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A reflexive toy-model for financial market

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  • Palatella, Luigi

Abstract

We propose a reflexive toy model for market dynamics, based on the idea that existing reflexive loops are generated by the conviction, shared by many market operators, that a certain price follows a certain model. Their trading behaviour will therefore increase the probability that the model predictions are in fact fulfilled. We analytically write the equations generating a reflexive loop stemming from a simple linear regression model, and we show that the resulting toy model yields a peculiar intermittent behavior. The presence of two unstable fixed points is apparent from our numerical calculation and the residence-time distribution density in these points asymptotically follows an inverse-power-law tail. The exponent of this tail, as well as the scaling properties of the model output, are close to those stemming from real-price time series.

Suggested Citation

  • Palatella, Luigi, 2010. "A reflexive toy-model for financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 315-322.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:2:p:315-322
    DOI: 10.1016/j.physa.2009.09.037
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    References listed on IDEAS

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    1. C. P. Kwong, 2009. "Mathematical analysis of Soros's theory of reflexivity," Papers 0901.4447, arXiv.org.
    2. Palatella, Luigi & Perelló, Josep & Montero, Miquel & Masoliver, Jaume, 2005. "Diffusion Entropy technique applied to the study of the market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 131-137.
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    Cited by:

    1. Palatella, Luigi & Grigolini, Paolo, 2012. "Noise-induced intermittency of a reflexive model with symmetry-induced equilibrium manifold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5900-5907.

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