Changes of hierarchical network in local and world stock market

Abstract

We consider the cross-correlation coefficients of the daily returns in the local and global stock markets. We generate the minimal spanning tree (MST) using the correlation matrix. We observe that the MSTs change their structure from chain-like networks to star-like networks during periods of market uncertainty. We quantify the measure of the hierarchical network utilizing the value of the hierarchy measured by the hierarchical path. The hierarchy and betweenness centrality characterize the state of the market regarding the impact of crises. During crises, the non-financial company is established as the central node of the MST. However, before the crisis and during stable periods, the financial company is occupying the central node of the MST in the Korean and the U.S. stock markets. The changes in the network structure and the central node are good indicators of an upcoming crisis.