An Entropy-Based Early Warning Indicator for Systemic Risk

The purpose of this paper is the construction of an early warning indicator for systemic risk using entropy measures. The analysis is based on the cross-sectional distribution of marginal systemic risk measures such as Marginal Expected Shortfall, Delta CoVaR and network connectedness. These measures are conceived at a single institution for the financial industry in the Euro area. We estimate entropy on these measures by considering different definitions (Shannon, Tsallis and Renyi). Finally, we test if these entropy indicators show forecasting abilities in predicting banking crises. In this regard, we use the variable presented in Babeck? et al. (2012) and Alessi and Detken (2011) from European Central Bank. Entropy indicators show promising forecast abilities to predict financial and banking crisis. The proposed early warning signals reveal to be effective in forecasting financial distress conditions.

[1]  D. F. Ahelegbey,et al.  Bayesian Graphical Models for Structural Vector Autoregressive Processes , 2012, Journal of Applied Econometrics.

[2]  Rama CONT.  Measuring systemic risk , 2008 .

[3]  N. Wagner,et al.  Are Systemically Important Eurozone Banks Undercapitalized? A Stress Testing Approach , 2017 .

[5]  Guanrong Chen,et al.  Cross-border Portfolio Investment Networks and Indicators for Financial Crises , 2013, Scientific Reports.

[6]  阿部 純義,et al.  Nonextensive statistical mechanics and its applications , 2001 .

[7]  Ehsan S. Soofi,et al.  Bayes Estimate and Inference for Entropy and Information Index of Fit , 2008 .

[8]  Sanjiv Ranjan Das,et al.  Systemic Risk and International Portfolio Choice , 2002 .

[9]  Daniel Martin,et al.  Early warning of bank failure: A logit regression approach , 1977 .

[10]  G. Löffler,et al.  Robustness and Informativeness of Systemic Risk Measures , 2013, SSRN Electronic Journal.

[11]  Hali J. Edison,et al.  Do Indicators of Financial Crises Work? An Evaluation of an Early Warning System , 2000 .

[12]  Anil K. Bera,et al.  Optimal Portfolio Diversification Using the Maximum Entropy Principle , 2008 .

[13]  Wlodzislaw Duch,et al.  Comparison of Shannon, Renyi and Tsallis Entropy Used in Decision Trees , 2006, ICAISC.

[14]  J. Rochet,et al.  Interbank Lending and Systemic Risk , 1996 .

[15]  E. Davis,et al.  Comparing early warning systems for banking crises , 2008 .

[16]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[17]  Vasco M. Carvalho,et al.  The Network Origins of Aggregate Fluctuations , 2011 .

[18]  Guofu Zhou,et al.  Asymmetry in Stock Returns : An Entropy Measure ∗ , 2014 .

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

[20]  Christian Beck,et al.  Application of generalized thermostatistics to fully developed turbulence , 2000 .

[21]  Claudio Borio,et al.  Stress-Testing Macro Stress Testing: Does it Live Up to Expectations? , 2012 .

[22]  A. Lo,et al.  A Survey of Systemic Risk Analytics , 2012 .

[23]  Kenneth S. Rogoff,et al.  From Financial Crash to Debt Crisis , 2010 .

[24]  D. Garlaschelli,et al.  Early-warning signals of topological collapse in interbank networks , 2013, Scientific Reports.

[25]  Christian P. Robert,et al.  The Bayesian choice , 1994 .

[26]  François Gourio.  Disaster Risk and Business Cycles , 2010 .

[27]  Celia Anteneodo,et al.  Nonextensive statistical mechanics and economics , 2003, ArXiv.

[28]  Lasse Loepfe,et al.  Towards a Proper Assignment of Systemic Risk: The Combined Roles of Network Topology and Shock Characteristics , 2013, PloS one.

[29]  Tuomas A. Peltonen,et al.  Assessing systemic risks and predicting systemic events , 2013 .

[30]  A. Lo,et al.  Econometric Measures of Connectedness and Systemic Risk in the Finance and Insurance Sectors , 2011 .

[31]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[32]  Kuldeep Kumar,et al.  Modelling Financial Time Series with S‐PLUS , 2007 .

[33]  G. Caldarelli,et al.  Credit Default Swaps networks and systemic risk , 2014, Scientific Reports.

[34]  F. Diebold,et al.  Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring , 2015 .

[35]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[36]  A. Demirguc-Kunt.  Monitoring banking sector fragility : a multivariate logit approach with an application to the 1996-97 banking crises , 1999 .

[37]  Systemic Risk in Europe , 2015 .

[38]  Rui Menezes,et al.  Entropy: A new measure of stock market volatility? , 2012 .

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

[40]  Tomas Havranek,et al.  Banking, debt, and currency crises in developed countries: Stylized facts and early warning indicators , 2014 .

[41]  Markus K. Brunnermeier,et al.  Federal Reserve Bank of New York , 2009 .

[42]  M. Bussière,et al.  Towards a New Early Warning System of Financial Crises , 2002, SSRN Electronic Journal.

[43]  Constantino Tsallis,et al.  I. Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Status , 2001 .

[44]  Andrew Ang,et al.  Systemic Sovereign Credit Risk: Lessons from the U.S. and Europe , 2011 .

[45]  Jing Hu,et al.  Financial Crisis, Omori's Law, and Negative Entropy Flow , 2013, SBP.

[46]  Luc Laeven,et al.  Systemic Banking Crises Database , 2013 .

[47]  T. Minka.  Bayesian inference, entropy, and the multinomial distribution , 2003 .

[48]  R. Solé,et al.  Information Theory of Complex Networks: On Evolution and Architectural Constraints , 2004 .

[49]  Anat R. Admati,et al.  Fallacies, Irrelevant Facts, and Myths in the Discussion of Capital Regulation: Why Bank Equity is Not Socially Expensive , 2013 .

[50]  Wiston Adrián Risso,et al.  The informational efficiency and the financial crashes , 2008 .

[51]  F. Diebold,et al.  UNIVERSITY OF SOUTHERN CALIFORNIA Center for Applied Financial Economics (CAFE) On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms , 2011 .

[52]  Rangaraj M. Rangayyan,et al.  Measures of angular spread and entropy for the detection of architectural distortion in prior mammograms , 2012, International Journal of Computer Assisted Radiology and Surgery.

[53]  J. Bernardo.  Expected Information as Expected Utility , 1979 .

[54]  Dong Xiang,et al.  Information-theoretic measures for anomaly detection , 2001, Proceedings 2001 IEEE Symposium on Security and Privacy. S&P 2001.

[55]  Kenneth S. Rogoff,et al.  Growth in a Time of Debt , 2010 .

[56]  Lucia Alessi,et al.  'Real Time' Early Warning Indicators for Costly Asset Price Boom/Bust Cycles: A Role for Global Liquidity , 2009 .

[57]  A. Reynolds.  Superstatistical mechanics of tracer-particle motions in turbulence. , 2003, Physical review letters.

[58]  Tatsuaki Wada,et al.  The κ-Generalizations of Stirling Approximation and Multinominal Coefficients , 2013, Entropy.

[59]  Jean-Charles Rochet,et al.  Systemic risk, interbank relations and liquidity provision by the Central Bank , 2000 .

[60]  Franklin Allen,et al.  Systemic risk and macroprudential regulation , 2012 .

[61]  Jiahui Wang,et al.  Modeling Financial Time Series with S-PLUS® , 2003 .

[62]  J. Alvarez,et al.  A multiscale entropy approach for market efficiency , 2012 .

[63]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[64]  Hao Jiang,et al.  Tail Risk and Asset Prices , 2013 .

[65]  Vyas Sekar,et al.  An empirical evaluation of entropy-based traffic anomaly detection , 2008, IMC '08.

[66]  N. Bloom.  The Impact of Uncertainty Shocks , 2007 .

[67]  Luc Laeven,et al.  Systemic Banking Crises: A New Database , 2008, SSRN Electronic Journal.

[68]  Chonghui Guo,et al.  Entropy optimization of scale-free networks’ robustness to random failures , 2005, cond-mat/0506725.

[69]  Rongxi Zhou,et al.  Applications of Entropy in Finance: A Review , 2013, Entropy.

[70]  Ernesto P. Borges,et al.  Mixing and equilibration: Protagonists in the scene of nonextensive statistical mechanics , 2001, cond-mat/0109506.

[71]  Til Schuermann,et al.  Stress Testing Banks , 2013 .

[72]  S. Abe,et al.  Nonextensive Statistical Mechanics and Its Applications , 2010 .

[73]  Jean-Christophe Chazalette.  The European Sovereign Debt Crisis , 2013 .

[74]  Gilson A. Giraldi,et al.  Computing the q-index for Tsallis Nonextensive Image Segmentation , 2009, 2009 XXII Brazilian Symposium on Computer Graphics and Image Processing.

[75]  Arnold Zellner,et al.  Bayesian Methods and Entropy in Economics and Econometrics , 1991 .

[76]  Lucia Alessi,et al.  Identifying Excessive Credit Growth and Leverage , 2014, SSRN Electronic Journal.

[77]  Katerina Smidkova,et al.  Banking, Debt and Currency Crises: Early Warning Indicators for Developed Countries , 2012, SSRN Electronic Journal.

[78]  L. Lorne Campbell.  Averaging entropy , 1995, IEEE Trans. Inf. Theory.

[79]  W. Greene,et al.  计量经济分析 = Econometric analysis , 2009 .