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Arbitrage-free self-organizing markets with GARCH properties: Generating them in the lab with a lattice model

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  • Dupoyet, B.
  • Fiebig, H.R.
  • Musgrove, D.P.

Abstract

We extend our studies of a quantum field model defined on a lattice having the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is realized as a numerical simulation of the one-asset version. The gauge field background enforces minimal arbitrage, yet allows for statistical fluctuations. The new feature added to the model is an updating prescription for the simulation that drives the model market into a self-organized critical state. Taking advantage of some flexibility of the updating prescription, stylized features and dynamical behaviors of real-world markets are reproduced in some detail.

Suggested Citation

  • Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2012. "Arbitrage-free self-organizing markets with GARCH properties: Generating them in the lab with a lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4350-4363.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:18:p:4350-4363
    DOI: 10.1016/j.physa.2012.04.017
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    References listed on IDEAS

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    Cited by:

    1. Paolinelli, Giovanni & Arioli, Gianni, 2018. "A path integral based model for stocks and order dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 387-399.
    2. Giovanni Paolinelli & Gianni Arioli, 2018. "A model for stocks dynamics based on a non-Gaussian path integral," Papers 1809.01342, arXiv.org, revised Oct 2018.
    3. Giovanni Paolinelli & Gianni Arioli, 2018. "A path integral based model for stocks and order dynamics," Papers 1803.07904, arXiv.org.
    4. Paolinelli, Giovanni & Arioli, Gianni, 2019. "A model for stocks dynamics based on a non-Gaussian path integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 499-514.

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