Advanced Search
MyIDEAS: Login

A Noise Trader Model As A Generator Of Apparent Financial Power Laws And Long Memory

Contents:

Author Info

  • ALFARANO, SIMONE
  • LUX, THOMAS

Abstract

In various agent-based models, the stylized facts of financial markets (unit roots, fat tails, and volatility clustering) have been shown to emerge from the interactions of agents. However, the complexity of these models often limits their analytical accessibility. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing these ubiquitous statistical properties. The simplicity of our approach permits us to derive some analytical insights using concepts from statistical mechanics. In our model, traders are divided into two groups, fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by A. Kirman (Ants, rationality, and recruitment, Quarterly Journal of Economics 108, 137 156, 1993). The statistical analysis of simulated data points toward long-term dependence in the autocorrelations of squared and absolute returns and hyperbolic decay in the tail of the distribution of raw returns, both with estimated decay parameters in the same range as those of empirical data. Theoretical analysis, however, excludes the possibility of true scaling behavior because of the Markovian nature of the underlying process and the boundedness of returns. The model, therefore, only mimics power law behavior. Similarly to the phenomenological volatility models analyzed by LeBaron (Stochastic volatility as a simple generator of apparent financial power laws and long memory, Quantitative Finance 1, 621 631, 2001), the usual statistical tests are not able to distinguish between true and pseudo-scaling laws in the dynamics of our artificial market.

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://journals.cambridge.org/abstract_S1365100506060299
File Function: link to article abstract page
Download Restriction: no

Bibliographic Info

Article provided by Cambridge University Press in its journal Macroeconomic Dynamics.

Volume (Year): 11 (2007)
Issue (Month): S1 (November)
Pages: 80-101

as in new window
Handle: RePEc:cup:macdyn:v:11:y:2007:i:s1:p:80-101_06

Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page: http://journals.cambridge.org/jid_MDYProvider-Email:journals@cambridge.org

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

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. KIRMAN, Alan & TEYSSIÈRE, Gilles, . "Microeconomic models for long memory in the volatility of financial time series," CORE Discussion Papers RP -1593, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Andersson, Michael K. & Eklund, Bruno & Lyhagen, Johan, 1999. "A Simple Linear Time Series Model with Misleading Nonlinear Properties," Working Paper Series in Economics and Finance 300, Stockholm School of Economics.
  3. P. Bak & M. Paczuski & M. Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Working Papers 96-09-075, Santa Fe Institute.
  4. Lux, Thomas & Schornstein, Sascha, 2002. "Genetic learning as an explanation of stylized facts of foreign exchange markets," Discussion Paper Series 1: Economic Studies 2002,29, Deutsche Bundesbank, Research Centre.
  5. Giulia Iori, 1999. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Finance 9905005, EconWPA.
  6. Gaunersdorfer, A. & Hommes, C.H., 2000. "A Nonlinear Structural Model for Volatility Clustering," CeNDEF Working Papers 00-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  7. Simone Alfarano & Thomas Lux, 2002. "A minimal noise trader model with realistic time series," Computing in Economics and Finance 2002 317, Society for Computational Economics.
  8. B. LeBaron, 2001. "Stochastic volatility as a simple generator of apparent financial power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 621-631.
  9. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
  10. Youssefmir, Michael & Huberman, Bernardo A., 1997. "Clustered volatility in multiagent dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 32(1), pages 101-118, January.
  11. J. Doyne Farmer & Shareen Joshi, 2000. "The Price Dynamics of Common Trading Strategies," Working Papers 00-12-069, Santa Fe Institute.
  12. B. B. Mandelbrot, 2001. "Stochastic volatility, power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 558-559.
  13. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  14. Wagner, Friedrich, 2003. "Volatility cluster and herding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 607-619.
  15. D. Challet & A. Chessa & M. Marsili & Y-C. Zhang, 2001. "From Minority Games to real markets," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 168-176.
  16. Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2000. "Bifurcation Routes to Volatility Clustering," CeNDEF Working Papers 00-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  17. I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics 9605004, EconWPA, revised 26 Sep 1996.
  18. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
  19. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
  20. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
  21. 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).
  22. Bak, P. & Paczuski, M. & Shubik, M., 1997. "Price variations in a stock market with many agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 430-453.
  23. Georges, Christophre, 2006. "Learning with misspecification in an artificial currency market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(1), pages 70-84, May.
  24. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-48, May.
  25. Jeffrey A. Frankel & Kenneth A. Froot, 1987. "The Dollar as an Irrational Speculative Bubble: A Tale of Fundamentalisists," NBER Working Papers 1854, National Bureau of Economic Research, Inc.
  26. Chen, Shu-Heng & Lux, Thomas & Marchesi, Michele, 2001. "Testing for non-linear structure in an artificial financial market," Journal of Economic Behavior & Organization, Elsevier, vol. 46(3), pages 327-342, November.
  27. LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June.
  28. Chen, Shu-Heng & Yeh, Chia-Hsuan, 2002. "On the emergent properties of artificial stock markets: the efficient market hypothesis and the rational expectations hypothesis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 217-239, October.
  29. Arifovic, Jasmina & Gencay, Ramazan, 2000. "Statistical properties of genetic learning in a model of exchange rate," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 981-1005, June.
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:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

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:cup:macdyn:v:11:y:2007:i:s1:p:80-101_06. 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: (Keith Waters).

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.