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.
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T. Adrian and H. S. Shin. Financial intermediary leverage and value-at-risk. Federal Reserve Bank of New York Staff Reports, (338), 2008.
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.
F. Allen and D. Gale. Financial contagion. Journal of Political Economy, 108(1):1–33, 2000.
H. Amini, R. Cont, and A. Minca. Resilience to Contagion in Financial Networks. SSRN eLibrary, 2010.
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.
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.
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.
B. Bollobás. The asymptotic number of unlabelled regular graphs. J. London Math. Soc. (2), 26(2):201–206, 1982.
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.
M. Boss, H. Elsinger, M. Summer, and S. Thurner. The network topology of the interbank market. Quantitative Finance, (4):677–684, 2004.
M. K. Brunnermeier. Deciphering the liquidity and credit crunch 2007–2008.Journal of Economic Perspectives, 23(1):77–100, 2009.
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.
R. Cifuentes, G. Ferrucci, and H. Shin. Liquidity risk and contagion.Journal of the European Economic Association, 3:556–566, 2005.
R. Cont and A. Minca. Credit default swaps and systemic risk. Working Paper, 2011.
R. Cont and A. Minca. Recovering portfolio default intensities implied by CDO quotes.Mathematical Finance, 2011.
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.
R. Cont and L. Wagalath. Running for the exit: distressed selling and endogenous correlation in financial markets.Mathematical Finance, 2011.
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.
D. W. Diamond and R. G. Rajan. Fear of Fire Sales and the Credit Freeze. SSRN eLibrary, 2009.
X. Ding, K. Giesecke, and P. I. Tomecek. Time-changed birth processes and multiname credit derivatives.Oper. Res., 57(4):990–1005, 2009.
D. Duffie. The failure mechanics of dealer banks.Journal of Economic Perspectives, 24(1):51–72, 2010.
L. Eisenberg and T. H. Noe. Systemic Risk in Financial Systems. Management Science, 47(2):236–249, 2001.
P. Erdős and A. Rényi. On random graphs. I.Publ. Math. Debrecen, 6:290–297, 1959.
P. Erdős and A. Rényi. On the evolution of random graphs.Publ. Math. Inst. Hung. Acad. Sci, 5:17–61, 1960.
E. Errais, K. Giesecke, and L. R. Goldberg. Affine point processes and portfolio credit risk. SIAM J. Financial Math., 1:642–665, 2010.
P. Gai and S. Kapadia. Contagion in Financial Networks.Proceedings of the Royal Society A, 466(2120):2401–2423, 2010.
P. Gai and S. Kapadia. Liquidity hoarding, network externalities, and interbank market collapse.Mimeo, Bank of England, 2010.
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.
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.
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.
A. G. Haldane and R. M. May. Systemic risk in banking ecosystems.Nature, 469:351–355, 2011.
M. Hellwig. Systemic aspects of risk management in banking and finance. Swiss Journal of Economics and Statistics, 131:723–737, 1995.
S. Janson, T. Łuczak, and A. Rucinski.Random graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley-Interscience, New York, 2000.
R. Jarrow and P. Protter. Structural versus reduced form models: a new information based perspective.Journal of Investment Management, 2(2):34–43, 2004.
N. Kiyotaki and J. Moore. Credit chains. Mimeo, Walras-Bowley Lecture to the North American Meeting of the Econometric Society, Iowa City, IA, 1996.
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.
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.
S. Morris and H. S. Shin. Illiquidity component of credit risk. Working paper, 2009.
M. Newman, Albert-László Barabási, and D. J. Watts.The Structure and Dynamics of Networks. Princeton University Press, 2006.
M. E. J. Newman. Spread of epidemic disease on networks. Phys. Rev. E, 66(1):016128, Jul 2002.
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.
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.
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.
C. Upper. Simulation methods to assess the danger of contagion in interbank markets. Journal of Financial Stability, 7:111–125, 2011.
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.
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.
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Amini, H., Minca, A. (2012). Mathematical Modeling of Systemic Risk. In: Kranakis, E. (eds) Advances in Network Analysis and its Applications. Mathematics in Industry, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30904-5_1
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