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We extend our studies of a quantum field model defined on a lattice havingthe dilation group as a local gauge symmetry. The model is relevant in thecross-disciplinary area of econophysics. A corresponding proposal by Ilinskiaimed at gauge modeling in non-equilibrium pricing is realized as a numericalsimulation of the one-asset version. The gauge field background enforcesminimal arbitrage, yet allows for statistical fluctuations. The new featureadded to the model is an updating prescription for the simulation that drivesthe model market into a self-organized critical state. Taking advantage of someflexibility of the updating prescription, stylized features and dynamicalbehaviors of real-world markets are reproduced in some detail.

Arbitrage-free Self-organizing Markets with GARCH Properties: Generating them in the Lab with a Lattice Model