Network Models of Financial Systemic Risk (13frg184)

Arriving in Banff, Alberta Sunday, May 5 and departing Sunday May 12, 2013


(McMaster University)

(University of Calgary)


Statement of Objectives: During the proposed one week session at BIRS we intend to address the following specific research objectives:

1. Double cascade model of illiquidity and insolvency. We aim to complete a draft paper currently being written by eight coauthors, seven of whom are planning to attend the BIRS session. This paper dramatically extends models of Gai, Haldane and Kapadia, (also Hurd and Gleeson), to models of a double cascade of liquidity stresses and default shocks in a theoretical financial network. In this work we have developed a number of probabilistic methods that lead to detailed analytical formulas for dynamics that more typically are dealt with by large scale Monte Carlo simulations. We also intend to brainstorm whether our techniques are also transferable to information cascades in networks that arise naturally in other areas, such as social networks and epidemic modelling.

2. Phase structure of hypothetical financial systems: We will spend part of the week running our analytical and simulation methods to explore the relation between basic network parameters such as connectivity, homogeneity and uncertainty, and macroscopic systemic risk measures. Such relationships are non-intuitive, non-linear and difficult to predict. By analogy with condensed matter physics we expect in advance that there will be phase transitions and non-monotonicity in these relations. Such emergent features will reflect profound properties of real world financial networks that can be understood by first looking at our deliberately simplified network models. Simulation studies of complex hypothetical financial networks that map out these types of features will lead to improved intuitive understanding of the resilience of networks, and perhaps ultimately to pragmatic rules of thumb for network participants. This line of inquiry also links systemic network theory strongly to other areas of network science, from which we may draw additional ideas and intuition.

3. The real world networks: Our group has initiated an investigation into a systemic risk database for the EU financial network in 2011. We have also made contact with the Financial Stability Group at the Bank of Canada who we hope will share an even larger scale database for the interbank network in Canada. We intend to undertake a preliminary exploration of the characteristics of both databases during our BIRS week, with the aim to arrive at realistic parametrizations of our theoretical systemic models. This study will in principle enable us to make specific conclusions about real financial networks that can be a starting point for a promising collaboration with central bank researchers.

4. Meeting with senior researchers: Hurd, Lehar and Grasselli intend to spend at least one day discussing the wider implications of our 3 year GRI funded research project "Financial Systemic Risk: a Network Science Approach". Other GRI project researchers, Paul Glasserman and James Gleeson, will hopefully participate remotely.

This project will contribute materially to furthering the understanding of this critical issue for Canadian society, and worldwide. The question of systemic risk has surfaced in the economic community as of paramount importance, in light of the crisis of 2007-08, and mathematical implications have not yet been deeply explored. At this moment, research groups worldwide are gearing up to understand such questions and our focussed research group is well placed to make an important contribution.


Elsinger, H., Lehar, A., and Summer, M. Risk assessment for banking systems. Management Science 52, 9 (2006), 1301–1314.

Gai, P., Haldane, A., and Kapadia, S. Complexity, concentration and contagion. Journal of Monetary Economics 58 (2011), 453-470.

Gai, P., and Kapadia, S. Contagion in financial networks. Proceedings of the Royal
Society A 466, 2120 (2010), 2401–2423.

Gleeson, J. P., Hurd, T. R., Melnik, S., and Hackett, A. Systemic risk in banking networks without Monte Carlo simulation. In Advances in Network Analysis and its Applications, E. Kranakis, Ed., vol. 18 of Mathematics in Industry. Springer Verlag, Berlin Heidelberg New York, June 2012.

Hurd, T. R., and Gleeson, J. P. A framework for analyzing contagion in banking networks. arXiv:1110.4312 [q-fin.GN], October 2011.

Hurd, T. R., and Gleeson, J. P. On Watts Cascade Model with Random Link Weights. arXiv:1211.5708 [physics.soc-ph], November 2012.

Upper, C. Simulation methods to assess the danger of contagion in interbank markets. J. Financial Stability (2011).