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

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  • Tanya Araujo
  • Francisco Louçã

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 Araujo & Francisco Louçã, 2005. "The Geometry of Crashes - A Measure of the Dynamics of Stock Market Crises," Working Papers Department of Economics 2005/15, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
  • Handle: RePEc:ise:isegwp:wp152005
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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.
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    9. 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.
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    11. Matteo Marsili, 2002. "Dissecting financial markets: Sectors and states," Papers cond-mat/0207156, arXiv.org.
    12. 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.
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    Citations

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    Cited by:

    1. Rui Faustino, 2016. "Portuguese National Accounts: a network approach," Working Papers Department of Economics 2016/18, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    2. Tanya Araújo & Francisco Louçã, 2008. "Bargaining Clouds, or Mathematics as a Metaphoric Exploration of the Unexpected," Working Papers Department of Economics 2008/27, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    3. Tanya Araujo & João Dias & Samuel Eleutério & Francisco Louçã, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Working Papers Department of Economics 2012/21, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    4. Cajueiro, Daniel O. & Tabak, Benjamin M. & Werneck, Filipe K., 2009. "Can we predict crashes? The case of the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1603-1609.
    5. Araújo, Tanya & Spelta, Alessandro, 2014. "Structural changes in cross-border liabilities: A multidimensional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 277-287.
    6. 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.
    7. Tanya Ara'ujo & Jo~ao Dias & Samuel Eleut'erio & Francisco Louc{c}~a, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Papers 1207.1202, arXiv.org.
    8. Samuel Eleut'erio & Tanya Ara'ujo & R. Vilela Mendes, 2011. "Portfolios and the market geometry," Papers 1108.4102, arXiv.org.
    9. Tanya Araujo & Francisco Louçã, 2007. "The Seismography of Crashes in Financial Markets," Working Papers Department of Economics 2007/05, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    10. Alessandro Spelta & Tanya Araujo, 2012. "Interlinkages and structural changes in cross-border liabilities: a network approach," Working Papers Department of Economics 2012/19, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    11. Lee, Junghoon & Youn, Janghyuk & Chang, Woojin, 2012. "Intraday volatility and network topological properties in the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1354-1360.
    12. Araújo, Tanya & Dias, João & Eleutério, Samuel & Louçã, Francisco, 2013. "A measure of multivariate kurtosis for the identification of the dynamics of a N-dimensional market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3708-3714.

    More about this item

    Keywords

    financial markets; stochastic geometry; complexity; market spaces; market structures.;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • G1 - Financial Economics - - General Financial Markets

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