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A simple financial market model with chartists and fundamentalists: Market entry levels and discontinuities

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

Abstract

We present a simple financial market model with interacting chartists and fundamentalists. Since some speculators only become active when a certain misalignment level has been crossed, the model dynamics is driven by a discontinuous piecewise linear map. Recent mathematical techniques allow a comprehensive study of the model's dynamical system. One of its surprising features is that model simulations may appear to be chaotic, although only regular dynamics can emerge. While our deterministic model is able to produce stylized bubbles and crashes we also show that a stochastic version of our model is able to match the finer details of financial market dynamics.

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  • 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.
    • Handle: RePEc:eee:matcom:v:108:y:2015:i:c:p:16-40
    DOI: 10.1016/j.matcom.2013.06.002
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    1. 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.
    2. Francesca Grassetti & Cristiana Mammana & Elisabetta Michetti, 2018. "Poverty trap, boom and bust periods and growth. A nonlinear model for non-developed and developing countries," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 145-162, November.
    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. 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.
    5. 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.
    6. 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.
    7. Jochen Jungeilges & Elena Maklakova & Tatyana Perevalova, 2022. "Stochastic sensitivity of bull and bear states," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 165-190, January.
    8. Nguyen Tien Zung, 2017. "Second order stochastic differential models for financial markets," Papers 1707.05419, arXiv.org.
    9. Giovanni Campisi & Silvia Muzzioli & Fabio Tramontana, 2021. "Uncertainty about fundamental and pessimistic traders: a piecewise-linear maps approach," Department of Economics 0186, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    10. 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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