、t-Copula、Clayton-Copula、Frank-Copula和Gumbel-Copula，结果表明：基于Copula算法计算的VaR的绝对值在大多数情况下普遍大于传统算法计算的结果，说明传统的VaR计算方法低估了风险。Copula函数由于更加充分地考虑了变量之间的相关性，而且不囿于正态性假设，所以能更大程度地考虑风险。
[Abstract]:Financial markets are full of risks, and investors face two important questions: first, will other financial markets be affected when there is great volatility in one financial market? The second is how much risk investors face when holding a certain portfolio, and how to measure the in-risk value VaR? of the portfolio. Considering that the Copula function can capture the relevant information between financial assets more effectively, it has unique advantages in tail correlation analysis between financial markets and VaR measurement of portfolio, In this paper, Copula function is used to study these two problems, including two parts of empirical analysis. The first problem to be solved is to derive the tail correlation between the two financial markets based on the Copula function. Taking the daily return series of the Shanghai and Shenzhen 300 index and the Hang Seng Index of Hong Kong as the research object, the related structural changes between the two are analyzed. From the two evaluation indexes of rank correlation and square Euclidean distance, which of the five Copula function family models can better fit the observed data is obtained. Secondly, the second problem to be solved is to apply Copula technology to the VaR measurement of portfolio and compare it with the traditional method. The selected Copula function family includes normal Copula,t-Copula,Clayton-Copula,Frank-Copula and Gumbel-Copula, results show that the absolute value of VaR calculated based on Copula algorithm is generally larger than that calculated by traditional algorithm in most cases. It is shown that the traditional VaR calculation method underestimates the risk. Copula function can consider the risk to a greater extent because it considers the correlation between variables more fully and is not confined to the normality hypothesis.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

【参考文献】