Advanced Search
MyIDEAS: Login to save this paper or follow this series

Imitation and contrarian behavior: hyperbolic bubbles, crashes and chaos

Contents:

Author Info

  • A. Corcos

    (Univ. Picardie)

  • J. -P. Eckmann

    (Univ. Geneve)

  • A. Malaspinas

    (Univ. Geneve)

  • Y. Malevergne

    (ISFA-Lyon and Univ. Nice/CNRS)

  • D. Sornette

    (Univ. Nice/CNRS and UCLA)

Abstract

Imitative and contrarian behaviors are the two typical opposite attitudes of investors in stock markets. We introduce a simple model to investigate their interplay in a stock market where agents can take only two states, bullish or bearish. Each bullish (bearish) agent polls m "friends'' and changes her opinion to bearish (bullish) if there is (1) either a majority of bearish agents or (2) too strong a majority of bullish agents. The condition (1) (resp. (2)) corresponds to imitative (resp. antagonistic) behavior. In the limit where the number N of agents is infinite, the dynamics of the fraction of bullish agents is deterministic and exhibits chaotic behavior in a significant domain of the parameter space of the model. A typical chaotic trajectory is characterized by intermittent phases of chaos, quasi-periodic behavior and super-exponentially growing bubbles followed by crashes. A typical bubble starts initially by growing at an exponential rate and then crosses over to a nonlinear power law growth rate leading to a finite-time singularity. The reinjection mechanism provided by the contrarian behavior introduces a finite-size effect, rounding off these singularities and leads to chaos. We document the main stylized facts of this model in the symmetric and asymmetric cases. This model is one of the rare agent-based models that give rise to interesting non-periodic complex dynamics in the ``thermodynamic'' limit (of an infinite number N of agents). We also discuss the case of a finite number of agents, which introduces an endogenous source of noise superimposed on the chaotic dynamics.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://arxiv.org/pdf/cond-mat/0109410
File Function: Latest version
Download Restriction: no

Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/0109410.

as in new window
Length:
Date of creation: Sep 2001
Date of revision:
Publication status: Published in Quantitative Finance 2, 264--281 (2002)
Handle: RePEc:arx:papers:cond-mat/0109410

Contact details of provider:
Web page: http://arxiv.org/

Related research

Keywords:

Other versions of this item:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  2. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 4(02), pages 170-196, June.
  3. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July.
  4. Robert J. Shiller, 1984. "Stock Prices and Social Dynamics," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 719R, Cowles Foundation for Research in Economics, Yale University.
  5. Brock, W.A., 1988. "Nonlinearity And Complex Dynamics In Economics And Finance," Working papers, Wisconsin Madison - Social Systems 360, Wisconsin Madison - Social Systems.
  6. J. Doyne Farmer, 1998. "Market Force, Ecology, and Evolution," Research in Economics 98-12-117e, Santa Fe Institute.
  7. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, Econometric Society, vol. 53(5), pages 995-1045, September.
  8. Huang, Zhi-Feng & Solomon, Sorin, 2001. "Finite market size as a source of extreme wealth inequality and market instability," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 294(3), pages 503-513.
  9. B. M. Roehner & D. Sornette, 1998. "The sharp peak-flat trough pattern and critical speculation," Papers cond-mat/9802234, arXiv.org.
  10. Grossman, Sanford J & Shiller, Robert J, 1981. "The Determinants of the Variability of Stock Market Prices," American Economic Review, American Economic Association, American Economic Association, vol. 71(2), pages 222-27, May.
  11. Robert J. Shiller, 1980. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," NBER Working Papers 0456, National Bureau of Economic Research, Inc.
  12. van der Ploeg, F, 1986. "Rational Expectations, Risk and Chaos in Financial Markets," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 96(380a), pages 151-62, Supplemen.
  13. Grossman, Sanford J, 1977. "The Existence of Futures Markets, Noisy Rational Expectations and Informational Externalities," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 44(3), pages 431-49, October.
  14. Kenneth D. West, 1988. "Bubbles, Fads, and Stock Price Volatility Tests: A Partial Evaluation," NBER Working Papers 2574, National Bureau of Economic Research, Inc.
  15. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, Elsevier, vol. 3(1), pages 15-102, May.
  16. Rama Cont & Jean-Philippe Bouchaud, 1997. "Herd behavior and aggregate fluctuations in financial markets," Science & Finance (CFM) working paper archive 500028, Science & Finance, Capital Fund Management.
  17. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 246(3), pages 407-418.
  18. Trueman, Brett, 1994. "Analyst Forecasts and Herding Behavior," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 7(1), pages 97-124.
  19. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
  20. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, Econometric Society, vol. 40(2), pages 289-303, March.
  21. Sushil Bikhchandani & David Hirshleifer & Ivo Welch, 2010. "A theory of Fads, Fashion, Custom and cultural change as informational Cascades," Levine's Working Paper Archive 1193, David K. Levine.
  22. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, Econometric Society, vol. 47(3), pages 655-78, May.
  23. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, American Economic Association, vol. 70(3), pages 393-408, June.
  24. Challet, Damien & Marsili, Matteo & Zhang, Yi-Cheng, 2000. "Modeling market mechanism with minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 276(1), pages 284-315.
  25. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
  26. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 1(1), pages 83-106, June.
  27. Egenter, E. & Lux, T. & Stauffer, D., 1999. "Finite-size effects in Monte Carlo simulations of two stock market models," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 268(1), pages 250-256.
  28. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, Elsevier, vol. 4(2-3), pages 213-239, June.
  29. Day, Richard H, 1983. "The Emergence of Chaos from Classical Economic Growth," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 98(2), pages 201-13, May.
  30. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161, arXiv.org.
  31. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, American Finance Association, vol. 46(5), pages 1839-77, December.
  32. Zhi-Feng Huang & Sorin Solomon, 2001. "Finite market size as a source of extreme wealth inequality and market instability," Papers cond-mat/0103170, arXiv.org.
  33. Zwiebel, Jeffrey, 1995. "Corporate Conservatism and Relative Compensation," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 103(1), pages 1-25, February.
  34. Scharfstein, David. & Stein, Jeremy C., 1988. "Herd behavior and investment," Working papers WP 2062-88., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  35. Welch, Ivo, 1992. " Sequential Sales, Learning, and Cascades," Journal of Finance, American Finance Association, American Finance Association, vol. 47(2), pages 695-732, June.
  36. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(4), pages 452-471.
  37. Shleifer, Andrei, 2000. "Inefficient Markets: An Introduction to Behavioral Finance," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198292272, October.
  38. 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.
  39. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, American Economic Association, vol. 72(3), pages 406-14, June.
  40. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 185-215, July.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Didier Sornette & Ryan Woodard, 2009. "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Papers 0905.0220, arXiv.org.
  2. Deng, Lei & Liu, Yun & Xiong, Fei, 2013. "An opinion diffusion model with clustered early adopters," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 392(17), pages 3546-3554.
  3. T. Kaizoji & M. Leiss & A. Saichev & D. Sornette, 2011. "Super-exponential endogenous bubbles in an equilibrium model of rational and noise traders," Papers 1109.4726, arXiv.org, revised Mar 2014.
  4. Li Lin & Didier Sornette, 2009. "Diagnostics of Rational Expectation Financial Bubbles with Stochastic Mean-Reverting Termination Times," Papers 0911.1921, arXiv.org.
  5. D. Sornette & R. Woodard, . "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers, ETH Zurich, Chair of Systems Design CCSS-09-003, ETH Zurich, Chair of Systems Design.
  6. Omurtag, Ahmet & Sirovich, Lawrence, 2006. "Modeling a large population of traders: Mimesis and stability," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 61(4), pages 562-576, December.
  7. Jean-Philippe Bouchaud, 2002. "An introduction to statistical finance," Science & Finance (CFM) working paper archive 313238, Science & Finance, Capital Fund Management.
  8. Carmen Pellicer-Lostao & Ricardo Lopez-Ruiz, 2010. "Transition from Exponential to Power Law Distributions in a Chaotic Market," Papers 1011.5187, arXiv.org.
  9. Hongler, Max-Olivier & Gallay, Olivier & Hülsmann, Michael & Cordes, Philip & Colmorn, Richard, 2010. "Centralized versus decentralized control—A solvable stylized model in transportation," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 389(19), pages 4162-4171.
  10. Liudmila G. Egorova, 2014. "The Effectiveness Of Different Trading Strategies For Price-Takers," HSE Working papers, National Research University Higher School of Economics WP BRP 29/FE/2014, National Research University Higher School of Economics.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:arx:papers:cond-mat/0109410. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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