An interacting-agent model of financial markets from the viewpoint of nonextensive statistical mechanics

In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders to be influenced by the other traders’ investment attitudes [Kaizoji, Physica A 287 (2000) 493], and formulate the traders’ decision-making regarding investment as the maximum entropy principle for nonextensive entropy [C. Tsallis, J. Stat. Phys. 52 (1988) 479]. We demonstrate that the equilibrium probability distribution function of the traders’ investment attitude is the q-exponential distribution. We also show that the power-law distribution of the volatility of price fluctuations, which is often demonstrated in empirical studies can be explained naturally by our model which originates in the collective crowd behavior of many interacting-agents.