A Framework for Analyzing Contagion in Banking Networks

24 Pages Posted: 19 Oct 2011 Last revised: 28 Nov 2018

See all articles by Thomas R. Hurd

Thomas R. Hurd

McMaster University - Department of Mathematics and Statistics

James P. Gleeson

University of Limerick, Ireland

Date Written: October 16, 2011

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 R0 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.

Keywords: Systemic risk, banking network, contagion, random graph, cascade condition, credit risk, financial mathematics, assortativity

Suggested Citation

Hurd, Thomas R. and Gleeson, James P., A Framework for Analyzing Contagion in Banking Networks (October 16, 2011). Michael J. Brennan Irish Finance Working Paper Series Research Paper No. 18-14, Available at SSRN: https://ssrn.com/abstract=1945748 or http://dx.doi.org/10.2139/ssrn.1945748

Thomas R. Hurd

McMaster University - Department of Mathematics and Statistics ( email )

Canada

James P. Gleeson (Contact Author)

University of Limerick, Ireland ( email )

MACSI
Dept of Mathematics and Statistics
Limerick
Ireland

HOME PAGE: http://www.ul.ie/gleesonj

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