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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.
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437109007377
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 389 (2010)
    Issue (Month): 1 ()
    Pages: 107-116

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    Handle: RePEc:eee:phsmap:v:389:y:2010:i:1:p:107-116

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Econophysics; Financial markets; Statistical field theory; Gauge invariance;

    References

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    1. 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.
    2. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
    3. Prasad V. Bidarkota & Brice V. Dupoyet, 2004. "The Impact of Fat Tails on Equilibrium Rates of Return and Term Premia," Working Papers 0411, Florida International University, Department of Economics.
    4. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
    5. Kirill Ilinski & Alexander Stepanenko, 1998. "Electrodynamical model of quasi-efficient financial market," Finance 9805007, EconWPA.
    6. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
    7. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    8. J. Doyne Farmer, 1999. "Physicists Attempt to Scale the Ivory Towers of Finance," Working Papers 99-10-073, Santa Fe Institute.
    9. 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.
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    Citations

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    Cited by:
    1. 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.
    2. 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.

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