Copula Models And Its Application In The Stock Market Relevance

With the international trade deepening and restrictions on capital flows, technology transfer and the provision of services between different countries released, the global economy and financial markets have formed an interdependent and interrelated organic economy and finance whole. Price collaborative movement between global financial markets makes local fluctuations in the financial markets in any country would quickly spread and magnify to other financial markets, resulting in a huge butterfly effect. The correlation between financial markets become more and more complex, which show an asymmetric, nonlinear and tail related structures. Nevertheless, the Copula function proposed by Sklar has many unparalleled advantages which the traditional methods of measuring correlation can’t achieve. It can capture the non-linear correlation between random variables. Meanwhile, the Copula function can quickly and effectively capture the non-normal and tail asymmetric relevant information. When we use Copula theory to establish financial series model, the marginal distribution of the variables and the correlated structure between them can be studied separately where the correlated structure can be described by a Copula function, which greatly simplifies the variables modeling problem. Therefore, the study of correlations between financial markets using Copula theory has very important theoretical significance and application value.The focus of this research papers includes three parts. Firstly, we discuss the nature of Copula function and its family in detail and introduce several intuitive graphical test methods in the correlation measure including by observing the sample rank pairs to judge the correlations between variables and proposing the Chi-plot and K-plot testing methods on the basis of the sample rank pairs. Secondly, the parameter estimation method and semi-parametric valuation method are made a brief comparison, analyzing the advantages and disadvantages of both. Meanwhile, we introduce a method in testing the effect of model fitting on basis of semi-parametric estimation, Sn method.Thirdly, using the parameter estimation method and the semi-parametric valuation methods empirical analyze the correlation between the index return series of Shanghai and Shenzhen stock market. Through a variety of Copulas function screening, we found that the ability of Gumbel Copula function and t-Copula function to describe the overall correlation structure are better, but when we examine the tail correlation, M-Copula function is more suitable.The innovations of this paper lie in introducing several intuitive graphical test methods in the correlation measure and analyzing the correlation between the indices return series of Shanghai and Shenzhen stock market.