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Crashes As Critical Points

Author

Listed:
  • ANDERS JOHANSEN

    (Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095, USA)

  • OLIVIER LEDOIT

    (Anderson Graduate School of Management, University of California, Box 90095-1481, 110 Westwood Plaza, Los Angeles, CA 90095-1481, USA)

  • DIDIER SORNETTE

    (Institute of Geophysics and Planetary Physics, Department of Earth and Space Science, University of California, Los Angeles, CA 90095, USA;
    Laboratoire de Physique de la Matière Condensée, CNRS UMR6622 and Université de Nice-Sophia Antipolis, B.P. 70, Parc Valrose, 06108 Nice Cedex 2, France)

Abstract

We study a rational expectation model of bubbles and crashes. The model has two components: (1) our key assumption is that a crash may be caused bylocalself-reinforcing imitation between noise traders. If the tendency for noise traders to imitate their nearest neighbors increases up to a certain point called the "critical" point, all noise traders may place the same order (sell) at the same time, thus causing a crash. The interplay between the progressive strengthening of imitation and the ubiquity of noise is characterized by the hazard rate, i.e. the probability per unit time that the crash will happen in the next instant if it has not happened yet. (2) Since the crash is not a certain deterministic outcome of the bubble, it remains rational for traders to remain invested provided they are compensated by a higher rate of growth of the bubble for taking the risk of a crash. Our model distinguishes between the end of the bubble and the time of the crash: the rational expectation constraint has the specific implication that the date of the crash must be random. The theoretical death of the bubble is not the time of the crash because the crash could happen at any time before, even though this is not very likely. The death of the bubble is the most probable time for the crash. There also exists a finite probability of attaining the end of the bubble without crash. Our model has specific predictions about the presence of certain critical log-periodic patterns in pre-crash prices, associated with the deterministic components of the bubble mechanism. We provide empirical evidence showing that these patterns were indeed present before the crashes of 1929, 1962 and 1987 on Wall Street and the 1997 crash on the Hong Kong Stock Exchange. These results are compared with statistical tests on synthetic data.

Suggested Citation

  • Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
  • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:02:n:s0219024900000115
    DOI: 10.1142/S0219024900000115
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