2003/11/30 by M. Bartolozzi, A. W. Thomas · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #physics.soc-ph #q-fin.ST
paper · pdf · doi:10.1103/physreve.69.046112
17 pages and 7 figures
openalex publication_date 2004/04/27 · arxiv created 2005/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two-dimensional grid. Active traders are characterized by the decision to buy, sigma(i) (t)=+1, or sell, sigma(i) (t)=-1, a stock at a certain discrete time step. The remaining cells are inactive, sigma(i) (t)=0. The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Extreme, intermittent events, such as crashes or bubbles, are triggered by a phase transition in the state of the bigger clusters present on the grid, where almost all the active traders come to share the same spin orientation. Most of the stylized aspects of the financial market time series, including multifractal proprieties, are reproduced by the model. A direct comparison is made with the daily closures of the S&P 500 index.