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Nonlinear effects in a discrete-time dynamic model of a stock market

Author

Listed:
  • Gian-Italo Bischi

    (Università di Urbino)

  • Vincenzo Valori

    (Dipartimento di Matematica per le Decisioni - Università degli Studi di Firenze)

Abstract

The time evolution of prices and savings in a stock market is modeled by a discrete time nonlinear dynamical system. The model proposed has a unique and unstable steady-state, so that the time evolution is determined by the nonlinear effects acting out of the equilibrium. The nonlinearities strongly influence the kind of long-run dynamics of the system. In particular, the global geometric properties of the noninvertible map of the plane, whose iteration gives the evolution of the system, are important to understand the global bifurcations which change the qualitative properties of the asymptotic dynamics. Such global bifurcations are studied by geometric and numerical methods based on the theory of critical curves, a powerful tool for the characterization of the global dynamical properties of noninvertible mappings of the plane. The model unfolds more complex chaotic and unpredictable trajectories as a consequence of increasing agents' "speculative" or "capital gain realizing" attitudes. The global analysis indicates that, for some ranges of the parameter values, the system has several coexisting attractors, and it may not be robust with respect to exogenous shocks due to the complexity of the basin of attraction.

Suggested Citation

  • Gian-Italo Bischi & Vincenzo Valori, 2000. "Nonlinear effects in a discrete-time dynamic model of a stock market," Working Papers - Mathematical Economics 2000-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    • Handle: RePEc:flo:wpaper:2000-01
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    References listed on IDEAS

    as
    1. Bischi, Gian-Italo & Stefanini, Luciano & Gardini, Laura, 1998. "Synchronization, intermittency and critical curves in a duopoly game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(6), pages 559-585.
    2. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
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    Cited by:

    1. Loretti I. Dobrescu & Dumitru Opris, 2008. "Hopf bifurcation and chaos analysis of a discrete-delay dynamic model for a stock market," "Marco Fanno" Working Papers 0082, Dipartimento di Scienze Economiche "Marco Fanno".
    2. Melecký, Jan & Sergyeyev, Artur, 2008. "A simple finite-difference stock market model involving intrinsic value," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 769-777.
    3. Loretti I. Dobrescu & Mihaela Neamtu & Dumitru Opris, 2011. "A Discrete--Delay Dynamic Model for the Stock Market," Discussion Papers 2012-11, School of Economics, The University of New South Wales.
    4. Matassini, Lorenzo, 2001. "The trading rectangle strategy within book models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 449-456.
    5. Matassini, Lorenzo & Franci, Fabio, 2001. "On financial markets trading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 526-542.
    6. David Gray, 2014. "Central European foreign exchange markets: a cross-spectral analysis of the 2007 financial crisis," The European Journal of Finance, Taylor & Francis Journals, vol. 20(6), pages 550-567, June.
    7. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2462-2468.

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