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A hierarchical model of financial crashes


  • Sornette, Didier
  • Johansen, Anders


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.

Suggested Citation

  • Sornette, Didier & Johansen, Anders, 1998. "A hierarchical model of financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 581-598.
  • Handle: RePEc:eee:phsmap:v:261:y:1998:i:3:p:581-598 DOI: 10.1016/S0378-4371(98)00433-6

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    References listed on IDEAS

    1. L. Ingber, 1990. "Statistical mechanical aids to calculating term structure models," Lester Ingber Papers 90ac, Lester Ingber.
    2. Gennotte, Gerard & Leland, Hayne, 1990. "Market Liquidity, Hedging, and Crashes," American Economic Review, American Economic Association, vol. 80(5), pages 999-1021, December.
    3. Bak, P. & Paczuski, M. & Shubik, M., 1997. "Price variations in a stock market with many agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 430-453.
    4. Stauffer, Dietrich & Sornette, Didier, 1998. "Log-periodic oscillations for biased diffusion on random lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 252(3), pages 271-277.
    5. L. Ingber & M.F. Wehner & G.M. Jabbour & T.M. Barnhill, 1991. "Application of statistical mechanics methodology to term-structure bond-pricing models," Lester Ingber Papers 91as, Lester Ingber.
    6. Takayasu, Hideki & Miura, Hitoshi & Hirabayashi, Tadashi & Hamada, Koichi, 1992. "Statistical properties of deterministic threshold elements — the case of market price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 184(1), pages 127-134.
    7. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    8. A. Arnéodo & J.-F. Muzy & D. Sornette, 1998. "”Direct” causal cascade in the stock market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 2(2), pages 277-282, March.
    9. S. Gluzman & V. I. Yukalov, 1997. "Renormalization Group Analysis of October Market Crashes," Papers cond-mat/9710336,, revised Apr 1998.
    10. Alain Arneodo & Jean-Philippe Bouchaud & Rama Cont & Jean-Francois Muzy & Marc Potters & Didier Sornette, 1996. "Comment on "Turbulent cascades in foreign exchange markets"," Science & Finance (CFM) working paper archive 9607120, Science & Finance, Capital Fund Management.
    11. Barnett,William A. & Geweke,John & Shell,Karl (ed.), 1989. "Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity," Cambridge Books, Cambridge University Press, number 9780521355636, March.
    12. L. Ingber, 1996. "Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading," Lester Ingber Papers 96nf, Lester Ingber.
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