Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank

We consider a dynamical model of distress propagation on complex network= s, which we apply to the study of financial contagion in networks of banks = connected to each other by direct exposures. The model that we consider is = an extension of the DebtRank algorithm, recently introduced in the literatu= re. The mechanics of distress propagation is very simple: When a bank suffe= rs a loss, distress propagates to its creditors, who in turn suffer losses,= and so on. The original DebtRank assumes that losses are propagated linear= ly between connected banks. Here we relax this assumption and introduce a o= ne-parameter family of non-linear propagation functions. As a case study, w= e apply this algorithm to a data-set of 183 European banks, and we study ho= w the stability of the system depends on the non-linearity parameter under = different stress-test scenarios. We find that the system is characterized b= y a transition between a regime where small shocks can be amplified and a r= egime where shocks do not propagate, and that the overall stability of the = system increases between 2008 and 2013.