Classical mechanics of economic networks
(09.12.2014)Zusammenfassung
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 ünstable" 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 ünstable" 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.