On Equities Networks Of SZSE 100 Price Index Constituent Stocks Based On Copula Function

Network of equities contains a large number of economic information, in which speculators and investors are both active. From the perspective of national economic development, the stock market management, regulation, and general investment, the study of the stock market has an important significance. Network of equities is an effective tool to the correlation of the underlying assets in the financial market. Minimum spanning tree is an approach to building stocks network. Through the study of the network topology structures and clustering in network of equities, we can effectively understand the local and global performance. However, the traditional linear correlation coefficient can not describe the nonlinear correlation among variables and correlation in extreme state. The theoretical and empirical analysis of Shenzhen 100 Index constituent stocks illustrate the validity of the Copula theory.In this thesis, five kinds of relevant measures, including Pearson p, kendallr, kendall?l, based on t-Copula, kendall?G based on Gaussian Copula, kendall?Gum based on Gumbel Copula are used to define the Euclidean distances. Then, the method of minimum spanning tree is used to construct equities networks of the Shenzhen 100 Index, and its clustering, degree probability distribution, distance, and betweenness centrality are described. In addition, based on kendall?Gl, a series of dynamic evolving networks of Shenzhen 100 index are constructed and analyzed.The results show that the network constructed by kendall?l, based on t-Copula function has better clustering, closer dependence among stocks, and higher overall integration. Besides, we also constructe dynamic network by kendallr, and find some important conclusions from the dynamics of correlation structure in stock market. The volatility of the diameter and average path length in the dyanmic network with no weight are approximation reverse anastomosis with Shenzhen 100 Index. In the weighted dyanmic network, the average distance is reverse with the index and shows a high degree of negative correlation with variance. The distance among network nodes is distributed in peak and thick state. Compared with no weighted dynamic network, the weighted dyanmic network give very good reflection of the overall trend of the stock price. The dynamic change of network centric potential index is consistent with index volatility. Betweenness centrality fluctuates with index fluctuation, but the degree and direction of the change of different stocks are not consistent.