%0 Journal Article %1 Smerlak2015Mapping %A Smerlak, Matteo %A Stoll, Brady %A Gupta, Agam %A Magdanz, James S. %D 2015 %E Masuda, Naoki %J PLOS ONE %K systemic-risk banks financial-networks cascades %N 7 %P e0130948+ %R 10.1371/journal.pone.0130948 %T Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks %U http://dx.doi.org/10.1371/journal.pone.0130948 %V 10 %X The recent financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent studies of this problem have relied on numerical simulations. In this paper, we report analytical results in a network model of interbank lending based on directly relevant financial parameters such as interest rates and leverage ratios. Using a mean-field approach, we obtain a closed-form formula for the "critical degree", viz. the number of creditors per bank below which an individual shock can cascade throughout the network. We relate the failures distribution (probability that a single shock induces \$F\$ failures) to the degree distribution (probability that a bank has \$k\$ creditors), showing in particular that the former is fat-tailed whenever the latter is. Remarkably, our criterion for the onset of contagion turns out to be isomorphic to a simple rule for the evolution of cooperation on graphs and social networks, supporting recent calls for a methodological rapprochement between finance and ecology.

@article{Smerlak2015Mapping, abstract = {{The recent financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent studies of this problem have relied on numerical simulations. In this paper, we report analytical results in a network model of interbank lending based on directly relevant financial parameters such as interest rates and leverage ratios. Using a mean-field approach, we obtain a closed-form formula for the "critical degree", viz. the number of creditors per bank below which an individual shock can cascade throughout the network. We relate the failures distribution (probability that a single shock induces \$F\$ failures) to the degree distribution (probability that a bank has \$k\$ creditors), showing in particular that the former is fat-tailed whenever the latter is. Remarkably, our criterion for the onset of contagion turns out to be isomorphic to a simple rule for the evolution of cooperation on graphs and social networks, supporting recent calls for a methodological rapprochement between finance and ecology.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Smerlak, Matteo and Stoll, Brady and Gupta, Agam and Magdanz, James S.}, biburl = {https://www.bibsonomy.org/bibtex/226792b5cc22d57bd37f47ffcf94fa2e1/nonancourt}, citeulike-article-id = {13054949}, citeulike-linkout-0 = {http://dx.doi.org/10.1371/journal.pone.0130948}, citeulike-linkout-1 = {http://arxiv.org/abs/1402.4783}, citeulike-linkout-2 = {http://arxiv.org/pdf/1402.4783}, day = 24, doi = {10.1371/journal.pone.0130948}, editor = {Masuda, Naoki}, eprint = {1402.4783}, interhash = {df357b5eb10c44a89dc036a45b7b0378}, intrahash = {26792b5cc22d57bd37f47ffcf94fa2e1}, issn = {1932-6203}, journal = {PLOS ONE}, keywords = {systemic-risk banks financial-networks cascades}, month = jul, number = 7, pages = {e0130948+}, posted-at = {2014-02-20 09:59:18}, priority = {2}, timestamp = {2019-07-31T12:52:15.000+0200}, title = {{Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks}}, url = {http://dx.doi.org/10.1371/journal.pone.0130948}, volume = 10, year = 2015 }