Network Topologies of Financial Market During the Global Financial Crisis

We consider the effects of the global financial crisis through a local Korean financial market around the 2008 crisis. We analyze 185 individual stock prices belonging to the KOSPI (Korea Composite Stock Price Index), cosidering three time periods: the time before, during, and after the crisis. The complex networks generate from the fully connected correlation network by using the cross-correlation coefficients among the stock price time series of the companies. We generate the threshold networks (TN), the minimal spanning tees (MST), and the hierarchical network (HN) from the fully connected cross-correlation networks. By assigning a threshold value of the cross-correlation coefficient, we obtain the threshold networks. We observe the power law of the degree distribution in the limited range of the threshold. The degree distribution of the largest cluster in the threshold networks during the crisis is fatter than other periods. The clustering coefficient of the threshold networks follows the power law in the scaling range. We also generate the minimal spanning trees from the fully connected correlation networks. The MST during the crisis period shrinks in comparison to the periods before and after the crisis. The cophenetic correlation coefficient increases during the crisis, indicating that the hierarchical structure increases during this period. When the crisis hit the market, the companies behave synchronously and their correlations become stronger than the normal period.