IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v368y2006i1p183-190.html
   My bibliography  Save this article

Fat tails and multi-scaling in a simple model of limit order markets

Author

Listed:
  • Krause, Andreas

Abstract

We use a simple model where traders submit limit orders which are cleared in a double auction market. The limit prices are set by traders randomly, for buyers around a long-term trend and for sellers in a narrow band around their purchase price. Orders which are not filled within a specific time frame are randomly assigned a new limit price. In this framework we find evidence for the endogenous emergence of fat tails in the distribution of returns and multi-scaling whose origin is attributed to the market structure.

Suggested Citation

  • Krause, Andreas, 2006. "Fat tails and multi-scaling in a simple model of limit order markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 183-190.
    • Handle: RePEc:eee:phsmap:v:368:y:2006:i:1:p:183-190
    DOI: 10.1016/j.physa.2005.12.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106000021
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2005.12.038?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
    2. Stauffer, Dietrich & Sornette, Didier, 1999. "Self-organized percolation model for stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 271(3), pages 496-506.
    3. Iori, Giulia, 2002. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 269-285, October.
    4. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    5. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    6. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    7. Gode, Dhananjay K & Sunder, Shyam, 1993. "Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 119-137, February.
    8. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    9. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    10. Giulia Iori & Carl Chiarella, 2002. "A simple microstructure model of double auction markets," Computing in Economics and Finance 2002 44, Society for Computational Economics.
    11. Marco Licalzi & Paolo Pellizzari, 2003. "Fundamentalists clashing over the book: a study of order-driven stock markets," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 470-480.
    12. Cohen, Kalman J & Maier, Steven F & Schwartz, Robert A & Whitcomb, David K, 1981. "Transaction Costs, Order Placement Strategy, and Existence of the Bid-Ask Spread," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 287-305, April.
    13. 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, vol. 1(1), pages 83-106, June.
    14. Dhananjay K. Gode & Shyam Sunder, 1997. "What Makes Markets Allocationally Efficient?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 603-630.
    15. Hugh Luckock, 2003. "A steady-state model of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 385-404.
    16. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
    17. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(2), pages 170-196, June.
    18. Crato, Nuno & de Lima, Pedro J. F., 1994. "Long-range dependence in the conditional variance of stock returns," Economics Letters, Elsevier, vol. 45(3), pages 281-285.
    19. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    20. Kwapień, J. & Oświe¸cimka, P. & Drożdż, S., 2005. "Components of multifractality in high-frequency stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 466-474.
    21. Raberto, Marco & Cincotti, Silvano & Focardi, Sergio M. & Marchesi, Michele, 2001. "Agent-based simulation of a financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 319-327.
    22. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    23. Maslov, Sergei, 2000. "Simple model of a limit order-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 571-578.
    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


    Cited by:

    1. Withanawasam, R.M. & Whigham, P.A. & Crack, Timothy Falcon, 2013. "Characterizing limit order prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5346-5355.
    2. Withanawasam, R.M. & Whigham, P.A. & Crack, T.F., 2013. "Characterising trader manipulation in a limit-order driven market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 43-52.
    3. Jiahua Wang & Hongliang Zhu & Dongxin Li, 2018. "Price Dynamics in an Order-Driven Market with Bayesian Learning," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    4. Xinyang Li & Andreas Krause, 2011. "An evolutionary multi‐objective optimization of trading rules in call markets," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 18(1), pages 1-14, January.
    5. Cerqueti, Roy & Giacalone, Massimiliano & Panarello, Demetrio, 2019. "A Generalized Error Distribution Copula-based method for portfolios risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 687-695.

    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. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    2. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    3. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    4. Alessio Emanuele Biondo, 2020. "Information versus imitation in a real-time agent-based model of financial markets," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(3), pages 613-631, July.
    5. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    6. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    7. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    8. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 9, Edward Elgar Publishing.
    9. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    10. Sandrine Jacob Leal & Mauro Napoletano & Andrea Roventini & Giorgio Fagiolo, 2016. "Rock around the clock: An agent-based model of low- and high-frequency trading," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 49-76, March.
    11. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p4oq9ig8k is not listed on IDEAS
    12. Alessio Emanuele Biondo, 2018. "Order book microstructure and policies for financial stability," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 35(1), pages 196-218, March.
    13. Jiahua Wang & Hongliang Zhu & Dongxin Li, 2018. "Price Dynamics in an Order-Driven Market with Bayesian Learning," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    14. Noemi Schmitt & Ivonne Schwartz & Frank Westerhoff, 2022. "Heterogeneous speculators and stock market dynamics: a simple agent-based computational model," The European Journal of Finance, Taylor & Francis Journals, vol. 28(13-15), pages 1263-1282, October.
    15. Biondo, Alessio Emanuele, 2017. "Learning to forecast, risk aversion, and microstructural aspects of financial stability," Economics Discussion Papers 2017-104, Kiel Institute for the World Economy (IfW Kiel).
    16. Wang, Yougui & Stanley, H.E., 2009. "Statistical approach to partial equilibrium analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1173-1180.
    17. Johann Lussange & Ivan Lazarevich & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2021. "Modelling Stock Markets by Multi-agent Reinforcement Learning," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 113-147, January.
    18. Alessio Emanuele Biondo, 2019. "Order book modeling and financial stability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(3), pages 469-489, September.
    19. LiCalzi, Marco & Pellizzari, Paolo, 2006. "Breeds of risk-adjusted fundamentalist strategies in an order-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 619-633.
    20. Biondo, Alessio Emanuele, 2018. "Learning to forecast, risk aversion, and microstructural aspects of financial stability," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-21.
    21. Kyubin Yim & Gabjin Oh & Seunghwan Kim, 2016. "Understanding Financial Market States Using an Artificial Double Auction Market," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-15, March.

    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:eee:phsmap:v:368:y:2006:i:1:p:183-190. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.