【作者】 韦艳华；

【导师】 张世英；

【作者基本信息】 天津大学 ， 管理科学与工程， 2004， 博士

【摘要】 本文主要研究Copula理论及其在多变量金融时间序列分析上的应用。论文在深入研究Copula理论的基础上，构建了基于Copula理论的多变量金融时间序列模型并系统地研究了它们的动态建模问题，最后研究了Copula模型在金融风险管理上的应用。论文的主要工作和创新点如下:1、针对线性相关系数与传统分析方法的不足，将Copula理论引入金融分析领域。在深入探讨Copula理论的基础上，系统研究了可由Copula函数导出的非线性相关性测度和尾部相关性测度，并论述了Copula理论在金融分析上的应用。2、相关性分析是多变量金融分析中的一个中心问题，论文在详细讨论几种重要Copula 函数在相关性分析上的应用特点的基础上，构建了基于Copula理论的多变量金融时间序列模型：Copula-GARCH和Copula-SV模型并探讨了它们的参数估计及检验问题。运用M-Copula-GARCH-t模型对上海和深圳股市之间的相关程度和相关模式进行了研究，结果表明该模型能够准确、全面地捕捉到各个时期市场间相关性的变化，正确地反映两个市场之间非对称的相关模式。3、分析了时变相关正态Copula模型和时变相关Joe-Clayton Copula模型两种常用的时变二元Copula模型及它们相关参数的动态演进过程，对上海各板块指数收益序列的实证研究表明，时变相关二元正态Copula模型可以较好的描述对各板块间动态的相关结构，其对序列间相关关系的刻画能力和预测能力均优于静态的常相关二元正态Copula模型。4、变结构是金融模型的基本特征，为了进一步研究金融市场之间相关结构的动态变化，提出了三类变结构Copula模型：分阶段构建的Copula模型、具有尾部变结构特性的RS-Copula模型和具有变结构边缘分布的变结构Copula模型，并研究了二元正态Copula模型变结构点的诊断方法。分别运用分阶段构建的Copula模型和RS-Copula模型对中国股市进行了研究，结果表明在刻画金融收益序列之间相关结构的能力上，变结构二元正态Copula模型优于时变相关二元正态Copula模型，RS-Copula模型优于相应的静态Copula模型。5、金融风险管理是Copula模型的重要应用领域。论文不仅深入的研究了可用于投资组合VaR分析的Monte Carlo仿真技术，还探讨了变结构Copula模型在金融传染分析中的一些具体运用。对上海股市的实证研究表明，结合具有不同边缘分布的Copula-GARCH模型和Monte Carlo模拟法来计算资产投资组合的VaR是可行、有效的。更多还原

【Abstract】 In this dissertation, copula theory and its applications in multivariate financial time series analysis are studied intensively. As a result of those researches, several multivariate financial time series models based on copula theory are proposed. Methods of constructing dynamic models and applications of copula models in financial risk management are also investigated systematically. The key points and main achievements of this work are listed as follows:1. Copula theory is introduced into financial analysis to avoid defects of linear correlation coefficient and classical analysis methods. Based on fully understanding of copula theory, we investigated measure of non-linear dependence and measure of tail dependence that can be derived from copulas. Applications of copula theory in finance are also studied.2. Dependence analysis is a central issue in multivariate financial analysis. Characters of several important copulas used in dependence analysis are discussed in this thesis and multivariate financial time series models based on copula theory, such as Copula-GARCH model and Copula-SV model, are established. Estimation and test methods of copula models are studied too. Consequentially, M-Copula-GARCH-t model is constructed and used to study the degree and patterns of dependence between Shanghai and Shenzhen stock markets. The empirical results show that strong degree and asymmetrical pattern of dependence between two markets can be described correctly and thoroughly using M-Copula-GARCH-t model. 3. Time-varying normal copula model and time-varying Joe-Clayton copula model are investigated carefully and evolution equations of their parameters are provided particularly. The empirical results from Shanghai stock market show that time-varying Copula-GARCH model is better than constant normal copula in the ability of description and prediction of dependence between financial series.4. Structural change is a key character of financial models. In order to catch dynamic dependence between financial markets, three types of structural changing models are provided. They are staged copula model, RS-Copula model with <WP=5>structural change in tail distribution and copula model with structural change in marginal distribution. At the same time, change-points detection methods of bivariate normal copula model are given in this thesis. Chinese stock markets are studied using staged copula model and RS-Copula model. The empirical results show that bivariate normal copula model with structural change is superior to time-varying bivariate copula model and RS-Copula model prevail against the static copula model in describing dependence between financial series. 5. Financial risk management is an important application area of copula technique. Not only are Monte Carlo simulation techniques which can be use to estimate portfolio Value-at-Risk investigated, but also some applications in financial contagion using structural changing copula models are discussed in this dissertation. The empirical results getting from Shanghai stock markets indicate that estimation method of portfolio Value-at-Risk, which is constructed by combining Copula-GARCH model having different marginal distributions with Monte Carlo simulation techniques, is feasible and effective.更多还原