Studies on Systemic Risk and Contagion
The study of contagion in financial systems is very topical in light of
the recent global credit crisis and the resultant damage inflicted on
financial institutions. "Contagion" refers to the spread of defaults
through a system of financial institutions, with each successive
default causing increasing pressure on the remaining components of the
system. The term "systemic risk" refers to the contagion-induced threat
to the financial system as a whole, due to the default of one (or more)
of its component institutions.
It is widely held that financial systems, defined for example as the
collection of banks and financial institutions in a developed country,
can be modelled as a random network of nodes or vertices
with stylized balance sheets, connected by directed links or
edges that represent exposures ("interbank loans"), each edge with a
positive weight that represents the size of the exposure. If ever a
node becomes "insolvent" and ceases to operate as a bank, it will
create balance sheet shocks to other nodes, creating the potential of
chains of insolvency that we will call "default cascades".
Financial networks are difficult to observe because interbank data is
often not publicly available, but studies have indicated that
they share characteristics of other types of technological and
social networks, such as the world wide web and Facebook. For example,
the degree distributions of financial networks are thought to be
"fat-tailed" since a significant number of banks are very highly
connected. A less studied feature observed in financial networks (and
as it happens, also the world wide web) is that they are highly
"disassortative". This refers to the property that any bank's
counterparties (i.e. their graph neighbours) have a tendency to be
banks of an opposite character. For example, it is observed that small
banks tend to link preferentially to large banks rather than other
small banks. Commonly, social networks are observed to be assortative
rather than disassortative. Structural characteristics such as degree
distribution and assortativity are felt to be highly relevant to the
propagation of contagion in networks but the nature of such
relationships is far from clear.
The aim of our Systemic Risk Problem Solving Workshop is to develop
mathematical frameworks that will be able to determine the systemic
susceptibility in a rich class of random network models with
enough flexibility to include the most important structural
characteristics of real financial networks. Here is the original
research description for our workshop: SFN.pdf
- My Lecture Notes from the 2012 Winter School on Financial
Mathematics, Netherlands: Hours
- My Plenary Talk from Quantitative Methods in Finance Conference,
Cairns, Australia, July 2012: QMF
- Lionel's Report for
Random Graph Theory
- D. J. Watts. A simple model of global cascades on random
networks. PNAS, 99 (9):5766–5771, 2002.Watts02.pdf
- M. E. J. Newman. Networks: An Introduction. Oxford University
- M. Molloy and B. Reed. A critical point for random graphs with a
given degree sequence. Random Structures & Algorithms,
- B. Bollobas. Random Graphs. Cambridge studies in advanced
mathematics. Cambridge University Press, 2 edition, 2001.
Studies on Financial Systems
- Eisenberg, L. and Noe, T. H. 2001 Systemic risk in financial
systems,Management Science, 47, (2) 236–249. EisenbergNoe01
- C. Upper. Simulation methods to assess the danger of contagion in
interbank markets. J. Financial Stability, 2011.Upper
- FINANCIAL STABILITY REVIEW JUNE 2012: Financial
- Bisias, Dimitrios, Flood, Mark D., Lo, Andrew
W. and Valavanis, Stavros, A Survey of Systemic
Risk Analytics (January 11, 2012).
U.S. Department of Treasury, Office of Financial Research No. 0001.
- Nier, E., Yang, J., Yorulmazer, T., and Alentorn, A. 2007 Network
models and financial stability, J. Economic Dynamics & Control, 31,
New Research on Financial Networks
- P. Gai and S. Kapadia. Contagion in financial networks.
Proceedings of the Royal Society A, 466(2120):2401–2423, 2010.GaiKapadia10
- R. Cont, A. Moussa, and E. B. Santos. Network Structure and
Systemic Risk in Banking Systems. SSRN eLibrary, 2010.ContMoussaSantos10
- H. Amini, R. Cont, and A. Minca. Resilience to contagion in
financial networks. Working paper: arXiv:1112.5687v1 [q-fin.RM],
- P. Gai, A. Haldane, S. Kapadia, “Complexity, Concentration and
Contagion”, Journal of Monetary Economics, 58, 2011. GaiHaldaneKapadia11
- J. P. Gleeson, T. R. Hurd, S. Melnik, and A. Hackett. Systemic
risk in banking networks without Monte Carlo simulation. In E.
Kranakis, editor, Advances in Network Analysis and its Applications,
volume 18 of Mathematics in Industry. Springer Verlag, Berlin
Heidelberg New York, June 2012.Gleeson
- T. R. Hurd, James Gleeson "A framework for analyzing contagion in
banking networks", working paper, June 2011 Hurd Gleeson
- R. M. May and N. Arinaminpathy. Systemic risk: the dynamics of
model banking systems. Journal of The Royal Society Interface,
Stability of Financial Networks (International Problem Solving
The aim of this workshop ( Workshop
Website ) is to advance the mathematical understanding of the
financial system by using random graph techniques outlined in
July 16-20, 2012)
Tom Hurd (McMaster U), Matheus Grasselli (McMaster U), Huibin Cheng
(PDF, McMaster), Quentin Shao (PhD Student, McMaster U), Davide Cellai
(U of Limerick), Sergey Melnik (PDF, U of Limerick), Lionel Cassier
(Student, Ecole Polytechnique, Paris), Bernardo Costa Lima (PhD
student, McMaster U).
Challenges for the Team
- Prove the LTIA (locally treelike independence assumption) for the
infinite assortative configuration model described in Hurd-Gleeson 2012.
- Study the accuracy of the LTIA approximation in real networks by
comparing the approximation to "exact" Monte Carlo simulations.
- Improve the stochastic modelling of a bank's balance sheet. That
is, go beyond the Gai-Haldane-Kapadia 2011 model, to better
capture the stylized facts of balance sheet transactions.
- Study a new network database for the EU banking system. EU Banking Networks
- Apply measures of systemic risk a la Amini-Cont-Minca 2011.
- Apply and extend the Watts type analytic framework of
- Investigate policy alternatives that might reduce systemic risk
measures in a given system.