基于Bayes-Copula的金融市场相关性分析

发布时间：2018-05-24 13:05

本文选题：股票市场 + Copula函数　；参考：《湖南大学》2014年硕士论文

【摘要】：现如今，股票市场不管是一级市场还是二级市场，都是监管者与投资者关注的核心，也是投资者与筹资者互相博弈的一个市场，而市场分析者在投资者与筹资者之间起到桥梁作用。市场分析者在研究金融市场上独特的尖峰与厚尾特性的过程中，，使得以往使用基于正态分布假设的分析突显不足，本文主要利用Clayton、Gumbel及Frank三个Copula函数构建的混合Copula函数将金融市场之间的结构进行整体刻画。本文前几章对Copula函数的含义与性质进行了简单回顾，阐述了几种通用的Copula函数，并将该函数的参数与几种相关系数之间的对应关系进行了描述。接着介绍了金融市场上时间序列模型，包括参数与非参数估计，主要介绍核估计法。然后讲述了贝叶斯理论及贝叶斯的计算方法，并且将基于Mix-Copula函数与经验Copula的三元线性模型的似然函数与后验密度函数进行了贝叶斯推断。将bayesian理论运用到Mix-Copula函数当中权重系数的估计，对Experience-Copula函数与Mix-Copula函数进行线性拟合。文中将上证指数与深圳成指2009~2013年每日的历史收盘价作为样本进行分析，分析数据的基本统计特征，利用核估计法对两个样本变量进行边缘分布估计，然后利用阿基米德Copula函数建立四种不同Copula函数进行分析，运用欧氏距离对四种不同的函数进行拟合检验，最后选出一组相对最优的Copula函数，并将利用贝叶斯方法与非线性规划方法估计出的结果进行比较，通过比较结果来看，贝叶斯方法也能达到经典方法的效果，甚至更好，基于贝叶斯的混合Copula函数同时得到两者之间的上尾相关系数与下尾相关系数。
[Abstract]:Nowadays, the stock market, whether it is a primary market or a secondary market, is the core of the attention of regulators and investors, and is also a market in which investors and financiers play games against each other. Market analysts act as a bridge between investors and financiers. Market analysts in the process of studying the unique peak and thick tail characteristics of financial markets make the past analysis based on the normal distribution hypothesis highlighted the insufficiency. In this paper, the structure of financial markets is described as a whole by using the mixed Copula functions constructed by Clayton Gumbel and Frank functions. In the first chapters of this paper, the meaning and properties of Copula function are briefly reviewed, several general Copula functions are expounded, and the corresponding relations between the parameters of the function and several correlation coefficients are described. Then it introduces the time series model in financial market, including parametric and nonparametric estimation, and mainly introduces kernel estimation method. Then, the Bayesian theory and the calculation method of Bayesian are described, and the Bayesian inference of the likelihood function and the posterior density function of the ternary linear model based on Mix-Copula function and empirical Copula is carried out. The bayesian theory is applied to the estimation of the weight coefficient in the Mix-Copula function, and the linear fitting between the Experience-Copula function and the Mix-Copula function is carried out. In this paper, the daily historical closing price of Shanghai Stock Exchange Index and Shenzhen Chengdu Index from 2009 to 2013 are analyzed as samples, the basic statistical characteristics of the data are analyzed, and the marginal distribution of two sample variables is estimated by using kernel estimation method. Then four different Copula functions are established by using Archimedes Copula function to analyze, and Euclidean distance is used to test the fitting of four different functions. Finally, a group of relatively optimal Copula functions are selected. The results estimated by using Bayesian method and nonlinear programming method are compared. The results show that the Bayesian method can also achieve the effect of classical method, or even better. The mixed Copula function based on Bayesian is used to obtain the upper tail correlation coefficient and lower tail correlation coefficient.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.9

【参考文献】