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Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets

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

Abstract

We report on initial studies of a quantum field theory defined on a lattice with multi-ladder geometry and 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 implemented in a numerical simulation. We arrive at a probability distribution of relative gains which matches the high frequency historical data of the NASDAQ stock exchange index.

Suggested Citation

  • Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2010. "Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 107-116.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:1:p:107-116
    DOI: 10.1016/j.physa.2009.09.002
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    References listed on IDEAS

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    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
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    3. Kirill Ilinski & Alexander Stepanenko, 1998. "Electrodynamical model of quasi-efficient financial market," Finance 9805007, University Library of Munich, Germany.
    4. Bartolozzi, M. & Leinweber, D.B. & Thomas, A.W., 2006. "Scale-free avalanche dynamics in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 132-139.
    5. M. Bartolozzi & D. B. Leinweber & A. W. Thomas, 2006. "Scale-free avalanche dynamics in the stock market," Papers physics/0601171, arXiv.org, revised Jun 2006.
    6. Bidarkota, Prasad V. & Dupoyet, Brice V., 2007. "The impact of fat tails on equilibrium rates of return and term premia," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 887-905, March.
    7. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
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    Citations

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    Cited by:

    1. B. Dupoyet & H. R. Fiebig & D. P. Musgrove, 2010. "Replicating financial market dynamics with a simple self-organized critical lattice model," Papers 1010.4831, arXiv.org.
    2. 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.
    3. 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.
    4. Simone Farinelli & Hideyuki Takada, 2014. "Credit Bubbles in Arbitrage Markets: The Geometric Arbitrage Approach to Credit Risk," Papers 1406.6805, arXiv.org, revised Jul 2021.
    5. 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.
    6. Rudolf Fiebig & David Musgrove, 2014. "Testing for Detailed Balance in a Financial Market," Papers 1403.3584, arXiv.org.
    7. Giovanni Paolinelli & Gianni Arioli, 2018. "A path integral based model for stocks and order dynamics," Papers 1803.07904, arXiv.org.
    8. Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2011. "Replicating financial market dynamics with a simple self-organized critical lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3120-3135.
    9. 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.
    10. Hernández, Juan Antonio & Benito, Rosa Marı´a & Losada, Juan Carlos, 2012. "An adaptive stochastic model for financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 899-908.
    11. Fiebig, H.R. & Musgrove, D.P., 2015. "Testing for detailed balance in a financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 26-33.

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