A framework for analyzing contagion in banking networks

TL;DR

This paper introduces a probabilistic framework for analyzing contagion in banking networks, incorporating disassortative edge probabilities, and provides tools to predict systemic risk and cascade likelihood.

Contribution

It presents a novel probabilistic model that accounts for disassortative connections and derives a cascade condition analogous to epidemic models, with practical measures for systemic risk.

Findings

Cascade can be modeled as an iterated mapping converging to a fixed point.

Disassortative edge probabilities significantly influence systemic risk levels.

Analytic formulas for cascade frequency are derived from percolation theory.

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 edge-assortativity 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, large-scale Monte Carlo simulations are presented that demonstrate the applicability of the results to finite-sized networks. Finally, we propose a simple graph theoretic quantity, which we call "graph-assortativity", that seems to best capture systemic risk.