Replicating financial market dynamics with a simple self-organized critical lattice model

• Published in: Physica A 2011-09, Vol.390 (18-19), p.3120-3135
• Main Authors: Dupoyet, B., Fiebig, H.R., Musgrove, D.P.
• Format: Article
• Language: English
• Subjects: Econophysics; Financial markets; Gain; Lattices; Markets; Mathematical models; Self-organized criticality; Statistical field theory; Time series; Tuning; Volatility
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2011.04.017

We explore a simple lattice field model intended to describe statistical properties of high-frequency financial markets. The model is relevant in the cross-disciplinary area of econophysics. Its signature feature is the emergence of a self-organized critical state. This implies scale invariance of the model, without tuning parameters. Prominent results of our simulation are time series of gains, prices, volatility, and gains frequency distributions, which all compare favorably to features of historical market data. Applying a standard GARCH(1,1) fit to the lattice model gives results that are almost indistinguishable from historical NASDAQ data. ► Self-organized critical lattice model simulates prominent financial market features. ► Model yields fat tails of the gains distribution from its intrinsic dynamics. ► Gains time series exhibits volatility clustering. ► GARCH fits find model time series almost indistinguishable from real market data.