【作者】 陈功；

【导师】 程希骏；

【作者基本信息】 中国科学技术大学 ， 金融工程， 2009， 硕士

【摘要】 对金融资产间相关性的研究,是金融理论和实践中的一个基础性问题。在涉及到多个资产的许多场合,比如资产定价、资产选择、波动溢出以及风险管理中,都需要考虑资产间的相关性。而我们知道,金融市场是一个由复杂的动态系统,相关性结构也受到很多内外因素的影响,如果将相关性视为固定不变,会有失偏颇。因此在处理金融资产间的相关性时,考虑其动态结构是非常有意义的。对相关性动态演化过程的描述有几种不同的方法,本文考虑了其中的两种描述方法。一种是时变相关性模型,其特点是相关性在时刻变化。另一种是状态转换模型,其特点是相关性指标在某一状态下是固定不变的,而在不同状态之间则有所区别,在不同状态间的转移过程服从一个马氏链。在前一类模型中,具有代表性的是Engle提出的DCC模型,该模型简洁地刻画了相关性的时变演化过程,同时具有估计上的优势。我们通过引入Copula函数的概念,指出DCC模型是一种特殊的正态Copula模型,进而将其推广到广义形式。我们使用灵活的边缘分布来取代DCC模型中的正态假设,分别构建了正态Copula和t-Copula下的广义DCC模型。对我国股市的实证研究表明,使用厚尾分布如t分布、GED分布为边缘分布,可以更好地度量投资组合在99%置信水平下的VaR值。在后一类模型中,我们通过在Copula函数中引入状态变量,构建了一类含有状态转换的Copula模型。我们讨论了该模型下的一般应用,并分析了该模型在相关性度量上的特点。对于我国股市的实证研究表明,使用状态转换Copula模型可以很好地解释相关性在不同行情走势下的区别。更多还原

【Abstract】 The issue of dependence between financial assets is a foundational issue in modern financial theory and practice. In many applications related with assets of more than two, such as asset pricing, asset selection, volatility spillover and risk management, the measure of association between assets need to be taken into account. As we all know, financial markets are complicated dynamical systems. The dependence structure is impacted by lots of factors inside and outside the markets. It would be inappropriate to set the measure of association invariable. Therefore, when we deal with the measure of association between financial assets, the consideration of dynamic structure is meaningful.There are several different ways to describe the dynamic structure of the dependence. In this article, we have considered two description methods. One is the time-varying model; the measure of association is different at each time. The other is the regime switching model; the measure of association is constant within a regime but different across regimes. The transitions between the regimes are governed by a Markov chain.In the former kind of model, the Dynamic Conditional Correlation (DCC) model proposed by Engle is representative. The model describes the evolution path of the time-varying correlation with parsimonious parametric while providing a simple method of estimation. In this paper, we introduce the concept of Copula and point out that the DCC model is a particular case of multivariate Normal copula model, thus extend it to the general form. We use flexible marginal distribution to replace the normal distribution assumption, construct generalized DCC model under the multivariate Normal copula and the multivariate Student’t copula (t-Copula). Empirical study on Chinese stock markets have shown that using the heavy-tailed distribution such as student(t) distribution and Generalized error distribution for the marginal distribution can measure the Value at risk (VaR) of the portfolio in the 99% confidence level better .In the latter kind of model, through introducing state variable into Copula, we build one regime switching Copula model. We discuss the general application under this model and analyze the features of the measure of association in this model. Empirical study on Chinese stock markets have shown that regime switching Copula model can be applied to explain the differences in the dependence between different market quotation .更多还原