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

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.