title: Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks.
abstract: The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the "critical degree" (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.
authors.affiliation: Perimeter Institute for Theoretical Physics, 31 Caroline Street North, N2L 2Y5 Waterloo ON, Canada.
authors.forename: Matteo
authors.initials: M
authors.lastname: Smerlak
authors.affiliation: Department of Mechanical Engineering, University of Texas at Austin, 204 E. Dean Keaton, C2200, Austin, TX 78712, United States of America.
authors.forename: Brady
authors.initials: B
authors.lastname: Stoll
authors.affiliation: Indian Institute of Management Calcutta, Diamond Harbour Road, Joka, Kolkata, West Bengal 700104, India.
authors.forename: Agam
authors.initials: A
authors.lastname: Gupta
authors.affiliation: Resilience and Adaptation Program, University of Alaska Fairbanks, PO Box 757000, Fairbanks, AK 99775-7000, United States of America.
authors.forename: James S
authors.initials: JS
authors.lastname: Magdanz
mesh_terms: D000465:Algorithms; D003362:Cost-Benefit Analysis / Q000191:economics / Q000379:methods; D005376:Financial Management / Q000191:economics* / Q000379:methods*; D006801:Humans; D018803:Models, Economic; D016571:Neural Networks, Computer; D020414:Risk Sharing, Financial / Q000191:economics / Q000379:methods