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Systemic risk analytics: A data-driven multi-agent financial network (MAFN) approach

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Abstract

Systemic risk from financial intermediaries (FIs) refers to a negative externality problem, which is rife with fallacy of composition-type errors. To ‘see’ why seemingly rational behaviour at the level of an individual FI contributes to system-wide instability is a non-trivial exercise, which requires holistic visualization and modelling techniques. Paradox of volatility inherent to market price-based measures of systemic risk has made bilateral balance sheet and off balance data between FIs and network analysis essential for systemic risk management. There is both a data and a skills gap in implementing large-scale data-driven multi-agent financial network models that can operationalize macro-prudential policy. Different designs for a Pigou-type systemic risk surcharge are discussed with special reference to the Markose eigen-pair method, which simultaneously determines the degree of instability of the network of financial flows of obligors and also the rank order in the centrality of FIs contributing to it.

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REFERENCES AND NOTES

  • Buiter, W. (2009) The unfortunate uselessness of most ‘state of the art’ academic monetary economics. Available from: www.voxeu.org/index.php?q=node/3210, accessed 3 May 2013.

  • Stiglitz, J.E. (2011) Rethinking macroeconomics: What failed, and how to repair it. Journal of European Economic Association 9 (4): 591–645.

    Article  Google Scholar 

  • Blundell-Wignall, A. and Atkinson, P. (2008) The subprime crisis: Causal distortions and regulatory reform. In: P. Bloxham and C. Kent (eds.) Lessons from the Financial Turmoil of 2007 and 2008, Proceedings of a conference held at the H.C. Coombs Centre for Financial Studies; 14–15 July, Kirribilli. Sydney, Australia: Reserve Bank of Australia.

    Google Scholar 

  • Brunnermeier, M., Crockett, A., Goodhart, C., Persaud, A. and Shin, H. (2009) The Fundamental Principles of Financial Regulation. Geneva Reports on the World Economy 11, International Center for Money and Banking Studies.

  • Hellwig, M. (2010) Capital regulation after the crisis: Business as usual? CESifo DICE Report, Journal for Institutional Comparisons 8 (2): 40–46.

    Google Scholar 

  • Markose, S., Giansante, S., Gatkowski, M. and Shaghagi, A.R. (2010) Too Interconnected to Fail: Financial Contagion and Systemic Risk in Network Model of CDS and Other Credit Enhancement Obligations of US Banks. University of Essex Economics Department Discussion Paper Series. February, Discussion paper no. 683.

  • Buiter1 wrote: ‘… the typical graduate macroeconomics and monetary economics training received at Anglo-American universities during the past 30 years or so, may have set back by decades serious investigations of aggregate economic behaviour and economic policy-relevant understanding’. This view was echoed by Nobel Prize Winner Paul Krugman in the Economist, June 2010, ‘Most work in macro-economics in the past 30 years has been useless at best and harmful at worst’.

  • Wieland, V. (2010) Model comparison and robustness: A proposal for policy analysis after the financial crisis. Goethe University Frankfurt, CEPR and CFS (mimeo).

  • Colander, D., Howitt, P., Kirman, A., Leijonhufvud, A. and Meherling, P. (2008) Beyond DSGE models: Toward an empirically based macroeconomics. Papers and Proceedings of the American Economic Association. American Economic Review 98 (2): 236–240.

    Article  Google Scholar 

  • Gorton, G. and Metrick, A. (2012) Securitized banking and the run on Repo. Journal of Financial Economics 104 (3): 425–451.

    Article  Google Scholar 

  • Schularick, M. and Taylor, A. (2012) Credit booms gone bust: Monetary policy, leverage cycles, and financial crises, 1870–2008. American Economic Review 102 (2): 1029–1061.

    Article  Google Scholar 

  • Markose, S. and Loke, Y.J. (2003) Network effects of cash-card substitution in transactions and low interest rate regimes. Economic Journal 113 (487): 456–476.

    Article  Google Scholar 

  • Marimon, R., Nicolini, J.P. and Teles, P. (1997) Electronic Money: The End of Inflation? Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis. Discussion Paper 122.

  • Foresight Report 2012. Available from: www.bis.gov.uk/assets/foresight/docs/computer-trading/12-1086-future-of-computer-trading-in-financial-markets-report.pdf. This report gives ample evidence for the challenges posed by the low latency environment in which algorithms rather than direct human inputs are needed to execute trades, accessed 3 May 2013.

  • Markose, S. (2005) Computability and evolutionary complexity: Markets as complex adaptive systems (CAS). Economic Journal 115 (504): F159–F192.

    Article  Google Scholar 

  • Kirman, A. (1992) Whom or what does the representative individual represent? Journal of Economic Perspectives 6 (2): 117–136.

    Article  Google Scholar 

  • Kirman, A. (1997) The economy as an evolving network. Journal of Evolutionary Economics 7 (4): 339–353.

    Article  Google Scholar 

  • Caruana, J. (2010) Macroprudential Policy: Working towards a New Consensus. Speech at the emerging framework for financial regulation and monetary policy. Washington DC, 23 April.

  • Clement, P. (2010) The term ‘macroprudential’: Origins and evolution. BIS Quarterly Review, March.

  • Alessandri, P. and Haldane, A. (2009) Banking on the state. Paper based on presentation at the Federal Reserve Bank of Chicago, 12th International Banking Conference Chicago, IL.

  • These include payouts to Goldman Sachs ($14 billion), Merrill Lynch ($6.2 billion), Bank of America ($0.8 billion) and Wachovia ($1 billion). Foreign banks were also beneficiaries. The major ones were Société Générale ($16.5 billion), Deutsche Bank ($8.5 billion), UBS ($3.8 billion), Barclays ($1.5 billion) and Royal Bank of Scotland ($1.1 billion). See Table 2 of the 2009 SIGTARP Report for this as well as on the bailout provisions for other AIG obligations, such as $20 billion commercial paper, which had implications for the US money market mutual funds, http://online.wsj.com/public/resources/documents/aig111609.pdf.

  • Acharya, V., Pedersen, L., Philippon, T. and Richardson, M. (2009) Regulating systemic risk. In: V. Acharya and M. Richardson (eds.) Restoring Financial Stability: How to Repair a Failed System. New York: Wiley.

    Chapter  Google Scholar 

  • Bluhm, M., Faia, E. and Krahnen, J.P. (2013) Endogenous banks’ networks, cascades and systemic risk. Goethe University (mimeo).

  • Pigou, A.C. (1946) The Economics of Welfare 8th edn. London: Macmillan.

    Google Scholar 

  • Haldane, A. (2009) Rethinking the financial network. Speech delivered at the Financial Student Association, Amsterdam.

  • ECB Workshop on Recent Advances in Modelling Systemic Risk Using Network Analysis, 5 October 2009. Available from: www.ecb.europa.eu/pub/pdf/other/modellingsystemicrisk012010en.pdf?d216f976f3587224bcc087cc8149ed49, and also the IMF Workshop on Operationalizing Systemic Risk Monitoring, 26–28 May 2010. Available from: www.imf.org/external/np/seminars/eng/2010/MCM/index.htm, accessed 3 May 2013.

  • Flood, M., Mendelowitz, A. and Nichols, B. (2012) Monitoring financial stability in a complex world. In: V. Lemieux (ed.) Financial Analysis and Risk Management: Data Governance, Analytics, and Life Cycle Management., Springer Verlag: Vancouver.

  • Bisias, D., Flood, M., Lo, A. and Valavanis, S. (2012) A Survey of Systemic Risk Analytics. Office of Financial Research. Working paper no. 0001.

  • Huertas, T.F. (2011) The road to better resolution: From bail out to bail in. Available from www2.lse.ac.uk/fmg/events/conferences/2011/DBWorkshop_14Mar2011/4-ThomasHuertas.pdf, accessed 3 May 2013.

  • Dewatripont, M. and Freixas, X. (2010) Bank resolution. Financial Markets Group, ‘Bail-in’ and Special Resolution Workshop, London School of Economics.

  • FSB Progress Report on Resolution of SIFIs, November 2012. Available from: www.financialstabilityboard.org/publications/r_121031aa.pdf. See also, FSB Reducing the moral hazard posed by systemically important financial institutions. 20 October 2010. Available from: www.financialstabilityboard.org/publications/r_101111a.pdf, accessed 3 May 2013.

  • This challenging aspect of a systemic risk framework has been raised under items 14–16 of the Bank of England Record of Financial Committee Meeting (RFCM) held on 16 March 2012. Available from: www.bankofengland.co.uk/publications/Documents/records/fpc/pdf/2012/record1203.pdf, accessed 3 May 2013.

  • Markose, S. (2012) Systemic Risk from Global Financial Derivatives: A Network Analysis of Contagion and Its Mitigation with Super-Spreader Tax. International Monetary Fund working paper. November; 12(282). Available from: www.imf.org/external/pubs/ft/wp/2012/wp12282.pdf, accessed 3 May 2013.

  • Moosa, I. (2010) The myth of too big to fail. Journal of Banking Regulation 11 (4): 319–333.

    Article  Google Scholar 

  • Borio, C. and Drehmann, M. (2009) Towards an operational framework for financial stability: ‘Fuzzy’ measurement and its consequences. In: Banco Central de Chile (ed.) Financial Stability, Monetary Policy and Central Banking, Central Bank of Chile, Santiago. Also available as BIS Working paper no. 284.

  • Furfine, C.H. (2003) Interbank exposures: Quantifying the risk of contagion. Journal of Money, Credit and Banking 35 (1): 111–128.

    Article  Google Scholar 

  • Upper, C. (2011) Simulation methods to assess the danger of contagion in interbank markets. Journal of Financial Stability 7 (3): 111–125.

    Article  Google Scholar 

  • Yellen, J. (2013) Interconnectedness and systemic risk: Lessons from the financial crisis and policy implications. Board of Governors of the Federal Reserve System at the American Economic Association/American Finance Association Joint Luncheon, San Diego, CA.

  • May, R.M. (1972) Will a large complex system be stable? Nature 238 (5364): 413–414.

    Article  Google Scholar 

  • May, R.M. (1974) Stability and Complexity in Model Ecosystems. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Biasis et al28 cite the trade association Clearing House for 17 of the world’s largest commercial banks on this: ‘there are significant open questions regarding the purported theoretical and policy foundations, as well as appropriate calibration, for a G-SIB surcharge’.

  • Thornton, H. (1938) An enquiry into the nature and effects of the paper credit of Great Britain; 1802. Introduction by Hayek, F. Printed for J. Hatchard, bookseller to the Queen, (opposite York House) Piccadilly, and messrs. F. and C. Rivington, St. Paul’s Church Yard, London.

  • Singh, M. and Aitken, J. (2010) The (Sizable) Role of Rehypothecation in the Shadow Banking System. IMF Working paper 10/172.

  • I first encountered this in Singh and Aitken.43 Rehypothecation refers to the reuse of the same collateral to obtain funds by different parties before its maturity.

  • Singh, M. (2011) Velocity of Pledged Collateral- Analysis and Implications. IMF Working paper 11/256.

  • Milne, A. (2013) Register, cap and trade: A proposal for containing systemic liquidity risk. Economics: The Open-Access, Open-Assessment E-Journal. Available from: http://dx.doi.org/10.5018/economics-ejournal.ja.2013-7, accessed 3 May 2013.

  • See Milne46 for an interesting discussion on this. Stiglitz2 (pp. 603–609) has commented on this centuries-long unsolved problem in capitalism.

  • Markose, S., Giansante, S. and Shaghaghi, A. (2012) Too interconnected to fail financial network of U.S. CDS market: Topological fragility and systemic risk. Journal of Economic Behavior and Organization 83 (3): 627–646.

    Article  Google Scholar 

  • Markose, S., Oluwasegun, B. and Giansante, S. (2012) Multi-Agent Financial Network (MAFN) model of US Collateralized Debt Obligations (CDO): Regulatory capital arbitrage, negative CDS carry trade and systemic risk analysis. In: B. Alexandrova-Kabadjova, S. Martinez-Jaramillo, A.L. Garcia-Almanza, E. Tsang, (eds.) Simulation in Computational Finance and Economics: Tools and Emerging Applications., IGI Global, Pennsylvania. August. Also available from University of Essex Economics Discussion Papers 714.

  • Darby, M. (1994) Over the Counter Derivatives and Systemic Risk to the Global Financial System. NBER Working paper no. 4801.

  • Verstein, A. (2011) The misregulation of person-to-person lending. UC Davis Law Review 45: 445–529.

    Google Scholar 

  • Hayek, F.A. (1976) Denationalization of money. 3rd edn. London: Institute of Economic Affairs.

  • Electronic peer-to-peer (P2P) lending between ultimate end users and fund surplus units (see Economist, 15–21 December 2012) bypasses the dysfunctional fractional intermediating banking sector. Platforms facilitating P2P lending do not suffer maturity mismatch or ‘runs’ as in banks as P2P lenders cannot withdraw funds once they have been lent and can expect repayment at a fixed maturity date (p. 466).51 The electronic matching platform is an evolutionary development that is made feasible by the IT revolution. Note, the latter has facilitated the substitution away from state-supplied notes and coins in economic transactions that Hayek52 had hypothesized as the only permanent way to end inflation. Of course, Hayek52 did not anticipate the IT payment innovations such as EFTPOS (electronic funds transfer at point of sale) and e-commerce that have vitiated the use of cash in transactions.

  • Schularick and Taylor11 state that ‘it is a mishap of history that just at the time when credit mattered more than ever before, the reigning doctrine had sentenced it to playing no constructive role in monetary policy. In terms of policymakers and researchers history demonstrates that they ignore credit at their peril’.

  • White, W. (2006) Is Price Stability Enough? Bank of International Settlements Working paper no. 205.

  • Borio, C. and White, W. (2004) Whither Monetary and Financial Stability? The Implications of Evolving Policy Regimes. BIS Working paper no. 147.

  • Pozsar, Z., Adrian, T., Ashcraft, A. and Boesky, H. (2012) Shadow Banking. Federal Reserve Bank of New York Staff Report no. 458.

  • Skaperdas, S. (2011) Policy Making in the Eurozone and the Core vs. Periphery Problem. CESifo Forum, Ifo Institute for Economic Research at the University of Munich, Vol. 12, Issue 2, pp. 12–18.

  • In the case of Spain, the fastest growing housing bubble, which outstripped the one in the United States, was financed by French and German banks with the sale of mortgage-backed covered bonds primarily by Spanish Cajas, which grew from a mere €50 billion in 2003 to over €350 billion by 2007. See Table 1 in http://www.ecbc.eu/uploads/attachements/45/64/3.27%20Spain.pdf. The website and reports are those of the European Covered Bonds Council of the European Mortgage Federation.

  • Bean, C., Paustian, M., Penalver, A. and Taylor, T. (2010) Monetary Policy after the Fall. Federal Reserve Bank of Kansas City Annual Conference; 26–28 August, Jackson Hole, WY.

  • Castren, O. and Kavonius, I.K. (2009) Balance Sheet Interlinkages and Macro-Financial Risk Analysis in the Euro Area. ECB Working paper no. 1124.

  • Barwell, R. and Burrows, O. (2011) Growing Fragilities? Balance Sheets in the Great Moderation. Financial Stability. Bank of England Discussion paper no. 10.

  • Buchanan, M. (2009) Meltdown modelling: Could agent-based computer models prevent another financial crisis? Nature 460 (7256): 680–682.

    Article  Google Scholar 

  • Farmer, D. and Foley, D. (2009) The economy needs agent based modelling. Nature 460 (7256): 685–686.

    Article  Google Scholar 

  • Markose, S. (2011) Multi-Agent Financial Modelling and Complexity Approach to Systemic Risk Monitoring for G10 and BRICs: A Post 2007 Perspective. Talk given at Reserve Bank of India, Financial Stability Unit, August 2010.

  • Haldane, A. (2013) Speech at BCBS Workshop on Regulatory Data and Systemic Risk Analytics, Bank of England.

  • Haldane’s speech at the 2013 January BCBS Workshop66 described this as the Star Trek vision of a large electronic screen displaying financial data as an interconnected system.

  • Tesfatsion, L. and Judd, K.L. (eds.) (2006) Handbook of Computational Economics, Volume 2: Agent-based Computational Economics, Handbooks in Economics Series. Amsterdam: North-Holland.

    Google Scholar 

  • LeBaron, B. (2000) Agent based computational finance: Suggested readings and early research. Journal of Economic Dynamics and Control 24 (5–7): 679–702.

    Article  Google Scholar 

  • Schelling, T. (1971) Dynamic models of segregation. Journal of Mathematical Sociology 1 (2): 143–186.

    Article  Google Scholar 

  • Arthur, W.B., Holland, J., LeBaron, B., Palmer, R. and Taylor, P. (1997) Asset pricing under endogenous expectations in an artificial stock market. In: W.B. Arthur, S. Durlauf and D. Lane (eds.) The Economy as an Evolving Complex System II. Reading, MA: Addison Wesley, pp. 15–44.

    Google Scholar 

  • Thurner, S., Farmer, J.D. and Geanakoplos, J. (2012) Leverage causes fat tails and clustered volatility. Quantitative Finance 12 (5): 695–707.

    Article  Google Scholar 

  • Johnson, J. (2011) Hypernetworks in the Science of Complex Systems. London: Imperial College Press.

    Google Scholar 

  • Johnson, J. (2006) Hypernetworks for Reconstructing the Dynamics of Multi-Level Systems. European Conference on Complex Systems. Oxford University, Oxford, 25–29 September.

  • Balakrishnan, S. et al. (2010) Midas: Integrating Public Financial Data. Proceedings of the 2010 International Conference on Management of Data; 6–11 June, Indianapolis.

  • Hernandez, M., Ho, M., Koutrika, R., Popa, L., Stanni, S. and Vaithyanathan, S. (2010) Unleashing the Power of Public Data for Financial Risk Measurement, Regulation and Governance. IBM research report RJ 10475(A1011-018).

  • This Special Issue contains developments in large-scale financial data-based modelling in different countries such as the United States, Austria and others.

  • Deissenberg, C., Dawid, H. and Van der Hoog, S. (2008) EURACE: A massively parallel agent-based model of the European economy. Applied Mathematics and Computation 204 (2): 541–552.

    Article  Google Scholar 

  • Aikman, D. et al (2009) Funding Liquidity Risk in Quantitative Model of Systemic Stability. Bank of England working paper no. 372.

  • The Bank of England Electronic Reporting Service (BEERS) obtains quarterly financial statements from all banks operating in the United Kingdom in an electronic format. However, the data is then aggregated to yield the balance sheet information for the Monetary and Financial Institutions Sector and also for the Table on Derivatives for all UK banks. Available from: www.bankofengland.co.uk/statistics/Pages/bankstats/2012/Dec12/default.aspx, accessed 3 May 2013.

  • Markose, S., Amadeo, A., Stephen, M. and Yang, J. (2012) Designing Large Value Payment Systems: An Agent-Based Approach. Economics Department University of Essex Working paper no. 700. Number 67.

  • Erev, I. and Roth, A. (1998) Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. American Economic Review 88 (4): 848–881.

    Google Scholar 

  • A limited attempt at this was done in Markose et al81 for an agent-based model for CHAPS data-based RTGS (Real Time Gross Settlement) liquidity posting decision problem. Erev and Roth82 reinforcement learning capabilities were given to RTGS participants in the ACE model to see if they could learn to play socially efficient outcomes rather than individually rational ones that result in payment gridlocks.

  • Kane, E. (2010) Redefining and containing systemic risk. Boston College (mimeo).

  • Eichengreen, B. (2010) Globalization and the Crisis. Institute for Economic Research University of Munich CESifo Forum Journal 11 (3): 20–24.

  • Mistrulli, P.E. (2011) Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns. Journal of Banking & Finance 35 (5): 1114–1127.

    Article  Google Scholar 

  • Cont, R., Moussa, A. and Santos, E. (2010) Network structure and systemic risk in banking systems. Available from SSRN: http://ssrn.com/abstract=1733528. Also available from: http://dx.doi.org/10.2139/ssrn.1733528, accessed 3 May 2013.

  • Craig, B. and Von Peter, G. (2010) Interbank Tiering and Money Center Banks. BIS working paper no. 322.

  • Hamilton, J.D. (1989) A new approach to the economic analysis of non stationary time series and business cycle. Econometrica 57 (2): 357–384.

    Article  Google Scholar 

  • Ang, A. and Bekaert, G. (2004) How do regimes affect asset allocation. Financial Analysts Journal 60 (2): 86–99.

    Article  Google Scholar 

  • Minsky, H. (1982) The financial-instability hypothesis: Capitalist processes and the behavior of the economy. In: C.P. Kindleberger and J. Laffargue (eds.) Financial Crises: Theory, History, and Policy. Cambridge: University Press.

    Google Scholar 

  • Figure 5(a) was the one which I used in my talk at the 2010 IMF Workshop on Operationalizing Systemic Risk.

  • Segoviano, M. and Goodhart, C. (2009) Banking Stability Measures. IMF working paper 09/04.

  • I am an avid fan of Goodhart’s law, but have to part company here.

  • Adrian, T. and Brunnermeier, M.K. (2009) CoVaR. Federal Reserve Bank of New York Staff Reports. No. 348.

  • Acharya, V., Pedersen, L., Philippon, T. and Richardson, M. (2010) Measuring Systemic Risk. Federal Reserve Bank of Cleveland working paper 1002.

  • Chan-Lau, Jorge A. (2010) Regulatory Capital Charges for Too-Connected-to-Fail Institutions: A Practical Proposal. IMF discussion paper 98/10.

  • Huang, X., Zhou, H. and Zhu, H. (2010) Systemic Risk Contribution. BIS working paper 60-63.

  • Tarashev, N., Borio, C. and Tsatsaronis, K. (2009) The systemic importance of financial institutions. BIS Quarterly Review, September 75–87.

  • Gauthier, C., Lehar, A. and Souissi, M. (2009) Macroprudential Capital Requirements and Systemic Risk. Ottawa: Bank of Canada. Working paper.

  • Danielsson, J., James, K., Valenzuela, M. and Zer, I. (2011) Model risk of systemic risk models. London School of Economics (mimeo).

  • Martinez Jaramillo, S., Alexandrova-Kabadjova, B., Bravo-Benitez, B. and Solorzano-Margain, J.P. (2012) An Empirical Study of the Mexican Banking System’s Network and Its Implications for Systemic Risk. Bank of Mexico working paper 2012-07.

  • Bluhm, M. and Krahnen, J.P. (2011) Default risk in an interconnected banking system with endogenous asset markets. Goethe University (mimeo).

  • Kirman, A., Markose, S., Giansante, S. and Pin, P. (2007) Marginal contribution, reciprocity, and equity in segregated groups: Bounded rationality and self-organization in social networks. Journal of Economic Dynamics and Control 31 (6): 2085–2107.

    Article  Google Scholar 

  • Myerson, R. (1977) Graphs and cooperation in games. Mathematical Operation Research 2 (3): 225–229.

    Article  Google Scholar 

  • That is, the weight, pi,s, is the same for all networks with the same number of nodes and is given by pi,s= if i∈S. Here, |S| denotes the cardinality of a set S, where S is a subset of set of all nodes, N, and S includes the ith FI. The MSV is given by the formula: φiMSV(v(c(g(S))= Here, v is the value function, such as the system value-at- risk, of a connected subgraph, in our case here of financial liabilities between FIs, respectively denoted by c(g(S)) and v(c(g(S\i)) is the value function calculation done for the connected subnetwork without i. This is explained in Section 3.1 of Kirman et al.104.

  • Node strength here is a simple measure given by the row sum of the matrix.

  • Wang, Y., Chakrabarti, D., Wang, C. and Faloutsos, C. (2003) Epidemic Spreading in Real Networks: An Eigenvalue Viewpoint. Reliable Distributed Systems, IEEE Symposium; 6–8 October, Florence.

  • In principle, this should be adjusted for master agreements that permit bilateral netting and also for collateral.

  • Denoting the row sum of the ith row of Θ′ by Si=Σjθji, λmax⩽max Si.

  • Giakkoupis, G., Gionis, A., Terzi, E. and Tsaparas, P. (2011) Models and algorithms for network immunization. University of Helsinki (mimeo).

  • Gai, P., Haldane, A. and Kapadia, S. (2010) Complexity, concentration and contagion. Journal of Monetary Economics 58 (5): 453–470.

    Article  Google Scholar 

  • Winter, S. (2010) Testimony submitted to the Congress of the United States, House Science and Technology Committee, 20 June.

  • In general, the unconstrained case of (A.1) is used, ujq. That is, the indicator function that signifies only banks that fail at q no longer applies and we have a weighted sum of the impact of all j counterparty banks, j≠i in the second term.

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Acknowledgements

This article has benefitted from discussions with Alistair Milne, Rosa Lastra, Patrick McGuire, Teressa Glasser, Michael Bennett, Liz Dixon, David Bholat, Ulrich Krüger and other participants at the Future of Regulatory Data and Systemic Risk Analytics, Bank of England Workshop, 17–18 January 2012. I am grateful for inputs from anonymous referees and from Dalwinder Singh, the Editor of the journal. All views, errors and omissions are mine and cannot be attributed to any of the institutions mentioned above.

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    Sheri M Markose

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Appendix

Appendix

The dynamics characterizing transmission of ‘infection’ in a financial networked system can be given by:

Here, we have an FI’s own metric of failure at q, which is given by u iq =(1−C iq /Ci0), where C iq /Ci0 is the ratio of capital at q and capital at initial date. The second term in (A.1) involves the losses from counterparties, j, that fail at q and these are denoted by an indicator function, which is set equal to 1. The sum of ‘infection rates’ defined by the sum of net liabilities of its j failed counterparties relative to its own capital is given by the term

In order for the eigen-pair stability analysis to be used, in matrix notation the dynamics of financial contagion takes the following form:114

Here, Θ′ is the transpose of the matrix in (1) with each element θ ij ′=θ ji and I is the identity matrix.

The system stability of (A.2) will be evaluated on the basis of the power iteration of the matrix Q. From (A.2), U q takes the form:

Markose33 shows how the stability of the system in (A.3) as q tends to infinity requires that the maximum eigenvalue, λmax, is less than the common threshold on capital, ρ.

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Markose, S. Systemic risk analytics: A data-driven multi-agent financial network (MAFN) approach. J Bank Regul 14, 285–305 (2013). https://doi.org/10.1057/jbr.2013.10

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