In Search of Lost Edges: A Case Study on Reconstructing FInancial Networks

To capture the systemic complexity of international financial systems, network data is an important prerequisite. However, dyadic data is often not available, raising the need for methods that allow for reconstructing networks based on limited information. In this paper, we are reviewing different methods that are designed for the estimation of matrices from their marginals and potentially exogenous information. This includes a general discussion of the available methodology that provides edge probabilities as well as models that are focussed on the reconstruction of edge values. Besides summarizing the advantages, shortfalls and computational issues of the approaches, we put them into a competitive comparison using the SWIFT (Society for Worldwide Interbank Financial Telecommunication) MT 103 payment messages network (MT 103: Single Customer Credit Transfer). This network is not only economically meaningful but also fully observed which allows for an extensive competitive horse race of methods. The comparison concerning the binary reconstruction is divided into an evaluation of the edge probabilities and the quality of the reconstructed degree structures. Furthermore, the accuracy of the predicted edge values is investigated. To test the methods on different topologies, the application is split into two parts. The first part considers the full MT 103 network, being an illustration for the reconstruction of large, sparse financial networks. The second part is concerned with reconstructing a subset of the full network, representing a dense medium-sized network. Regarding substantial outcomes, it can be found that no method is superior in every respect and that the preferred model choice highly depends on the goal of the analysis, the presumed network structure and the availability of exogenous information.

[1]  W. Deming,et al.  On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known , 1940 .

[2]  Kei Imakubo,et al.  The Transaction Network in Japan fs Interbank Money Markets , 2010 .

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

[4]  S. Siegert.  Simplifying and generalising Murphy's Brier score decomposition , 2017 .

[5]  Giorgio Fagiolo,et al.  Enhanced reconstruction of weighted networks from strengths and degrees , 2013, 1307.2104.

[6]  Gang Pan,et al.  Understanding bike trip patterns leveraging bike sharing system open data , 2017, Frontiers of Computer Science.

[7]  S. Fienberg.  An Iterative Procedure for Estimation in Contingency Tables , 1970 .

[8]  Teruyoshi Kobayashi,et al.  Network Models of Financial Systemic Risk: A Review , 2017 .

[9]  Liansheng Tan,et al.  Traffic matrix estimation: A neural network approach with extended input and expectation maximization iteration , 2016, J. Netw. Comput. Appl..

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

[11]  Luciano da Fontoura Costa,et al.  The structure and resilience of financial market networks. , 2012, Chaos.

[12]  A. H. Murphy.  A New Vector Partition of the Probability Score , 1973 .

[13]  G. Sheldon,et al.  Interbank Lending and Systemic Risk: An Empirical Analysis for Switzerland , 1998 .

[14]  Christian Upper,et al.  Simulation methods to assess the danger of contagion in interbank markets , 2011 .

[15]  Axel Gandy,et al.  A Bayesian Methodology for Systemic Risk Assessment in Financial Networks , 2016, Manag. Sci..

[16]  L. Bargigli,et al.  Statistical Ensembles for Economic Networks , 2014 .

[17]  Zhihan Lv,et al.  Modeling network traffic for traffic matrix estimation and anomaly detection based on Bayesian network in cloud computing networks , 2017, Ann. des Télécommunications.

[18]  Rodney Garratt,et al.  The missing links : A global study on uncovering fi nancial network structures from partial data 夽 , 2018 .

[19]  Axel Gandy,et al.  Adjustable Network Reconstruction with Applications to CDS Exposures , 2017, J. Multivar. Anal..

[20]  Carsten Lund,et al.  An information-theoretic approach to traffic matrix estimation , 2003, SIGCOMM '03.

[21]  D. Garlaschelli,et al.  Reconstruction methods for networks: The case of economic and financial systems , 2018, Physics Reports.

[22]  Jens Keilwagen,et al.  PRROC: computing and visualizing precision-recall and receiver operating characteristic curves in R , 2015, Bioinform..

[23]  T. Mayer,et al.  Gravity Equations: Workhorse, Toolkit, and Cookbook , 2013 .

[24]  G. Fagiolo,et al.  Post-Mortem Examination of the International Financial Network , 2012 .

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

[26]  Y. Vardi,et al.  Network Tomography: Estimating Source-Destination Traffic Intensities from Link Data , 1996 .

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

[28]  Zijun Liu,et al.  Banking Sector Interconnectedness: What is it, How Can We Measure it and Why Does it Matter? , 2015 .

[29]  Helmut Elsinger,et al.  Handbook on Systemic Risk: Network Models and Systemic Risk Assessment , 2013 .

[30]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[31]  Edoardo M. Airoldi,et al.  Estimating Latent Processes on a Network From Indirect Measurements , 2012, 1212.0178.

[32]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[33]  K. Head,et al.  The Puzzling Persistence of the Distance Effect on Bilateral Trade , 2004 .

[34]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[35]  Kartik Anand,et al.  Filling in the blanks: network structure and interbank contagion , 2014, SSRN Electronic Journal.

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

[37]  G. Kauermann,et al.  Regression-based Network Reconstruction with Nodal and Dyadic Covariates and Random Effects , 2019, 1903.11886.

[38]  Walter E. Beyeler,et al.  The topology of interbank payment flows , 2007 .

[39]  Kimmo Soramaki,et al.  The Global Network of Payment Flows , 2014 .

[40]  Robert Nowak,et al.  Network Tomography: Recent Developments , 2004 .

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

[42]  Luca Scrucca,et al.  GA: A Package for Genetic Algorithms in R , 2013 .

[43]  Eric D. Kolaczyk,et al.  Statistical Analysis of Network Data , 2009 .

[44]  Kimmo Soramäki,et al.  SinkRank: An Algorithm for Identifying Systemically Important Banks in Payment Systems , 2013 .

[45]  Albert G. Greenberg,et al.  Fast accurate computation of large-scale IP traffic matrices from link loads , 2003, SIGMETRICS '03.

[46]  Paul Erdös,et al.  On random graphs, I , 1959 .

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