Mathematical Modeling of Systemic Risk

Chapter
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 18)

Abstract

Since the onset of the financial crisis in 2007, more than 370 of the almost 8,000 US banks insured by the Federal Deposit Insurance Corporation have failed. By comparison, between 2000 and 2004 there were around 30 failures and no failures occurred between 2005 and the beginning of 2007.

Keywords

Random Graph Balance Sheet Degree Sequence Giant Component Financial Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We would like to thank Rama Cont and Damir Filipović for helpful comments and discussions that improved the presentation of this chapter. Andreea Minca would like to thank the Natixis Foundation for Quantitative Research who supported this work. Hamed Amini gratefully acknowledges financial support from the Austrian Science Fund (FWF) though project P21709.

References

  1. 1.
    T. Adrian and H. S. Shin. Financial intermediary leverage and value-at-risk. Federal Reserve Bank of New York Staff Reports, (338), 2008.Google Scholar
  2. 2.
    T. Adrian and H. S. Shin. The changing nature of financial intermediation and the financial crisis of 2007–2009. Annual Review of Economics, 2(1):603–618, 2010.CrossRefGoogle Scholar
  3. 3.
    F. Allen and D. Gale. Financial contagion. Journal of Political Economy, 108(1):1–33, 2000.CrossRefGoogle Scholar
  4. 4.
    H. Amini, R. Cont, and A. Minca. Resilience to Contagion in Financial Networks. SSRN eLibrary, 2010.Google Scholar
  5. 5.
    H. Amini, R. Cont, and A. Minca. Stress testing the resilience of financial networks. To appear in the International Journal of Theoretical and Applied Finance, 2011.Google Scholar
  6. 6.
    S. Battiston, D. D. Gatti, M. Gallegati, B. Greenwald, and J. E. Stiglitz. Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk. Preprint available at http://www.nber.org/papers/w15611, 2009.
  7. 7.
    E. A. Bender and E. R. Canfield. The asymptotic number of labeled graphs with given degree sequences.Journal of Combinatorial Theory, Series A, 24:296–307, 1978.Google Scholar
  8. 8.
    B. Bollobás. The asymptotic number of unlabelled regular graphs. J. London Math. Soc. (2), 26(2):201–206, 1982.Google Scholar
  9. 9.
    B. Bollobás and O. M. Riordan. Mathematical results on scale-free random graphs. InHandbook of graphs and networks, pages 1–34. Wiley-VCH, Weinheim, 2003.Google Scholar
  10. 10.
    M. Boss, H. Elsinger, M. Summer, and S. Thurner. The network topology of the interbank market. Quantitative Finance, (4):677–684, 2004.Google Scholar
  11. 11.
    M. K. Brunnermeier. Deciphering the liquidity and credit crunch 2007–2008.Journal of Economic Perspectives, 23(1):77–100, 2009.Google Scholar
  12. 12.
    J. A. Chan-Lau, M. Espinosa, K. Giesecke, and J. A. Sole. Assessing the systemic implications of financial linkages. In Global Financial Stability Report. International Monetary Fund, 2009.Google Scholar
  13. 13.
    R. Cifuentes, G. Ferrucci, and H. Shin. Liquidity risk and contagion.Journal of the European Economic Association, 3:556–566, 2005.Google Scholar
  14. 14.
    R. Cont and A. Minca. Credit default swaps and systemic risk. Working Paper, 2011.Google Scholar
  15. 15.
    R. Cont and A. Minca. Recovering portfolio default intensities implied by CDO quotes.Mathematical Finance, 2011.Google Scholar
  16. 16.
    R. Cont, A. Moussa, and E. B. Santos. Network Structure and Systemic Risk in Banking Systems. Preprint available at http://papers.ssrn.com/sol3/id=1733528, 2010.
  17. 17.
    R. Cont and L. Wagalath. Running for the exit: distressed selling and endogenous correlation in financial markets.Mathematical Finance, 2011.Google Scholar
  18. 18.
    C. Cooper and A. M. Frieze. The size of the largest strongly connected component of a random digraph with a given degree sequence.Combinatorics, Probability & Computing, 13(3):319–337, 2004.Google Scholar
  19. 19.
    D. W. Diamond and R. G. Rajan. Fear of Fire Sales and the Credit Freeze. SSRN eLibrary, 2009.Google Scholar
  20. 20.
    X. Ding, K. Giesecke, and P. I. Tomecek. Time-changed birth processes and multiname credit derivatives.Oper. Res., 57(4):990–1005, 2009.Google Scholar
  21. 21.
    D. Duffie. The failure mechanics of dealer banks.Journal of Economic Perspectives, 24(1):51–72, 2010.Google Scholar
  22. 22.
    L. Eisenberg and T. H. Noe. Systemic Risk in Financial Systems. Management Science, 47(2):236–249, 2001.MATHCrossRefGoogle Scholar
  23. 23.
    P. Erdős and A. Rényi. On random graphs. I.Publ. Math. Debrecen, 6:290–297, 1959.Google Scholar
  24. 24.
    P. Erdős and A. Rényi. On the evolution of random graphs.Publ. Math. Inst. Hung. Acad. Sci, 5:17–61, 1960.Google Scholar
  25. 25.
    E. Errais, K. Giesecke, and L. R. Goldberg. Affine point processes and portfolio credit risk. SIAM J. Financial Math., 1:642–665, 2010.MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    P. Gai and S. Kapadia. Contagion in Financial Networks.Proceedings of the Royal Society A, 466(2120):2401–2423, 2010.Google Scholar
  27. 27.
    P. Gai and S. Kapadia. Liquidity hoarding, network externalities, and interbank market collapse.Mimeo, Bank of England, 2010.Google Scholar
  28. 28.
    K. Giesecke. Portfolio credit risk: top-down vs bottom-u. In Cont, R. (ed.) : Frontiers in quantitative finance: credit risk and volatility modeling. Wiley, 2008.Google Scholar
  29. 29.
    J. Gleeson, T. R. Hurd, S. Melnik, and A. Hackett. Systemic risk in banking networks without monte carlo simulation. In E. Kranakis, editor,Advances in Network Analysis and its Applications, Mathematics in Industry. Springer Verlag, Berlin Heidelberg New York, 2011.Google Scholar
  30. 30.
    A. G. Haldane. Rethinking the financial networks. Speech delivered at Financial Student Association in Amsterdam, http://www.bankofengland.co.uk/publications/speeches/2009/speech386.pdf, 2009.
  31. 31.
    A. G. Haldane and R. M. May. Systemic risk in banking ecosystems.Nature, 469:351–355, 2011.Google Scholar
  32. 32.
    M. Hellwig. Systemic aspects of risk management in banking and finance. Swiss Journal of Economics and Statistics, 131:723–737, 1995.Google Scholar
  33. 33.
    S. Janson, T. Łuczak, and A. Rucinski.Random graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley-Interscience, New York, 2000.Google Scholar
  34. 34.
    R. Jarrow and P. Protter. Structural versus reduced form models: a new information based perspective.Journal of Investment Management, 2(2):34–43, 2004.Google Scholar
  35. 35.
    N. Kiyotaki and J. Moore. Credit chains. Mimeo, Walras-Bowley Lecture to the North American Meeting of the Econometric Society, Iowa City, IA, 1996.Google Scholar
  36. 36.
    M. Molloy and B. Reed. A critical point for random graphs with a given degree sequence.Random Structures Algorithms, 6(2–3):161–179, 1995.Google Scholar
  37. 37.
    M. Molloy and B. Reed. The size of the giant component of a random graph with a given degree sequence.Combinatorics, Probability and Computing, 7:295–305, 1998.Google Scholar
  38. 38.
    S. Morris and H. S. Shin. Illiquidity component of credit risk. Working paper, 2009.Google Scholar
  39. 39.
    M. Newman, Albert-László Barabási, and D. J. Watts.The Structure and Dynamics of Networks. Princeton University Press, 2006.Google Scholar
  40. 40.
    M. E. J. Newman. Spread of epidemic disease on networks. Phys. Rev. E, 66(1):016128, Jul 2002.Google Scholar
  41. 41.
    M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64:026118, 2001.CrossRefGoogle Scholar
  42. 42.
    P. Schönbucher. Portfolio losses and the term structure of loss transition rates: a new methodology for the pricing of portfolio credit derivatives.Working paper, 2005.Google Scholar
  43. 43.
    K. Soramaki, M. L. Bech, J. Arnold, R. J. Glass, and W. E. Beyeler. The topology of interbank payment flows. Physica A: Statistical Mechanics and its Applications, 379(1):317–333, 2007.Google Scholar
  44. 44.
    C. Upper. Simulation methods to assess the danger of contagion in interbank markets. Journal of Financial Stability, 7:111–125, 2011.CrossRefGoogle Scholar
  45. 45.
    D. J. Watts. A simple model of global cascades on random networks. Proceedings of the National Academy of Sciences of the USA, 99(9):5766–5771, 2002.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.EPFLLausanneSwitzerland
  2. 2.ORIE DepartmentCornell UniversityIthacaUSA

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