基于极值理论的沪深股票市场相关性分析

发布时间：2018-02-11 16:25

本文关键词： 风险价值 TGARCH模型 POT模型 Copula函数　出处：《中央民族大学》2012年硕士论文　论文类型：学位论文

【摘要】：金融时间序列具有尖峰厚尾性、自相关性、波动集簇性和波动非对称性等特征,所以本文基于极值理论和GARCH理论,利用TGARCH-POT模型分别建立了上证指数和深圳成指的边缘分布函数。在经济全球化的背景下,金融市场不是封闭和孤立的,不同市场之间,或者不同资产之间,往往存在相互影响和波动的相关关系。描述两个市场相关结构的传统做法是选取t-Copula函数,但t-Copula函数具有对称性,对于变量间的非对称尾部相关并不适合。在阿基米德Copula函数中,Gumbel Copula和Clayton Copula函数的密度函数都具有非对称性,能够很好的描述市场间的尾部相关性。因此本文考虑从Gumbel Copula和Clayton Copula函数中选取一个适当的Copula函数来描述沪深股市的相关结构。我们选取上证指数和深圳成指2002年至2011年10年的数据做实证分析,运用Copula蒙特卡洛模拟计算出来的VaR与真实值比较得到2010年和2011年的不同置信水平下的失效天数。从中可以看到,(1) TGARCH-POT-Copula相比GARCH-t-Copula有效,这说明了利用极值理论中的POT模型改进了边缘分布,而GARCH-t-Copula显然低估了风险。(2)在201O年和2011年,TGARCH-POT-Gumbel Copula相比TGARCH-POT-Clayton Copula有效,主要原因可能是经过08年金融危机后,经济开始复苏,投资者信心开始增强,所以Gumbel Coupla函数比较适合描述这两个市场在这期间的相关结构。
[Abstract]:Financial time series have the characteristics of sharp peak and thick tail, autocorrelation, volatility cluster and volatility asymmetry. Therefore, based on the extreme value theory and GARCH theory, the TGARCH-POT model is used to establish the edge distribution function of Shanghai stock index and Shenzhen index respectively. In the context of economic globalization, financial markets are not closed and isolated, between different markets, or between different assets. The traditional way to describe the structure of two markets is to choose t-Copula function, but t-Copula function has symmetry. It is not suitable for asymmetric tail correlation between variables. In Archimedes Copula function, the density functions of Gumbel Copula and Clayton Copula are both asymmetric. Therefore, this paper considers choosing an appropriate Copula function from the Gumbel Copula and Clayton Copula functions to describe the relevant structure of Shanghai and Shenzhen stock markets. We choose the data of Shanghai Stock Exchange Index and Shenzhen Cheng Index from 2002 to 2011 for empirical analysis. By comparing the VaR calculated by Copula Monte Carlo simulation with the real value, the failure days of 2010 and 2011 at different confidence levels are obtained. It can be seen that TGARCH-POT-Copula is more effective than GARCH-t-Copula. This shows that the marginal distribution is improved by using the POT model in extreme value theory, while GARCH-t-Copula obviously underestimated the risk.) in 2010 and 2011, TGARCH-POT-Gumbel Copula was more efficient than TGARCH-POT-Clayton Copula, probably because the economy began to recover after the 2008 financial crisis. Investor confidence is beginning to grow, so the Gumbel Coupla function is more appropriate to describe the structure of the two markets during this period.
【学位授予单位】：中央民族大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F832.51

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