Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank

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.

[1]  Giacomo Livan,et al.  Financial instability from local market measures , 2012, 1207.0356.

[2]  Stefano Battiston,et al.  The Network of Global Corporate Control , 2011, PloS one.

[3]  Matteo Marsili,et al.  Diffusion and growth in an evolving network , 2006, Int. J. Game Theory.

[4]  Alessandro Vespignani,et al.  The GLEaMviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale , 2011, BMC infectious diseases.

[5]  Ingo Scholtes,et al.  Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks , 2013, Nature Communications.

[6]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[7]  A. Barabasi,et al.  The network takeover , 2011, Nature Physics.

[8]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[9]  Roma,et al.  Fitness model for the Italian interbank money market. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Guido Caldarelli,et al.  DebtRank: A Microscopic Foundation for Shock Propagation , 2015, PloS one.

[11]  Sebastian Heise,et al.  Derivatives and credit contagion in interconnected networks , 2012, 1202.3025.

[12]  Craig H. Furfine,et al.  Interbank Exposures: Quantifying the Risk of Contagion , 1999 .

[13]  Christoph Memmel,et al.  Contagion in the Interbank Market and its Determinants , 2013, SSRN Electronic Journal.

[14]  Prasanna Gai,et al.  Contagion in financial networks , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  Yamir Moreno,et al.  Theory of Rumour Spreading in Complex Social Networks , 2007, ArXiv.

[16]  Stefano Battiston,et al.  The Financial System as a Nexus of Interconnected Networks , 2016 .

[17]  Andreas Worms,et al.  Estimating Bilateral Exposures in the German Interbank Market: Is There a Danger of Contagion? , 2002 .

[18]  Christian Upper,et al.  Estimating Bilateral Exposures in the German Interbank Market: Is There a Danger of Contagion? , 2002, SSRN Electronic Journal.

[19]  S. Battiston,et al.  Liaisons Dangereuses: Increasing Connectivity, Risk Sharing, and Systemic Risk , 2009 .

[20]  Daniel N. Rockmore,et al.  Overlapping portfolios, contagion, and financial stability , 2015 .

[21]  Guido Caldarelli,et al.  Correction: DebtRank: A Microscopic Foundation for Shock Propagation , 2015, PloS one.

[22]  Cristopher Moore,et al.  Stability Analysis of Financial Contagion Due to Overlapping Portfolios , 2012, ArXiv.

[23]  L. Allen.  Some discrete-time SI, SIR, and SIS epidemic models. , 1994, Mathematical biosciences.

[24]  Stefan Thurner,et al.  DebtRank-transparency: Controlling systemic risk in financial networks , 2013, Scientific Reports.

[25]  M. Elliott,et al.  Financial Networks and Contagion , 2014 .

[26]  J. Kurths,et al.  Network synchronization, diffusion, and the paradox of heterogeneity. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Li Wang,et al.  The Topology of Overlapping Portfolio Networks , 2015 .

[28]  Leonidas Sandoval,et al.  Structure of a Global Network of Financial Companies Based on Transfer Entropy , 2014, Entropy.

[29]  Giulia Iori,et al.  Systemic Risk on the Interbank Market , 2004 .

[30]  Sheri M Markose,et al.  ‘Too interconnected to fail’ financial network of US CDS market: Topological fragility and systemic risk , 2012 .

[31]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[32]  Kwang-Il Goh,et al.  Impact of the Topology of Global Macroeconomic Network on the Spreading of Economic Crises , 2011, PloS one.

[33]  G. Caldarelli,et al.  DebtRank: Too Central to Fail? Financial Networks, the FED and Systemic Risk , 2012, Scientific Reports.

[34]  F. Sá,et al.  The Geographical Composition of National External Balance Sheets: 1980-2005 , 2010 .

[35]  Guido Caldarelli,et al.  Bootstrapping Topological Properties and Systemic Risk of Complex Networks Using the Fitness Model , 2012, Journal of Statistical Physics.

[36]  Giulio Cimini,et al.  Estimating topological properties of weighted networks from limited information , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Akira Namatame,et al.  Mitigating Cascading Failure with Adaptive Networking , 2015, New Math. Nat. Comput..

[38]  S. Battiston,et al.  Capital and contagion in financial networks , 2013 .

[39]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[40]  Guido Caldarelli,et al.  Pathways towards instability in financial networks , 2016 .

[41]  Stefano Battiston,et al.  Leveraging the network: A stress-test framework based on DebtRank , 2015, 1503.00621.

[42]  Guido Caldarelli,et al.  Default Cascades in Complex Networks: Topology and Systemic Risk , 2013, Scientific Reports.

[43]  Giulio Cimini,et al.  Systemic Risk Analysis on Reconstructed Economic and Financial Networks , 2014, Scientific Reports.

[44]  G. Zocchi,et al.  Local cooperativity mechanism in the DNA melting transition. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[46]  Fabio Caccioli,et al.  Heterogeneity, Correlations and Financial Contagion , 2011, 1109.1213.

[47]  H. Stanley,et al.  Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation , 2012, Scientific Reports.

[48]  Stefano Battiston,et al.  DebtRank and the Network of Leverage , 2016, The Journal of Alternative Investments.

[49]  Jure Leskovec,et al.  Meme-tracking and the dynamics of the news cycle , 2009, KDD.

[50]  James P. L. Tan.  Symmetric and Asymmetric Tendencies in Stable Complex Systems , 2015, Scientific Reports.

[51]  J. Yang,et al.  Network Models and Financial Stability , 2008 .

[52]  Edson Bastos e Santos,et al.  Network Structure and Systemic Risk in Banking Systems , 2010 .

[53]  S. Markose,et al.  Monetary and Capital Markets Department Systemic Risk from Global Financial Derivatives: A Network Analysis of Contagion and Its Mitigation with Super-Spreader Tax , 2012 .