Advanced Search
MyIDEAS: Login

Super-exponential endogenous bubbles in an equilibrium model of rational and noise traders

Contents:

Author Info

  • T. Kaizoji
  • M. Leiss
  • A. Saichev
  • D. Sornette

Abstract

We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility with respect to their allocation on the risky asset versus the risk-free asset. Noise traders are subjected to social imitation and follow momentum trading. Allowing for random time-varying herding propensity, we are able to reproduce several well-known stylized facts of financial markets such as a fat-tail distribution of returns and volatility clustering. In particular, we observe transient faster-than-exponential bubble growth with approximate log-periodic behavior and give analytical arguments why this follows from our framework. The model accounts well for the behavior of traders and for the price dynamics that developed during the dotcom bubble in 1995-2000. Momentum strategies are shown to be transiently profitable, supporting these strategies as enhancing herding behavior.

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/1109.4726
File Function: Latest version
Download Restriction: no

Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1109.4726.

as in new window
Length:
Date of creation: Sep 2011
Date of revision: Mar 2014
Handle: RePEc:arx:papers:1109.4726

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

Related research

Keywords:

This paper has been announced in the following NEP Reports:

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. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2002. "Speculative behaviour and complex asset price dynamics: a global analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 173-197, October.
  2. A. Corcos & J-P Eckmann & A. Malaspinas & Y. Malevergne & D. Sornette, 2002. "Imitation and contrarian behaviour: hyperbolic bubbles, crashes and chaos," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 264-281.
  3. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
  4. Markus K. Brunnermeier & Stefan Nagel, 2004. "Hedge Funds and the Technology Bubble," Journal of Finance, American Finance Association, vol. 59(5), pages 2013-2040, October.
  5. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  6. Harrison, J Michael & Kreps, David M, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, MIT Press, vol. 92(2), pages 323-36, May.
  7. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
  8. Eli Ofek & Matthew Richardson, 2003. "DotCom Mania: The Rise and Fall of Internet Stock Prices," Journal of Finance, American Finance Association, vol. 58(3), pages 1113-1138, 06.
  9. Robert Battalio & Paul Schultz, 2006. "Options and the Bubble," Journal of Finance, American Finance Association, vol. 61(5), pages 2071-2102, October.
  10. De Long, J Bradford, et al, 1990. " Positive Feedback Investment Strategies and Destabilizing Rational Speculation," Journal of Finance, American Finance Association, vol. 45(2), pages 379-95, June.
  11. De Bondt, Werner F M & Thaler, Richard, 1985. " Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
  12. Georges Harras & Didier Sornette, 2008. "How to grow a bubble: A model of myopic adapting agents," Papers 0806.2989, arXiv.org, revised Nov 2010.
  13. Miller, Edward M, 1977. "Risk, Uncertainty, and Divergence of Opinion," Journal of Finance, American Finance Association, vol. 32(4), pages 1151-68, September.
  14. Anders Johansen & Didier Sornette, 2010. "Shocks, Crashes and Bubbles in Financial Markets," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 53(2), pages 201-253.
  15. Harrison Hong & José Scheinkman & Wei Xiong, 2006. "Asset Float and Speculative Bubbles," Journal of Finance, American Finance Association, vol. 61(3), pages 1073-1117, 06.
  16. Chen, Joseph & Hong, Harrison & Stein, Jeremy C., 2002. "Breadth of ownership and stock returns," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 171-205.
  17. Kaizoji, Taisei, 2000. "Speculative bubbles and crashes in stock markets: an interacting-agent model of speculative activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 493-506.
  18. Abreu, Dilip & Brunnermeier, Markus K., 2002. "Synchronization risk and delayed arbitrage," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 341-360.
  19. 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.
  20. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
  21. Refet S. Gürkaynak, 2008. "Econometric Tests Of Asset Price Bubbles: Taking Stock ," Journal of Economic Surveys, Wiley Blackwell, vol. 22(1), pages 166-186, 02.
  22. Jarrow, Robert A, 1980. " Heterogeneous Expectations, Restrictions on Short Sales, and Equilibrium Asset Prices," Journal of Finance, American Finance Association, vol. 35(5), pages 1105-13, December.
  23. Aoki,Masanao & Yoshikawa,Hiroshi, 2007. "Reconstructing Macroeconomics," Cambridge Books, Cambridge University Press, number 9780521831062, November.
  24. Kaizoji, Taisei (kaizoji@icu.ac.jp), 2010. "A behavioral model of bubbles and crashes," MPRA Paper 35655, University Library of Munich, Germany.
  25. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
Full references (including those not matched with items on IDEAS)

Citations

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:1109.4726. 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.