IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v37y2013i11p2351-2370.html
   My bibliography  Save this article

The bull and bear market model of Huang and Day: Some extensions and new results

Author

Listed:
  • Tramontana, Fabio
  • Westerhoff, Frank
  • Gardini, Laura

Abstract

We develop a financial market model with interacting chartists and fundamentalists that embeds the famous bull and bear market model of Huang and Day as a special case. Their model is given by a one-dimensional continuous piecewise-linear map. Our model, on the other hand, is more flexible and is represented by a one-dimensional discontinuous piecewise-linear map. Nevertheless, we are able to provide a more or less complete analytical treatment of the model dynamics by characterizing its possible outcomes in parameter space. In addition, we show that quite different scenarios can trigger real-world phenomena such as bull and bear market dynamics and excess volatility.

Suggested Citation

  • Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2013. "The bull and bear market model of Huang and Day: Some extensions and new results," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2351-2370.
  • Handle: RePEc:eee:dyncon:v:37:y:2013:i:11:p:2351-2370
    DOI: 10.1016/j.jedc.2013.06.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188913001371
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jedc.2013.06.005?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    2. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    3. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Manzan, Sebastiano & Westerhoff, Frank H., 2007. "Heterogeneous expectations, exchange rate dynamics and predictability," Journal of Economic Behavior & Organization, Elsevier, vol. 64(1), pages 111-128, September.
    5. Gian Italo Bischi & Carl Chiarella & Iryna Sushko (ed.), 2013. "Global Analysis of Dynamic Models in Economics and Finance," Springer Books, Springer, edition 127, number 978-3-642-29503-4, June.
    6. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2010. "On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 187-205, June.
    7. J. Barkley Rosser Jr. (ed.), 2009. "Handbook of Research on Complexity," Books, Edward Elgar Publishing, number 3625, Summer.
    8. Huang, Weihong & Zheng, Huanhuan & Chia, Wai-Mun, 2010. "Financial crises and interacting heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1105-1122, June.
    9. Frank Westerhoff & Reiner Franke, 2012. "Converse trading strategies, intrinsic noise and the stylized facts of financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 12(3), pages 425-436, June.
    10. Vigfusson, Robert, 1997. "Switching between Chartists and Fundamentalists: A Markov Regime-Switching Approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 2(4), pages 291-305, October.
    11. Lukas Menkhoff & Mark P. Taylor, 2007. "The Obstinate Passion of Foreign Exchange Professionals: Technical Analysis," Journal of Economic Literature, American Economic Association, vol. 45(4), pages 936-972, December.
    12. Weihong Huang & Huanhuan Zheng & Wai-Mun Chia, 2013. "Asymmetric returns, gradual bubbles and sudden crashes," The European Journal of Finance, Taylor & Francis Journals, vol. 19(5), pages 420-437, May.
    13. Fabio Tramontana & Laura Gardini & Frank Westerhoff, 2011. "Heterogeneous Speculators and Asset Price Dynamics: Further Results from a One-Dimensional Discontinuous Piecewise-Linear Map," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 329-347, October.
    14. Beja, Avraham & Goldman, M Barry, 1980. "On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-248, May.
    15. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    16. Huang, Weihong & Zheng, Huanhuan, 2012. "Financial crises and regime-dependent dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 445-461.
    17. Chiarella, Carl & He, Xue-Zhong & Huang, Weihong & Zheng, Huanhuan, 2012. "Estimating behavioural heterogeneity under regime switching," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 446-460.
    18. Guido VENIER, 2008. "A New Model For Stock Price Movements," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(3(5)_Fall), pages 329-350.
    19. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2015. "A simple financial market model with chartists and fundamentalists: Market entry levels and discontinuities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 16-40.
    20. Gu, M., 1993. "An Empirical Examination of the Deterministic Component in Stock price Volatility," Papers 9308, Southern California - Department of Economics.
    21. Gu, Mu, 1993. "An empirical examination of the deterministic component in stock price volatility," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 239-252, October.
    22. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    23. Richard Day, 1997. "Complex Dynamics, Market Mediation and Stock Price Behavior," North American Actuarial Journal, Taylor & Francis Journals, vol. 1(3), pages 1-16.
    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. Saskia ter Ellen & Willem F.C. Verschoor, 2017. "Heterogeneous beliefs and asset price dynamics: a survey of recent evidence," Working Paper 2017/22, Norges Bank.
    2. Fabio Tramontana & Laura Gardini & Frank Westerhoff, 2011. "Heterogeneous Speculators and Asset Price Dynamics: Further Results from a One-Dimensional Discontinuous Piecewise-Linear Map," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 329-347, October.
    3. Sushko, Iryna & Tramontana, Fabio & Westerhoff, Frank & Avrutin, Viktor, 2015. "Symmetry breaking in a bull and bear financial market model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 57-72.
    4. Saskia ter Ellen & Willem F. C. Verschoor, 2018. "Heterogeneous Beliefs and Asset Price Dynamics: A Survey of Recent Evidence," Dynamic Modeling and Econometrics in Economics and Finance, in: Fredj Jawadi (ed.), Uncertainty, Expectations and Asset Price Dynamics, pages 53-79, Springer.
    5. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2015. "A simple financial market model with chartists and fundamentalists: Market entry levels and discontinuities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 16-40.
    6. Brianzoni, Serena & Campisi, Giovanni, 2020. "Dynamical analysis of a financial market with fundamentalists, chartists, and imitators," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    7. Chiarella, Carl & He, Xue-Zhong & Zwinkels, Remco C.J., 2014. "Heterogeneous expectations in asset pricing: Empirical evidence from the S&P500," Journal of Economic Behavior & Organization, Elsevier, vol. 105(C), pages 1-16.
    8. Schmitt, Noemi & Westerhoff, Frank, 2014. "Speculative behavior and the dynamics of interacting stock markets," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 262-288.
    9. Jungeilges, Jochen & Maklakova, Elena & Perevalova, Tatyana, 2021. "Asset price dynamics in a “bull and bear market”," Structural Change and Economic Dynamics, Elsevier, vol. 56(C), pages 117-128.
    10. Huang, Weihong & Zheng, Huanhuan, 2012. "Financial crises and regime-dependent dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 445-461.
    11. Giovanni Campisi & Silvia Muzzioli & Fabio Tramontana, 2021. "Uncertainty about fundamental, pessimistic and overconfident traders: a piecewise-linear maps approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 707-726, December.
    12. Dieci, Roberto & Gardini, Laura & Westerhoff, Frank, 2022. "On the destabilizing nature of capital gains taxes," International Review of Financial Analysis, Elsevier, vol. 83(C).
    13. Cafferata, Alessia & Tramontana, Fabio, 2019. "A financial market model with confirmation bias," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 252-259.
    14. Schmitt, Noemi & Westerhoff, Frank, 2017. "On the bimodality of the distribution of the S&P 500's distortion: Empirical evidence and theoretical explanations," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 34-53.
    15. En-Guo Gu, 2020. "On the Price Dynamics of a Two-Dimensional Financial Market Model with Entry Levels," Complexity, Hindawi, vol. 2020, pages 1-23, August.
    16. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2011. "The dynamic behaviour of asset prices in disequilibrium: a survey," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 101-139.
    17. Chiarella, Carl & He, Xue-Zhong & Huang, Weihong & Zheng, Huanhuan, 2012. "Estimating behavioural heterogeneity under regime switching," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 446-460.
    18. Gardini, L. & Radi, D. & Schmitt, N. & Sushko, I. & Westerhoff, F., 2022. "Causes of fragile stock market stability," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 483-498.
    19. Changtai Li & Weihong Huang & Wei-Siang Wang & Wai-Mun Chia, 2023. "Price Change and Trading Volume: Behavioral Heterogeneity in Stock Market," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 677-713, February.
    20. Fabio Tramontana, 2013. "The role of cognitively biased imitators in a small scale agent-based financial market," DEM Working Papers Series 029, University of Pavia, Department of Economics and Management.

    More about this item

    Keywords

    Heterogeneous interacting agents; Bull and bear market dynamics; Piecewise-linear maps; Border collision bifurcations;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

    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:eee:dyncon:v:37:y:2013:i:11:p:2351-2370. 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: . General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.elsevier.com/locate/jedc .

    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.