# Systemic Risk in Banking Networks Without Monte Carlo Simulation

## Abstract

An analytical approach to calculating the expected size of contagion events in models of banking networks is presented. The method is applicable to networks with arbitrary degree distributions, permits cascades to be initiated by the default of one or more banks, and includes liquidity risk effects. Theoretical results are validated by comparison with Monte Carlo simulations, and may be used to assess the stability of a given banking network topology.

## Keywords

Liquidity Risk Debtor Bank Shock Transmission Banking Network External Asset## Notes

### Acknowledgements

We acknowledge the work of undergraduate students Niamh Delaney and Arno Mayrhofer on an early version of the simulation codes used in this paper. Discussions with the participants at the Workshop on Financial Networks and Risk Assessment, hosted by MITACS at the Fields Institute, Toronto in May 2010 (particularly Rama Cont and Andreea Minca) are also gratefully acknowledged, as are the comments of Sébastien Lleo and Mark Davis. This work was funded by awards from Science Foundation Ireland (06/IN.1/I366, 06/MI/005 and 11/PI/1026), from an INSPIRE: IRCSET-Marie Curie International Mobility Fellowship in Science Engineering and Technology, and from the Natural Sciences and Engineering Research Council of Canada.

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