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Dynamics of a financial market index after a crash

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  • Lillo, Fabrizio
  • Mantegna, Rosario N

Abstract

We discuss the statistical properties of index returns in a financial market just after a major market crash. The observed non-stationary behavior of index returns is characterized in terms of the exceedances over a given threshold. This characterization is analogous to the Omori law originally observed in geophysics. By performing numerical simulations and theoretical modelling, we show that the non-linear behavior observed in real market crashes cannot be described by a GARCH(1,1) model. We also show that the time evolution of the Value at Risk observed just after a major crash is described by a power-law function lacking a typical scale.

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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 338 (2004)
Issue (Month): 1 ()
Pages: 125-134

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Handle: RePEc:eee:phsmap:v:338:y:2004:i:1:p:125-134

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Econophysics; Financial markets; Crashes; Value at Risk;

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Cited by:
  1. Tanya Ara\'{u}jo & Francisco Lou\c{c}\~{a}, 2005. "The Geometry of Crashes - A Measure of the Dynamics of Stock Market Crises," Papers physics/0506137, arXiv.org, revised Jul 2005.
  2. Mu, Guo-Hua & Zhou, Wei-Xing, 2008. "Relaxation dynamics of aftershocks after large volatility shocks in the SSEC index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5211-5218.
  3. 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 - School of Economics and Management, Department of Economics, University of Lisbon.
  4. Xu, Hai-Chuan & Zhang, Wei & Liu, Yi-Fang, 2014. "Short-term market reaction after trading halts in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 103-111.
  5. Fernandez, Viviana & Lucey, Brian M., 2007. "Portfolio management under sudden changes in volatility and heterogeneous investment horizons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 612-624.
  6. Hai-Chuan Xu & Wei Zhang & Yi-Fang Liu, 2013. "Short-term Market Reaction after Trading Halts in Chinese Stock Market," Papers 1309.1138, arXiv.org, revised Jun 2014.
  7. Viviana Fernandez & Brian M Lucey, 2006. "Portfolio management implications of volatility shifts: Evidence from simulated data," Documentos de Trabajo 219, Centro de Economía Aplicada, Universidad de Chile.
  8. Brée, David S. & Joseph, Nathan Lael, 2013. "Testing for financial crashes using the Log Periodic Power Law model," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 287-297.

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