On Simple Mean-Field Stochastic Model of Market Dynamics

We propose a simple stochastic model of market behavior. Dividing market participants into two groups: trend-followers and fundamentalists, we derive the general form of a stochastic equation of market dynamics. The model has two characteristic time scales: the time of changes of market environment (tm) and the characteristic time of news flow (tn). Price behavior in the most general case is driven by three stochastic processes, attributed to trend-followers, fundamentalists, and news flow, respectively. The model demonstrates the wide range of peculiarities which are typical in real markets: multiscale behavior, clustered volatility, weak correlations between the price changes on successive trading days, etc.