数学理论与应用 ›› 2016, Vol. 36 ›› Issue (4): 106-115.

• • 上一篇    下一篇

Copula函数在金融市场中的应用

董智前, 李星野   

  1. 上海理工大学管理学院,上海,200093
  • 出版日期:2016-12-30 发布日期:2020-09-27

Application of Copula Function in Financial Market

Dong Zhiqian, Li Xingye   

  1. Business School,University of Shanghai for Science and Technology,Shanghai 200093,China
  • Online:2016-12-30 Published:2020-09-27

摘要:

本文旨在通过构造Copula模型,研究股市大盘和房地产(万科)股票之间的相关性与极值情况下的尾部相关性.在边缘分布的求取上,选用非参数核密度法分别估算出股市大盘和房地产股票的边缘分布函数值;在Copula函数的选择上,为选出最优Copula模型,选用多种方法结合包括二元分布直方图法、Q-Q图法、平方欧氏距离法;在Copula函数的参数估计上,采用惯用的极大似然估计法(MLE).其中,Q-Q图法首

次应用在检验无分布函数的数据上.分析结果展现出二元t-Copula模型相对其他Copula模型可以更佳地拟合出这两支股票的联合分布;大盘股票与万科股票趋于较强的正向相关性;而极值情况下的尾部相关性相比一般时刻的正向相关性有所降低.

关键词: 尾部相关性, 非参数核密度估计, Q-Q图法, 平方欧氏距离, t-Copula

Abstract: The paper studies the correlation between the stock market and the real estate stock(Vanke)and the tail dependence by establishing a copula model.Marginal distributions of the stock market and the real estate stock are estimated by the non-parametric kernel density estimation method.An optimal copula model is constructed by making use of the bivariate distribution histogram,quantile-quantile(Q-Q)plot,square Euclidean distance.Parameters in the model are estimated by the maximum likelihood estimation(MLE)method.Q-Q plot is applied on the test data without distribution function.The results show that the Binary t-copula model can fit the joint distribution of market and Vanke better than other models,the market and Vanke stock have a strong positive correlation,and the tail dependence under extreme cases is lower than the positive correlation under general cases.

Key words: Tail dependence, Non-parametric kernel density estimation, Q-Q plot, Square Euclidean distance, t-copula