基于Copula函数的GARCH模型的贝叶斯分析及实证

发布时间：2018-07-18 08:19

【摘要】：在金融市场中，GARCH模型对金融时间序列波动性的解释，已经得到大多数学者的认同。但是对于不同的市场之间，或者不同的资产之间，往往存在着相互影响波动的相关关系。同时为了分散、化解金融风险，，需要对多个资产进行组合，进行风险的对冲和规避，这些都是建立在对多个市场之间相关特性进行分析的基础之上。由于常用与研究多变量问题的多元GARCH模型在参数估计、多元分布假设等问题上存在一定的局限性，而Copula技术能解决这一些问题。Copula函数不仅为我们提供了一条在不考虑边缘分布的情况下分析多元分布相关结构的途径，还为求取联合分布函数提供了一条便捷的通道。而且若对变量作单调增的变换，相应的Copula函数不变，因而有Copula函数导出的一致性质和相关性测度的值也不会变化。本文结合Copula技术与GARCH模型来处理金融风险分析中多个资产间或多个市场间的相关性就方便多了。另外，在大多数文献中，对于GARCH模型、Copula函数的参数估计是采用频率学派的观点，而利用参数的先验信息采用贝叶斯参数估计，能更充分挖掘出数据中的信息，另一方面也扩充了模型估计的方法。最后本文的实证部分，针对上证综合指数和深证成指，利用T-Copula-GARCH-T模型预测0.05置信度下的1天提前期VaR值。
[Abstract]:The interpretation of financial time series volatility by GARCH model in financial markets has been accepted by most scholars. However, for different markets, or between different assets, there is often a correlation between the impact of volatility. At the same time, in order to disperse and resolve financial risks, it is necessary to combine multiple assets, hedge and circumvent the risks, which are based on the analysis of the related characteristics of multiple markets. The multivariate GARCH model, which is commonly used and studied for multivariate problems, has some limitations in parameter estimation, multivariate distribution assumptions, and so on. Copula technology can solve these problems. Copula function not only provides a way to analyze the correlation structure of multivariate distribution without considering the edge distribution, but also provides a convenient way to obtain the joint distribution function. Moreover, if the variable is monotonously increased, the corresponding Copula function is invariant, so the uniform property derived by the Copula function and the value of the correlation measure will not change. This paper combines Copula technology and GARCH model to deal with the correlation between multiple assets or markets in financial risk analysis. In addition, in most literatures, the parameter estimation of the Copula function of GARCH model is based on the viewpoint of frequency school, and Bayesian parameter estimation can be used to extract the information from the data more fully by using the prior information of the parameter. On the other hand, the method of model estimation is extended. Finally, in the empirical part of this paper, the T-Copula-GARCH-T model is used to predict the VaR value of 1-day lead time under the confidence level of 0.05 for Shanghai Composite Index and Shenzhen Stock Exchange Index.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;F224;O212.1

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