基于贝叶斯估计的Copula方法在金融分析上的应用

发布时间：2018-06-07 17:41

本文选题：Copula理论 + 贝叶斯估计　；参考：《湖南大学》2013年硕士论文

【摘要】：随着我国对外经济贸易的日渐开放，金融衍生产品不断地引进和完善，国内金融市场也日益复杂和多样化。处在金融危机频发的时代，如何采用合理的方法来度量金融市场的风险则显得相当重要。 Copula理论可以度量变量之间的非线性相关关系，并能够将边缘分布和联合分布分开来考虑，故其成为当下处理金融风险的一把利器。如何选择一个合适的边缘分布对于Copula建模起着至关重要的作用，很多实证表明GARCH-t模型能够很好地描述金融时间序列“尖峰厚尾”的特性，传统GARCH模型的参数估计采用的是极大似然估计方法，当遇到目标函数没有极大值时，传统方法很难实现目标函数的数值最优化。贝叶斯估计是建立在贝叶斯理论基础之上，将待估参数看成随机变量，结合先验信息和数据信息从而得到参数的后验密度，在此基础之上做进一步的统计推断。与传统方法相比，通常贝叶斯估计量具有更小的方差或平方误差，，能够得到更精确的预测结果，贝叶斯最大后验置信区间比不考虑参数先验信息的频率置信区间短。将贝叶斯估计方法应用于GARCH模型的参数估计，能够很好地解决传统估计中遇到的一系列问题，同时GARCH模型一系列的约束条件也适合用贝叶斯估计方法。本文在介绍Copula理论和贝叶斯理论的基础之上，采用贝叶斯估计方法来进行时变Copula-GARCH模型的建立，最后以农林、制造、运输、地产和文化五个指数作为研究对象，考察了其常相关和时变相关关系，并基于Z检验方法，考察了其变结构情况，研究结果表明：2011年11月份地产行业由于受国家政策限制、库存激增及地产商资金紧缺的影响，其与制造指数、文化指数的结构发生了显著变化。
[Abstract]:With the opening of China's foreign economy and trade, financial derivatives are continuously introduced and perfected, and the domestic financial market is becoming more and more complex and diversified. In the times of frequent financial crisis, it is very important to adopt reasonable methods to measure the risk of financial market. Copula theory can measure the nonlinear correlation between variables, and consider the edge distribution and joint distribution separately. Therefore, it has become a sharp weapon to deal with financial risks. How to choose an appropriate edge distribution plays an important role in Copula modeling. Many empirical results show that GARCH-t model can well describe the characteristics of financial time series "peak and thick tail". The parameter estimation of traditional GARCH model is based on the maximum likelihood estimation method. When the objective function has no maximum value, the traditional method is difficult to realize the numerical optimization of the objective function. The Bayesian estimation is based on Bayesian theory. The parameters to be estimated are regarded as random variables, and the posterior density of the parameters is obtained by combining the prior information with the data information, and further statistical inference is made on this basis. Compared with the traditional methods, Bayesian estimators usually have smaller variance or square error, and can obtain more accurate prediction results. The Bayesian maximum posterior confidence interval is shorter than the frequency confidence interval which does not take into account the prior parameter information. Applying Bayesian estimation method to parameter estimation of GARCH model can solve a series of problems encountered in traditional estimation. At the same time, a series of constraints of GARCH model are also suitable for Bayesian estimation. Based on the introduction of Copula theory and Bayesian theory, Bayesian estimation method is used to establish the time-varying Copula-GARCH model. Five indexes of transportation, real estate and culture were studied as the research object, and the variable structure was investigated based on the Z test method. The results show that the structure of real estate industry and manufacturing index and culture index changed significantly in November 2011 due to the restriction of national policy, the surge of inventory and the shortage of real estate capital.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;F224;O212.8

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