A multi-interacting-agent model for financial markets

Microscopic models, which resemble random magnetic systems, have been used recently in the literature for the description of financial markets. In the present work, a model with many interacting agents, similar to an Ising random magnet with infinite-range interactions, is investigated. The introduction of a local-field term, depending on the absolute value of a magnetization-like parameter—which measures the volatility of a financial market—leads to a significant improvement with respect to previously studied models in the literature. By investigating the return time series, we show that several features, characteristic of real financial markets, are better reproduced by the present model. In particular, within this approach one is able to provide a proper behavior for the following properties: (i) the power-law tails and the nonzero skewness of the probability distribution of returns; (ii) the exponential decay of the two-time autocorrelation function of returns, typical of high-frequency financial data; (iii) the so-called “leverage effect”, which corresponds to a negative correlation between past returns and future volatility.