摘要
随着金融全球化进程的加快，金融市场面临的风险日益复杂和多样化，金融市场和金融风险度量的相关模式呈现出非线性、非对称和尾部相关等特征。原有的基于正态分布假设的线性相关系数的分析方法已不再适合描述金融风险的相关信息。Copula函数是很好的描述相关结构的工具，可以非常好地度量金融市场的各种复杂相关模式和相关程度。所以本文从应用的角度全面系统地探讨了Copula函数在各种金融风险度量中的应用。
理论部分归纳整理了国内外关于Copula函数在主要金融风险中的研究现状，指出Copula函数的应用价值。在详细总结Copula函数的基本理论和特点基础上，对由Copula函数导出的相关性度量指标进行深入的分析。文章研究的重点是Copula函数在金融市场风险、信用风险、操作风险、整体风险度量和危机传染检验中的应用。
在实证研究中，针对市场风险应用基于极大似然思想的非参数核密度方法估计Copula函数的参数，并通过沪深两市相关结构的研究对方法进行了验证。实证结果表明：两市的相关程度比较强，相关结构是Frank Copula函数。该结论与当前中国股市的现状吻合。应用Copula函数不仅能得出两市的相关程度，还可以描述相关模式，其相关性刻画能力要优于传统的方法。关于信用风险的度量，主要是针对Credit Metrics模型的联合概率转移矩阵应用Copula理论，进行双参数Copula函数的参数估计。并用4只债券组合做例证，得到了基于Copula函数的信用VaR。Copula函数在信用评级方法较为完善系统时，能比较好地度量信用风险。另外，针对当前美国金融危机，用Copula方法对“金砖四国”的受传染效应进行了检验。通过对比危机发生前后的相关程度和相关模式，发现巴西是受传染程度最深的国家，中国目前受传染的迹象还不大明显。这个结果很具有现实意义。通过进一步分析，发现这种危机传染结果，与一国资本市场的开放程度、经济增长模式等因素有关。
With the fast development of financial globalization, the risks financial market faced become more complicated and diversified than ever before. Financial risks display non-linear, non-symmetric and tail dependence modes. The linear correlation coefficient based on traditional assumption of normal distribution has been no longer suitable to describe the dependent patterns of financial markets. Copula function is a good tool to describe dependence structure, which can measure both dependence modes and extents of financial market. The main points of this dissertation are exploring the applications of Copula function systematically in a variety of financial risk measurements from the perspective of the application.
The dissertation reviews the research status in the financial risk measurements of Copula function all over the world, points out Copula function's value and deeply analyzes the dependent indexes concluded by the Copula function. The focus is applications of the Copula function about measurements of financial market risk, credit risk, operational risk, integrated risk and test of financial crisis contagion.
During the empirical study on market risk, I choose non-parametric kernel density method based on the idea of maximum likelihood to estimate Copula functions' parameters, and tested the method by analyzing the dependent structure between Shanghai and Shenzhen stock markets. The empirical result shows that there exists a high extent of dependence and Frank Copula dependence mode between the two markets. This conclusion coincided to the real status of China stock market. Copula function is superior to traditional methods in the description of dependence. Not only can it measure the extent, but also can describe the pattern of dependence. On credit risk, the aim is to estimate the parameters of two-parameter Copula function. The method used in the article is applying Copula theory for joint probability transfer matrix in the Credit Metrics model. Four-bond portfolios have been used to do examples, and got the credit VaR based on the Copula theory. The advantages of this approach are simple and easy to operate, which can be more accurate to measure credit risk under the premise of perfect credit rating system. Finally, a test was done for financial crisis contagion about the "BRICs" with Copula methods under the current United States financial crisis. By comparing the extent and mode of dependence during pre-and post-crisis periods, points out that the Brazil is the most infected one among four countries, and China is the true "Bric", there are no obvious signs to reflect infection in China. This result is meaningful. The results are related to the degree of openness of capital markets, economic growth patterns and other factors by further analysis.
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