
A Framework for Analyzing Contagion in Banking Networks (Hurd T.R., Gleeson J.P.)Bank Systems Contagion in Banking
Abstract 
A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between banks, the possibility of disassortative edge probabilities (an above average tendency for small banks to link to large banks) is explicitly incorporated. We give a probabilistic analysis of the default cascade triggered by shocking the network. We find that the cascade can be understood as an explicit iterated mapping on a set of edge probabilities that converges to a fixed point. A cascade condition is derived that characterizes whether or not an infinitesimal shock to the network can grow to a finite size cascade, in analogy to the basic reproduction number $R_0$ in epidemic modeling. It provides an easily computed measure of the systemic risk inherent in a given banking network topology. An analytic formula is given for the frequency of global cascades, derived from percolation theory on the random network. Two simple examples are used to demonstrate that edgeassortativity can have a strong effect on the level of systemic risk as measured by the cascade condition. Although the analytical methods are derived for infinite networks, largescale Monte Carlo simulations are presented that demonstrate the applicability of the results to finitesized networks. Finally, we propose a simple graph theoretic quantity, which we call "graphassortativity", that seems to best capture systemic risk. 
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Hurd T.R., Gleeson J.P. (2011) "A Framework for Analyzing Contagion in Banking Networks", available on arXiv:1110.4312 

