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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, 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
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    1. 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.
    2. Kubin, Ingrid & Zörner, Thomas O. & Gardini, Laura & Commendatore, Pasquale, 2019. "A credit cycle model with market sentiments," Structural Change and Economic Dynamics, Elsevier, vol. 50(C), pages 159-174.
    3. 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.
    4. Herold, Florian & Kuzmics, Christoph, 2020. "The evolution of taking roles," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 38-63.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Schmitt, Noemi & Westerhoff, Frank, 2018. "Evolutionary Competition And Profit Taxes: Market Stability Versus Tax Burden," Macroeconomic Dynamics, Cambridge University Press, vol. 22(8), pages 2007-2031, December.
    10. 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.
    11. 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.
    12. March, Christoph & Sahm, Marco, 2017. "Asymmetric discouragement in asymmetric contests," Economics Letters, Elsevier, vol. 151(C), pages 23-27.
    13. 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.
    14. Zhang, Wei & Zhou, Zhong-Qiang & Xiong, Xiong, 2019. "Behavioral heterogeneity and excess stock price volatility in China," Finance Research Letters, Elsevier, vol. 28(C), pages 348-354.
    15. Fatoke Dato, Mafaizath A., 2015. "Impact of income shock on children’s schooling and labor in a West African country," MPRA Paper 64317, University Library of Munich, Germany.
    16. 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.
    17. 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.
    18. 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.
    19. González-Díaz, Julio & Herold, Florian & Domínguez, Diego, 2016. "Strategic sequential voting," BERG Working Paper Series 113, Bamberg University, Bamberg Economic Research Group.
    20. 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.
    21. Sahm, Marco, 2017. "Are sequential round-robin tournaments discriminatory?," BERG Working Paper Series 121, Bamberg University, Bamberg Economic Research Group.
    22. 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.
    23. Sahm, Marco, 2016. "Advance-purchase financing of projects with few buyers," BERG Working Paper Series 118, Bamberg University, Bamberg Economic Research Group.
    24. Sahm, Marco, 2017. "Risk aversion and prudence in contests," BERG Working Paper Series 120, Bamberg University, Bamberg Economic Research Group.
    25. 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.

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    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

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