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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.

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File URL: http://pascal.iseg.utl.pt/~depeco/wp/wp152005.pdf
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Bibliographic Info

Paper provided by ISEG - School of Economics and Management, Department of Economics, University of Lisbon in its series Working Papers Department of Economics with number 2005/15.

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Date of creation: 2005
Date of revision:
Handle: RePEc:ise:isegwp:wp152005

Contact details of provider:
Postal: Department of Economics, ISEG - School of Economics and Management, University of Lisbon, Rua do Quelhas 6, 1200-781 LISBON, PORTUGAL
Web page: https://aquila1.iseg.ulisboa.pt/aquila/departamentos/EC

Related research

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

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References

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  1. R. Vilela Mendes & Tanya Ara\'{u}jo & Francisco Lou\c{c}\~{a}, 2002. "Reconstructing an economic space from a market metric," Papers cond-mat/0211108, arXiv.org.
  2. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 11(1), pages 193-197, September.
  3. Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2001. "Levels of complexity in financial markets," Papers cond-mat/0104369, arXiv.org.
  4. Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2000. "High-frequency Cross-correlation in a Set of Stocks," Papers cond-mat/0009350, arXiv.org, revised Nov 2000.
  5. G. Bonanno & G. Caldarelli & F. Lillo & S. Micciche` & N. Vandewalle & R. N. Mantegna, 2004. "Networks of equities in financial markets," Papers cond-mat/0401300, arXiv.org.
  6. A. Johansen & D. Sornette, 2002. "Endogenous versus Exogenous Crashes in Financial Markets," Papers cond-mat/0210509, arXiv.org.
  7. T. Di Matteo & T. Aste & R. N. Mantegna, 2004. "An interest rates cluster analysis," Papers cond-mat/0401443, arXiv.org.
  8. Onnela, J.-P. & Chakraborti, A. & Kaski, K. & Kertész, J., 2003. "Dynamic asset trees and Black Monday," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 247-252.
  9. 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.
  10. 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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Citations

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Cited by:
  1. Alessandro Spelta & Tanya Araújo, 2012. "Interlinkages and structural changes in cross-border liabilities: a network approach," Quaderni di Dipartimento 181, University of Pavia, Department of Economics and Quantitative Methods.
  2. 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.
  3. Samuel Eleut\'erio & Tanya Ara\'ujo & R. Vilela Mendes, 2011. "Portfolios and the market geometry," Papers 1108.4102, arXiv.org.
  4. Tanya Araùjo & Alessandro Spelta, 2013. "Structural changes in cross-border liabilities: a multidimensional approach," DEM Working Papers Series 050, University of Pavia, Department of Economics and Management.
  5. Tanya Ara\'ujo & Jo\~ao Dias & Samuel Eleut\'erio & Francisco Lou\c{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.
  6. 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 - School of Economics and Management, Department of Economics, University of Lisbon.
  7. Tanya Araujo & Francisco Louçã, 2007. "The Seismography of Crashes in Financial Markets," Working Papers Department of Economics 2007/05, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Tanya Araújo & Francisco Louçã, 2008. "Bargaining Clouds, or Mathematics as a Metaphoric Exploration of the Unexpected," Working Papers Department of Economics 2008/27, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.

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