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From rational bubbles to crashes

Author

Listed:
  • Didier Sornette

    (EM - EMLyon Business School)

  • Yannick Malevergne

Abstract

We study and generalize in various ways the model of rational expectation (RE) bubbles introduced by Blanchard and Watson in the economic literature. Bubbles are argued to be the equivalent of Goldstone modes of the fundamental rational pricing equation, associated with the symmetry-breaking introduced by non-vanishing dividends. Generalizing bubbles in terms of multiplicative stochastic maps, we summarize the result of Lux and Sornette that the no-arbitrage condition imposes that the tail of the return distribution is hyperbolic with an exponent μ

Suggested Citation

  • Didier Sornette & Yannick Malevergne, 2001. "From rational bubbles to crashes," Post-Print hal-02312895, HAL.
    • Handle: RePEc:hal:journl:hal-02312895
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    References listed on IDEAS

    as
    1. Olivier J. Blanchard & Mark W. Watson, 1982. "Bubbles, Rational Expectations and Financial Markets," NBER Working Papers 0945, National Bureau of Economic Research, Inc.
    2. Y. Malevergne & D. Sornette, 2001. "Multi-dimensional rational bubbles and fat tails," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 533-541.
    3. Lux, Thomas & Sornette, Didier, 2002. "On Rational Bubbles and Fat Tails," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(3), pages 589-610, August.
    4. Shleifer, Andrei, 2000. "Inefficient Markets: An Introduction to Behavioral Finance," OUP Catalogue, Oxford University Press, number 9780198292272.
    5. D. Sornette, 2000. ""Slimming" of power law tails by increasing market returns," Papers cond-mat/0010112, arXiv.org, revised Sep 2001.
    6. De Vries, C.G. & Leuven, K.U., 1994. "Stylized Facts of Nominal Exchange Rate Returns," Papers 94-002, Purdue University, Krannert School of Management - Center for International Business Education and Research (CIBER).
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    Cited by:

    1. Neil Terry & Anne Macy & Amjad Abdullat, 2010. "Stock Market Volatility: A Comparison Of Computer And Cellular Hardware Companies," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 4(3), pages 11-24.
    2. Jennifer Jhun & Patricia Palacios & James Owen Weatherall, 2017. "Market Crashes as Critical Phenomena? Explanation, Idealization, and Universality in Econophysics," Papers 1704.02392, arXiv.org.
    3. Ariane Szafarz, 2015. "Market Efficiency and Crises:Don’t Throw the Baby out with the Bathwater," Bankers, Markets & Investors, ESKA Publishing, issue 139, pages 20-26, November-.
    4. Jaehyung Choi, 2011. "Spontaneous symmetry breaking of arbitrage," Papers 1107.5122, arXiv.org, revised Apr 2012.
    5. Fry, J. M., 2010. "Gaussian and non-Gaussian models for financial bubbles via econophysics," MPRA Paper 27307, University Library of Munich, Germany.
    6. Brière, Marie & Chapelle, Ariane & Szafarz, Ariane, 2012. "No contagion, only globalization and flight to quality," Journal of International Money and Finance, Elsevier, vol. 31(6), pages 1729-1744.
    7. Fry, J. M., 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," MPRA Paper 16027, University Library of Munich, Germany.
    8. Szafarz, Ariane, 2012. "Financial crises in efficient markets: How fundamentalists fuel volatility," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 105-111.
    9. D. Sornette, 2000. ""Slimming" of power law tails by increasing market returns," Papers cond-mat/0010112, arXiv.org, revised Sep 2001.
    10. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2021. "Financial Return Distributions: Past, Present, and COVID-19," Papers 2107.06659, arXiv.org.
    11. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.
    12. Fry, J. M., 2010. "Bubbles and crashes in finance: A phase transition from random to deterministic behaviour in prices," MPRA Paper 24778, University Library of Munich, Germany.
    13. Zhou, Wei-Xing & Sornette, Didier, 2003. "Evidence of a worldwide stock market log-periodic anti-bubble since mid-2000," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 543-583.
    14. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    15. Sornette, D., 2002. "“Slimming” of power-law tails by increasing market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 403-418.
    16. repec:dau:papers:123456789/7746 is not listed on IDEAS
    17. Fry, J. M., 2009. "Bubbles and contagion in English house prices," MPRA Paper 17687, University Library of Munich, Germany.
    18. Cajueiro, Daniel O. & Tabak, Benjamin M., 2006. "Testing for rational bubbles in banking indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 365-376.

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