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

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  • 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, 2012. "The bull and bear market model of Huang and Day : Some extensions and new results," BERG Working Paper Series 89, Bamberg University, Bamberg Economic Research Group.
  • Handle: RePEc:zbw:bamber:89
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    References listed on IDEAS

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    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. 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.
    6. 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.
    7. 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.
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    11. 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.
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    13. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    14. Huang, Weihong & Zheng, Huanhuan, 2012. "Financial crises and regime-dependent dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 445-461.
    15. 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.
    16. 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.
    17. 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.
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    Cited by:

    1. 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.
    2. González-Díaz, Julio & Herold, Florian & Domínguez, Diego, 2016. "Strategic sequential voting," BERG Working Paper Series 113, Bamberg University, Bamberg Economic Research Group.
    3. Bexheti, Abdylmenaf & Mustafi, Besime, 2015. "Impact of public funding of education on economic growth in Macedonia," BERG Working Paper Series 98, Bamberg University, Bamberg Economic Research Group.
    4. Schmitt, Noemi & Tuinstra, Jan & Westerhoff, Frank, 2017. "Side effects of nonlinear profit taxes in an evolutionary market entry model: Abrupt changes, coexisting attractors and hysteresis problems," Journal of Economic Behavior & Organization, Elsevier, vol. 135(C), pages 15-38.
    5. Sahm, Marco, 2017. "Are sequential round-robin tournaments discriminatory?," BERG Working Paper Series 121, Bamberg University, Bamberg Economic Research Group.
    6. Lena Dräger & Christian R. Proaño, 2015. "Cross-Border Banking and Business Cycles in Asymmetric Currency Unions," Macroeconomics and Finance Series 201501, University of Hamburg, Department of Socioeconomics.
    7. March, Christoph & Sahm, Marco, 2017. "Asymmetric discouragement in asymmetric contests," Economics Letters, Elsevier, vol. 151(C), pages 23-27.
    8. Fatoke-Dato, Mafaïzath A., 2015. "Impact of income shock on children's schooling and labor in a West African country," BERG Working Paper Series 102, Bamberg University, Bamberg Economic Research Group.
    9. Fabio Tramontana & Frank Westerhoff & Laura Gardini, 2014. "One-dimensional maps with two discontinuity points and three linear branches: mathematical lessons for understanding the dynamics of financial markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(1), pages 27-51, April.
    10. Herold, Florian & Kuzmics, Christoph, 2016. "The evolution of taking roles," BERG Working Paper Series 115, Bamberg University, Bamberg Economic Research Group.
    11. Lengnick, Matthias & Wohltmann, Hans-Werner, 2016. "Optimal monetary policy in a new Keynesian model with animal spirits and financial markets," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 148-165.
    12. Proaño, Christian R. & Lojak, Benjamin, 2015. "Debt stabilization and macroeconomic volatility in monetary unions under heterogeneous sovereign risk perceptions," BERG Working Paper Series 106, Bamberg University, Bamberg Economic Research Group.
    13. Fatoke-Dato, Mafaïzath A., 2015. "Impact of an educational demand-and-supply policy on girls' education in West Africa: Heterogeneity in income, school environment and ethnicity," BERG Working Paper Series 101, Bamberg University, Bamberg Economic Research Group.
    14. Meyer, Dietmar & Shera, Adela, 2015. "Remittances' impact on the labor supply and on the deficit of current account," BERG Working Paper Series 97, Bamberg University, Bamberg Economic Research Group.
    15. Lojak, Benjamin, 2016. "Sentiment-driven investment, non-linear corporate debt dynamics and co-existing business cycle regimes," BERG Working Paper Series 112, Bamberg University, Bamberg Economic Research Group.
    16. Sahm, Marco, 2016. "Advance-purchase financing of projects with few buyers," BERG Working Paper Series 118, Bamberg University, Bamberg Economic Research Group.
    17. Sahm, Marco, 2017. "Risk aversion and prudence in contests," BERG Working Paper Series 120, Bamberg University, Bamberg Economic Research Group.
    18. repec:taf:quantf:v:17:y:2017:i:8:p:1187-1203 is not listed on IDEAS
    19. Schmitt, Noemi & Westerhoff, Frank, 2015. "Evolutionary competition and profit taxes: market stability versus tax burden," BERG Working Paper Series 104, Bamberg University, Bamberg Economic Research Group.
    20. Noemi Schmitt & Frank Westerhoff, 2017. "Herding behaviour and volatility clustering in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1187-1203, August.

    More about this item

    Keywords

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

    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

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