Copula理论及其在金融市场相依性分析中的应用

发布时间：2018-03-06 19:11

本文选题：Copula函数　切入点：高频金融数据　出处：《电子科技大学》2013年硕士论文　论文类型：学位论文

【摘要】：掌握金融变量间的相依结构是研究金融体系的运作模式，提高投资策略准确率的基础和关键所在。Copula函数具有传统相关性分析方法不具备的刻画非线性、非对称相依结构的能力，尤其是在刻画尾部相关性的能力方面具有明显的优势，恰恰符合了研究者对金融变量相依结构分析的需求。论文从Copula函数的定义、主要性质、种类以及相应的相关性测度等方面对Copula理论做了系统的介绍，并梳理和总结了Copula模型的建立方法和步骤，包括边缘分布的确定方法，参数估计方法，Copula模型的选择和模型拟合优度评价，着重研究了Copula函数的参数估计方法，讨论了精确极大似然估计（EML估计）、分步估计（IFM估计）、基于样本经验分布函数的CML估计、基于核密度估计方法的MLK方法以及GenestRivest估计法，通过分析和蒙特卡洛模拟给出了它们的适用条件，并得到结论：当样本边缘分布难以确定，或者边缘分布拟合效果不好的时候，MLK估计是最佳参数估计方法。将Copula理论应用到高频金融数据的相依结构分析中。根据高频数据的特点，构造了结合BP神经网络拟合和Copula函数的新模型，并实证了该模型能够比较有效地刻画股指期货每分钟绝对收益率和成交量的相依结构。首先采用BP神经网络方法拟合并消除日历效应，再用核密度估计方法来确定边缘分布，并根据边缘分布的频率直方图，分别选取Gumbel Copula函数和混合阿基米德Copula函数对其进行拟合，最后利用多种相依性测度来评价模型拟合的效果。结果表明：相关参数为(?)=1.5421的Gumbel Copula模型很好的描述和刻画了股指期货每分钟绝对收益率和成交量之间的相依结构，捕捉到了两者之间明显的上尾相关性和下尾渐近独立性，并从投资行为学上进行解释：当市场波动剧烈时，即交易会导致较大的收益或者损失时，投资者为了获得收益或者保本，交易欲望就会增强，导致交易量的上涨，，而当市场波动很小时，投资者基于自己对未来市场的预期，会保持一定的交易量。
[Abstract]:Mastering the dependent structure among financial variables is the basis of studying the operation mode of financial system, improving the accuracy of investment strategy and the key. Copula function has the ability to describe the nonlinear and asymmetric dependent structure that the traditional correlation analysis method does not have. Especially, it has obvious advantages in the ability to depict the tail correlation, which is exactly in line with the researchers' demand for the analysis of the dependent structure of financial variables. This paper systematically introduces the Copula theory from the definition of Copula function, the main properties, the types and the corresponding correlation measures, and summarizes the methods and steps of establishing Copula model, including the method of determining the edge distribution. The method of parameter estimation is the selection of Copula model and the evaluation of model goodness of fit. The parameter estimation method of Copula function is emphatically studied, and the accurate maximum likelihood estimation, step estimation and CML estimation based on sample empirical distribution function are discussed. The MLK method and GenestRivest estimation method based on kernel density estimation method are analyzed and Monte Carlo simulations are used to give their applicable conditions, and the conclusion is drawn: when the sample edge distribution is difficult to determine, Or MLK estimation is the best parameter estimation method when the fitting effect of edge distribution is not good. The Copula theory is applied to the dependent structure analysis of high frequency financial data. According to the characteristics of high frequency data, a new model combining BP neural network fitting and Copula function is constructed. The model is proved to be able to describe the dependent structure of absolute yield per minute and turnover of stock index futures effectively. Firstly, BP neural network method is used to merge to eliminate calendar effect, and then the kernel density estimation method is used to determine the edge distribution. According to the frequency histogram of the edge distribution, the Gumbel Copula function and the mixed Archimedes Copula function are selected to fit them respectively. Finally, a variety of dependency measures are used to evaluate the effect of the model fitting. The Gumbel Copula model of Gui 1.5421 well describes and depicts the dependent structure between the absolute yield per minute and the trading volume of stock index futures, and captures the obvious correlation between the upper tail and the tail and the asymptotic independence of the lower tail. And explain from the view of investment behavior: when the market fluctuates violently, that is, when the trading will lead to a large profit or loss, the investor's desire to trade will increase in order to obtain the income or to keep the capital, which will lead to the increase of the trading volume. When the market volatility is very small, investors based on their future market expectations, will maintain a certain volume of trading.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.91

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