Systemic risk components in a network model of contagion

ABSTRACT

We show how to perform a systemic risk attribution in a network model of contagion with interlocking balance sheets, using the Shapley and Aumann–Shapley values. Along the way, we establish new results on the sensitivity analysis of the Eisenberg–Noe network model of contagion, featuring a Markov chain interpretation. We illustrate the design process for systemic risk attribution methods by developing several examples.

Keywords:

• Systemic risk
• contagion
• Eisenberg–Noe model
• risk components
• risk attribution
• risk allocation
• cost allocation

Acknowledgements

Some ideas of this article were presented earlier in Liu and Staum (2011, 2012). The authors thank Matthias Drehmann and Nikola Tarashev for discussions.

Funding

The first author gratefully acknowledges support from the FDIC Center for Financial Research and an IBM Faculty Award. Information presented in this article is provided by the authors independent of Magnetar Capital LLC (Magnetar) and any views or opinions presented in this article are solely those of the authors and do not necessarily represent those of Magnetar.

Additional information

Notes on contributors

Jeremy Staum

Jeremy Staum is an Associate Professor in the Department of Industrial Engineering and Management Sciences at Northwestern University. He earned a B.S. in Mathematics from the University of Chicago, an M.S. in Statistics from Stanford University, and a Ph.D. in Management Science from Columbia University. He is the Department Editor for financial engineering at IIE Transactions. His research interests include financial engineering, simulation experiment design and analysis, and Monte Carlo methods.

Mingbin Feng

Mingbin Feng is a Ph.D. candidate in the Department of Industrial Engineering and Management Sciences at Northwestern University. He is an Associate of the Society of Actuaries. His research interests include simulation experiment design and nonlinear optimization, with applications to finance and insurance.

Ming Liu

Ming Liu is a Quantitative Analyst at Magnetar Capital. He received his Ph.D. in Industrial Engineering and Management Sciences from Northwestern University.