Diffusion processes in a financial market under heterogeneous trading and learning

We consider a market populated by heterogeneous agents, and we derive, in an equilibrium perspective, a continuous time model for the evolution of the price of a risky asset which pays no dividends. We introduce three classes of traders: bounded rationality traders, feedback traders and noise traders. Bounded rationality is modelled by assuming that traders forecast the future price by a first order autoregressive learning mechanism. We find that the asset price follows a mean reverting process, around the level given by the forecasted price. Positive feedback strategies tend to increase the volatility of the price and generate positive serial correlation in returns. Conversely, bounded rationality trading makes the price less volatile and gives a negative contribute to serial correlation in returns. In addition, the price variance is a decreasing [resp. increasing] function of the memory according to whether there are enough [resp. not enough] bounded rationality traders.