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The Geometry of Crashes - A Measure of the Dynamics of Stock Market Crises

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  • Tanya Ara'ujo
  • Francisco Louc{c}~a

Abstract

This paper investigates the dynamics of stocks in the S&P500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose, which is a robust index of the dynamics of the market structure and provides information on the intensity and the sectoral impact of the crises. With this measure, we analyze the effects of some extreme phenomena on the geometry of the market. Nine crashes between 1987 and 2001 are compared by looking at the way they modify the shape of the manifold that describes the S&P500 market space. These crises are identified as (a) structural, (b) general and (c) local.

Suggested Citation

  • Tanya Ara'ujo & Francisco Louc{c}~a, 2005. "The Geometry of Crashes - A Measure of the Dynamics of Stock Market Crises," Papers physics/0506137, arXiv.org, revised Jul 2005.
    • Handle: RePEc:arx:papers:physics/0506137
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    References listed on IDEAS

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    1. G. Bonanno & F. Lillo & R. N. Mantegna, 2001. "High-frequency cross-correlation in a set of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 96-104.
    2. Mendes, R.Vilela, 2001. "Structure-generating mechanisms in agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 537-561.
    3. A. Johansen & D. Sornette, 2002. "Endogenous versus Exogenous Crashes in Financial Markets," Papers cond-mat/0210509, arXiv.org.
    4. Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N., 2001. "Levels of complexity in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 16-27.
    5. Vilela Mendes, R. & Araújo, Tanya & Louçã, Francisco, 2003. "Reconstructing an economic space from a market metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 635-650.
    6. Di Matteo, T. & Aste, T. & Mantegna, R.N., 2004. "An interest rates cluster analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(1), pages 181-188.
    7. Lillo, Fabrizio & Mantegna, Rosario N, 2004. "Dynamics of a financial market index after a crash," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 125-134.
    8. Kullmann, L & Kertész, J & Mantegna, R.N, 2000. "Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 412-419.
    9. G. Bonanno & G. Caldarelli & F. Lillo & S. Micciché & N. Vandewalle & R. Mantegna, 2004. "Networks of equities in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 38(2), pages 363-371, March.
    10. Matteo Marsili, 2002. "Dissecting financial markets: Sectors and states," Papers cond-mat/0207156, arXiv.org.
    11. Matteo Marsili, 2002. "Dissecting financial markets: sectors and states," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 297-302.
    12. Anders Johansen & Didier Sornette, 2000. "The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash," Papers cond-mat/0004263, arXiv.org, revised May 2000.
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    Cited by:

    1. Naylor, Michael J. & Rose, Lawrence C. & Moyle, Brendan J., 2007. "Topology of foreign exchange markets using hierarchical structure methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 199-208.

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