Microscopic spin model for the stock market with attractor bubbling on scale-free networks

A multi-agent spin model for changes of prices in the stock market based on the Ising-like cellular automaton with interactions between traders randomly varying in time is investigated by means of Monte Carlo simulations. The structure of interactions has topology of scale-free networks with degree distributions obeying a power scaling law with various scaling exponents. The scale-free networks are obtained as growing networks where new nodes (agents) are linked to the existing ones according to a preferential attachment rule with an initial attractiveness ascribed to each node. In certain ranges of parameters, depending on the exponent in the degree distribution, the time series of the logarithmic price returns exhibit intermittent bursting typical of volatility clustering, and the tails of the distributions of returns obey a power scaling law with exponents comparable to those obtained from the empirical data. The distributions of returns show also dependence on the number of agents, in particular in the case of networks with the scaling exponents of the degree distributions typical of the social and communications networks.