This paper provides a tractable theoretical framework for the study of the economic forces shap- ing the relationship between the structure of the financial network and systemic risk. We show that as long as the magnitude (or the number) of negative shocks is below a critical threshold, a more equal distribution of interbank obligations leads to less fragility. In particular, all else equal, the sparsely connected ring financial network (corresponding to a credit chain) is the most fragile of all configura- tions, whereas the highly interconnected complete financial network is the configuration least prone to contagion. In line with the observations made by Allen and Gale (2000), our results establish that, in the more complete networks, the losses of a distressed bank are passed to a larger number of counterparties, guaranteeing a more efficient use of the excess liquidity in the system in forestalling defaults.
We also show that when negative shocks are larger than a certain threshold, the second view on the relationship between the structure of the financial network and the extent of contagion prevails. In particular, completeness is no longer a guarantee for stability. Rather, in the face of large shocks, financial networks in which banks are only weakly connected to one another would be less prone to systemic failures. Such a “phase transition” is due to the fact that, the senior liabilities of banks, as well as the excess liquidity within the financial network, can act as shock absorbers. Weak interconnections guarantee that the more senior creditors of a distressed bank bear most of the losses and hence, protect the rest of the system against cascading defaults.
The model of cash-flow among the banks (see equation 1 at section 2.4) has at least some superficial similarities to a 2-D Ising Model, and the authors could probably capture the dynamics they're modeling with an even more parsimonious model than they've given in this paper. But it's encouraging to see economists moving in this direction. See An Economy Made of Glass.
On a not unrelated-note, they solve for equilibrium here with Brouwer's Fixed Point Theorem. I am aware of a historical explanation for this, but it still surprises me to see models being set up to be solved this way given the instrumental challenge of testing the same models with empirical data. I have an ongoing and unfulfilled wish to see folks like Acemoglu et al. take the time to meet and discuss their models with folks like Jon Kleinberg and Steve Strogatz at Cornell. Economists just don't seem to be getting enough leverage out of the more recent applied math on networks or glass transitions.