Financial networks are dynamic and to assess systemic importance and avert losses we needs models which take the time variations of the links and nodes into account. We develop a model that can predict the response of the financial network to a shock and propose a measure for the systemic importance of the banks, which we call BankRank. Using the European Bank Authority 2011 stress test exposure data, we apply our model to the bipartite network of the largest institutional holders of troubled European countries (Greece, Italy, Portugal, Spain, and Ireland). Simulation of the states in our model reveal that it has " calm " state , where shocks do not cause very major losses, and " panicked " states, in which devastating damages occur. Fitting the parameters to Eurocrisis data shows that , before the crisis, the  system was mostly in the " calm " regime while during the Eurocrisis it went into the " panicked " regime. The numerical solutions of the our model fit to a good degree to what really happened in the crisis. We also find that, while the largest holders are usually more important, sometimes smaller holders also exhibit systemic importance. In addition, we observe that asset diversification has no clear correlation with our BankRank. Thus diversification is neither reducing systemic, nor necessarily providing routes for contagion. These suggest that our model may provide a useful tool for determining the vulnerability of banks and assets to shocks and for simulating shared portfolio networks in general .
Financial networks are dynamic . To assess their systemic importance to the world-wide economic network and avert losses we need models that take the time variations of the links and nodes into account. Using the methodology of classical mechanics and Laplacian determinism we develop a model that can predict the response of the financial network to a shock . We also propose a way of measuring the systemic importance of the banks, which we call BankRank. Using European Bank Authority 2011 stress test exposure data, we apply our model to the bipartite network connecting the largest institutional debt holders of the troubled European countries (Greece, Italy, Portugal, Spain, and Ireland). From simulating our model we can determine whether a network is in a " stable " state in which shocks do not cause major losses, or a " unstable " state in which devastating damages occur. Fitting the parameters of the model, which play the role of physical coupling constants, to Eurozone crisis data shows that before the Eurozone crisis the system was mostly in a " stable " regime , and that during the crisis it transitioned into an " unstable " regime. The numerical solutions produced by our model match closely the actual time-line of events of the crisis. We also find that, while the largest holders are usually more important, in the unstable regime smaller holders also exhibit systemic importance. Our model also proves useful for determining the vulnerability of banks and assets to shocks . This suggests that our model may be a useful tool for simulating the response dynamics of shared portfolio networks .
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