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A hierarchical model of financial crashes

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  • Sornette, Didier
  • Johansen, Anders
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    Abstract

    We follow up our previous conjecture that large stock market crashes are analogous to critical points in statistical physics. The term “critical” refers to regimes of cooperative behavior, such as magnetism at the Curie temperature and liquid–gas transitions, and is characterized by the singular mathematical behavior of relevant observables. To illustrate the concept of criticality, we present a simple hierarchical model of traders exhibiting “crowd” behavior and show that it has a well-defined critical point, whose mathematical signature is a power law dependence of the price, modulated by log-periodic structures, as recently found in market data by several independent groups.

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    Bibliographic Info

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

    Volume (Year): 261 (1998)
    Issue (Month): 3 ()
    Pages: 581-598

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    Handle: RePEc:eee:phsmap:v:261:y:1998:i:3:p:581-598

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

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    Cited by:
    1. Askar Akaev & Alexei Fomin & Andrey Korotayev, 2011. "The Second Wave of the Global Crisis? A Log-Periodic Oscillation Analysis of Commodity Price Series," Papers 1107.0480, arXiv.org.
    2. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    3. Wosnitza, Jan Henrik & Denz, Cornelia, 2013. "Liquidity crisis detection: An application of log-periodic power law structures to default prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3666-3681.
    4. Siokis, Fotios M., 2012. "The dynamics of a complex system: The exchange rate crisis in Southeast Asia," Economics Letters, Elsevier, vol. 114(1), pages 98-101.
    5. Gee Kwang Randolph Tan & Xiao Qin, 2005. "Bubbles, Can We Spot Them? Crashes, Can We Predict Them?," Computing in Economics and Finance 2005 206, Society for Computational Economics.
    6. A. Johansen & D. Sornette, 2002. "Endogenous versus Exogenous Crashes in Financial Markets," Papers cond-mat/0210509, arXiv.org.
    7. Askar Akaev & Andrey Korotayev & Alexey Fomin, 2012. "Global Inflation Dynamics: regularities & forecasts," Papers 1207.4069, arXiv.org.
    8. Caetano, Marco Antonio Leonel & Yoneyama, Takashi, 2012. "A method for detection of abrupt changes in the financial market combining wavelet decomposition and correlation graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4877-4882.
    9. Jozef Barunik & Jiri Kukacka, 2013. "Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility," Papers 1302.7036, arXiv.org, revised May 2013.
    10. Anders Johansen & Didier Sornette & Olivier Ledoit, 1999. "Empirical and Theoretical Status of Discrete Scale Invariance in Financial Crashes," Finance 9903006, EconWPA.
    11. Kapopoulos, Panayotis & Siokis, Fotios, 2005. "Stock market crashes and dynamics of aftershocks," Economics Letters, Elsevier, vol. 89(1), pages 48-54, October.
    12. Caetano, Marco Antonio Leonel & Yoneyama, Takashi, 2009. "A new indicator of imminent occurrence of drawdown in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3563-3571.
    13. Negrea, Bogdan, 2014. "A statistical measure of financial crises magnitude," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 54-75.
    14. Siokis, Fotios M., 2012. "Stock market dynamics: Before and after stock market crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1315-1322.
    15. Caetano, Marco Antonio Leonel & Yoneyama, Takashi, 2011. "A model for the evaluation of systemic risk in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2368-2374.
    16. Mendes, G.A. & da Silva, L.R. & Herrmann, H.J., 2012. "Traffic gridlock on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 362-370.
    17. Sornette, Didier & Woodard, Ryan & Zhou, Wei-Xing, 2009. "The 2006–2008 oil bubble: Evidence of speculation, and prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1571-1576.
    18. W. -X. Zhou & D. Sornette, 2002. "Evidence of a Worldwide Stock Market Log-Periodic Anti-Bubble Since Mid-2000," Papers cond-mat/0212010, arXiv.org, revised Aug 2003.

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