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

General References

Introductory Lectures:

  1. My Lecture Notes from the 2012 Winter School on Financial Mathematics, Netherlands: Hours 1-3, Hours 4-5
  2. My Plenary Talk from Quantitative Methods in Finance Conference, Cairns, Australia, July 2012: QMF Talk
  3. Lionel's Report for Ecole Polytechnique

Random Graph Theory

  1. D. J. Watts. A simple model of global cascades on random networks. PNAS, 99 (9):5766–5771, 2002.Watts02.pdf
  2. M. E. J. Newman. Networks: An Introduction. Oxford University Press, 2010.
  3. M. Molloy and B. Reed. A critical point for random graphs with a given degree sequence. Random Structures & Algorithms, 6(2-3):161–180, 1995.MolloyReed95.pdf
  4. B. Bollobas. Random Graphs. Cambridge studies in advanced mathematics. Cambridge University Press, 2 edition, 2001.

Studies on Financial Systems

  1. Eisenberg, L. and Noe, T. H. 2001 Systemic risk in financial systems,Management Science, 47, (2) 236–249. EisenbergNoe01
  2. C. Upper. Simulation methods to assess the danger of contagion in interbank markets. J. Financial Stability, 2011.Upper Review Paper
  3. FINANCIAL STABILITY REVIEW JUNE 2012: Financial Stability Review
  4. 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. Risk Analytics
  5. Nier, E., Yang, J., Yorulmazer, T., and Alentorn, A. 2007 Network models and financial stability, J. Economic Dynamics & Control, 31, 2033–2060. Nieretal07

New Research on Financial Networks

  1. P. Gai and S. Kapadia. Contagion in financial networks. Proceedings of the Royal Society A, 466(2120):2401–2423, 2010.GaiKapadia10
  2. R. Cont, A. Moussa, and E. B. Santos. Network Structure and Systemic Risk in Banking Systems. SSRN eLibrary, 2010.ContMoussaSantos10
  3. H. Amini, R. Cont, and A. Minca. Resilience to contagion in financial networks. Working paper: arXiv:1112.5687v1 [q-fin.RM], December 2011.AminiContMinca11
  4. P. Gai, A. Haldane, S. Kapadia, “Complexity, Concentration and Contagion”, Journal of Monetary Economics, 58, 2011. GaiHaldaneKapadia11
  5. 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 et al
  6. T. R. Hurd, James Gleeson "A framework for analyzing contagion in banking networks", working paper, June 2011 Hurd Gleeson
  7. R. M. May and N. Arinaminpathy. Systemic risk: the dynamics of model banking systems. Journal of The Royal Society Interface, 7(46):823–838, 2010.ArinMay10.pdf

Stability of Financial Networks (International Problem Solving Workshop
July 16-20, 2012)

The aim of this workshop ( Workshop Website ) is to advance the mathematical understanding of the financial system by using random graph techniques outlined in Hurd-Gleeson 2012.

The Team

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

  1. Prove the LTIA (locally treelike independence assumption) for the infinite assortative configuration model described in Hurd-Gleeson 2012.
  2. Study the accuracy of the LTIA approximation in real networks by comparing the approximation to "exact" Monte Carlo simulations.
  3. 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.
  4. Study a new network database for the EU banking system. EU Banking Networks
  5. Apply measures of systemic risk a la Amini-Cont-Minca 2011.
  6. Apply and extend the Watts type analytic framework of Cassier-Cheng-Hurd.
  7. Investigate policy alternatives that might reduce systemic risk measures in a given system.

Workshop Website