基于强Copula混合理论的股市风险实证分析

发布时间：2018-02-25 02:22

本文关键词： 几何加权平均混合Copula 最小二乘估计 Gibbs抽样 GARCH　出处：《华南理工大学》2013年硕士论文　论文类型：学位论文

【摘要】：随着金融全球化和金融创新步伐的加快，金融市场的风险分析发展很快，Copula函数成为一种新兴的金融分析工具。由于Copula可以捕捉变量间非线性、非对称及尾部相关性，为投资者提供竞争优势和可观收益，故在国内外得到广泛应用。但简单的Copula函数适合特殊情形的金融市场，与现实复杂的金融市场仍存在较大差别。混合Copula函数不仅可以用来描述股票市场之间上尾相关、下尾相关和对称相关三种模式，还可以描述金融市场之间上尾、下尾相关并存的非对称相关模式，与具有复杂相关关系的金融市场更加接近。而我们常见的是线性Copula混合模型，本文提出一种新的Copula混合模型-几何加权平均混合模型。本文的重点是要验证该混合模型在实证中的有效性。本文以2007年1月4日到2012年12月31日金融和地产日收盘价指数收益共1460组数据为例，从以下方面进行模型构建： (1)边缘分布的确定。由于边缘分布不是本文考察的重点，故选取常用的GARCH(1,1)-t模型。但作为异方差模型必须首先进行ARCH效应检验，本文选取残差平方的相关图检验法。 (2)Copula函数参数的确定。为了采用Genest and Rivest非参数估计单一Copula模型的参数，本文总结出阿基米德Copula函数中kendall’s秩相关与参数的关系式。而混合模型中未知参数较多，，包括单一Copula函数中的参数和权重两大类。针对参数的研究，本文提出了最小二乘估计法与Gibbs抽样，有效地解决模型中参数确定问题。 (3)模型的有效性检验。通过联合分布直接求VaR相对比较复杂，本文结合MonteCarlo模拟近似估计几种模型的联合分布VaR，并对它们分别进行后验测试。通过分析后验测试结果，我们发现相对单一Copula模型而言，该混合Copula模型的失效天数相对较少。作为一种新型的混合模型，它提高了风险预测的精度，从而比较真实地描述投资组合的风险，具有一定的经济价值。
[Abstract]:With the acceleration of financial globalization and financial innovation, the risk analysis of financial markets has developed rapidly. Copula function has become a new financial analysis tool. Because Copula can capture the nonlinear, asymmetric and tail correlation between variables. It is widely used at home and abroad because it provides investors with competitive advantage and considerable income. But the simple Copula function is suitable for special financial market. The mixed Copula function can be used not only to describe the upper tail correlation, lower tail correlation and symmetric correlation among stock markets, but also to describe the upper tail of financial markets. The asymmetric correlation model with coexisting lower tail correlation is closer to the financial market with complex correlation, but we often use the linear Copula mixed model. In this paper, a new Copula hybrid model, geometric weighted average hybrid model, is proposed. The focus of this paper is to verify the validity of the hybrid model. This paper takes 1460 groups of financial and real estate daily closing index returns from January 4th 2007 to December 31st 2012 as an example to build the model from the following aspects:. (1) the determination of edge distribution. Because the edge distribution is not the focus of this paper, we select the commonly used GARCHN 1GARCHN 1T model. However, as a heteroscedasticity model, we must first test the ARCH effect, and select the correlation graph test method of the residual square in this paper. In order to use Genest and Rivest to estimate the parameters of a single Copula model, the relationship between kendall's rank correlation and parameters in Archimedes Copula function is summarized in this paper. There are two kinds of parameters and weights in a single Copula function. In this paper, the least square estimation method and Gibbs sampling are proposed to solve the problem of parameter determination in the model. It is relatively complex to obtain VaR directly by joint distribution. In this paper, the joint distribution of several models is estimated by using MonteCarlo simulation approximation, and a posteriori test is carried out on each model. By analyzing the results of a posteriori test, we find that the failure days of the hybrid Copula model are relatively small compared with a single Copula model. As a new hybrid model, it improves the accuracy of risk prediction. Therefore, it is of certain economic value to describe the risk of the investment portfolio more truthfully.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;O212.1

【参考文献】