title: Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank.
abstract: We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013.
authors.affiliation: Department of Banking and Finance, University of Zürich, Zürich, Switzerland.|London Institute for Mathematical Sciences, London, United Kingdom.
authors.forename: Marco
authors.initials: M
authors.lastname: Bardoscia
authors.affiliation: Department of Computer Science, University College London, London, United Kingdom.|Systemic Risk Centre, London School of Economics and Political Sciences, London, United Kingdom.
authors.forename: Fabio
authors.initials: F
authors.lastname: Caccioli
authors.affiliation: IMT: Institute for Advanced Studies, Lucca, Italy.
authors.forename: Juan Ignacio
authors.initials: JI
authors.lastname: Perotti
authors.affiliation: IMT: Institute for Advanced Studies, Lucca, Italy.
authors.forename: Gianna
authors.initials: G
authors.lastname: Vivaldo
authors.affiliation: IMT: Institute for Advanced Studies, Lucca, Italy.|London Institute for Mathematical Sciences, London, United Kingdom.|CNR-ISC: Institute for Complex Systems, Rome, Italy.
authors.forename: Guido
authors.initials: G
authors.lastname: Caldarelli
mesh_terms: D000465:Algorithms; D000067012:Banking, Personal; D005376:Financial Management; D018803:Models, Economic; D016571:Neural Networks, Computer