Systemic risk and hierarchical transitions of financial networks

In this paper, the change in topological hierarchy, which is measured by the minimum spanning tree constructed from the cross-correlations between the stock indices from the S & P 500 for 1998-2012 in a one year moving time window, was used to analyze a financial crisis. The hierarchy increased in all minor crises in the observation time window except for the sharp crisis of 2007-2008 when the global financial crisis occurred. The sudden increase in hierarchy just before the global financial crisis can be used for the early detection of an upcoming crisis. Clearly, the higher the hierarchy, the higher the threats to financial stability. The scaling relations were developed to observe the changes in hierarchy with the network topology. These scaling relations can also identify and quantify the financial crisis periods, and appear to contain the predictive power of an upcoming crisis.