IDEAS home Printed from https://ideas.repec.org/p/sfi/sfiwpa/500027.html

A Langevin approach to stock market fluctuations and crashes

Author

Listed:
  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Rama Cont

    (Science & Finance, Capital Fund Management)

Abstract

We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize the importance of feedback effects of price variations onto themselves. Risk aversion, in particular, leads to an up-down symmetry breaking term which is responsible for crashes, where `panic' is self reinforcing. It is also responsible for the sudden collapse of speculative bubbles. Interestingly, these crashes appear as rare, `activated' events, and have an exponentially small probability of occurence. We predict that the shape of the falldown of the price during a crash should be logarithmic. The normal regime, where the stock price exhibits behavior similar to that of a random walk, however reveals non trivial correlations on different time scales, in particular on the time scale over which operators perceive a change of trend.

Suggested Citation

  • Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
    • Handle: RePEc:sfi:sfiwpa:500027
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. A. Johansen & D. Sornette, 1998. "Stock market crashes are outliers," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 1(2), pages 141-143, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anders Johansen & Didier Sornette & Olivier Ledoit, 1999. "Empirical and Theoretical Status of Discrete Scale Invariance in Financial Crashes," Finance 9903006, University Library of Munich, Germany.
    2. Zhou, Wei-Xing & Sornette, Didier, 2009. "A case study of speculative financial bubbles in the South African stock market 2003–2006," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 869-880.
    3. Y. Malevergne & D. Sornette, 2003. "VaR-Efficient Portfolios for a Class of Super- and Sub-Exponentially Decaying Assets Return Distributions," Papers physics/0301009, arXiv.org.
    4. Johansen, Anders, 2003. "Characterization of large price variations in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 157-166.
    5. Harras, Georges & Sornette, Didier, 2011. "How to grow a bubble: A model of myopic adapting agents," Journal of Economic Behavior & Organization, Elsevier, vol. 80(1), pages 137-152.
    6. Takumi Sueshige & Didier Sornette & Hideki Takayasu & Misako Takayasu, 2019. "Classification of position management strategies at the order-book level and their influences on future market-price formation," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-19, August.
    7. Qian, Xi-Yuan & Song, Fu-Tie & Zhou, Wei-Xing, 2008. "Nonlinear behaviour of the Chinese SSEC index with a unit root: Evidence from threshold unit root tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 503-510.
    8. B. M. Roehner & D. Sornette, 2000. ""Thermometers" of Speculative Frenzy," Papers cond-mat/0001353, arXiv.org.
    9. Cornelis A. Los & Rossitsa M. Yalamova, 2004. "Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash," Finance 0409050, University Library of Munich, Germany.
    10. Negrea, Bogdan, 2014. "A statistical measure of financial crises magnitude," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 54-75.
    11. 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.
    12. Carlos Manuel Rodríguez-Martínez & Héctor Francisco Coronel-Brizio & Horacio Tapia-McClung & Manuel Enríque Rodríguez-Achach & Alejandro Raúl Hernández-Montoya, 2025. "On the Autocorrelation and Stationarity of Multi-Scale Returns," Mathematics, MDPI, vol. 13(17), pages 1-12, September.
    13. D. Sornette & R. Woodard, "undated". "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers CCSS-09-003, ETH Zurich, Chair of Systems Design.
    14. Lux, Thomas & Marchesi, Michele, 2002. "Journal of economic behavior and organization: special issue on heterogeneous interacting agents in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 143-147, October.
    15. Hans-Christian Graf v. Bothmer, 2003. "Significance of log-periodic signatures in cumulative noise," Papers cond-mat/0302507, arXiv.org, revised May 2003.
    16. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    17. Charles, Amelie & Darne, Olivier, 2006. "Large shocks and the September 11th terrorist attacks on international stock markets," Economic Modelling, Elsevier, vol. 23(4), pages 683-698, July.
    18. Fruehwirt, Wolfgang & Hochfilzer, Leonhard & Weydemann, Leonard & Roberts, Stephen, 2021. "Cumulation, crash, coherency: A cryptocurrency bubble wavelet analysis," Finance Research Letters, Elsevier, vol. 40(C).
    19. Stavroyiannis, S. & Makris, I. & Nikolaidis, V., 2010. "Non-extensive properties, multifractality, and inefficiency degree of the Athens Stock Exchange General Index," International Review of Financial Analysis, Elsevier, vol. 19(1), pages 19-24, January.
    20. Anders Johansen & Didier Sornette, 2000. "The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash," Papers cond-mat/0004263, arXiv.org, revised May 2000.

    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sfi:sfiwpa:500027. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/scfinfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.