Monte Carlo simulations of a trader-based market model

We present a detailed analysis of the stationary state and the parameter sensitivity of a trader-based market model suggested in Bak et al. (Physica A 246 (1997) 430). The model in question takes only so-called noise-traders into account and its properties are determined by mutual imitation of the traders and volatility feedback. We show that the stationary state of the model can be characterized by a log-normal distribution of the bid and ask prices relative to the current market price. In the stationary state the model is able to reproduce the so-called stylized facts of real markets. This property is stable under variation of the essential parameters of the model, number of traders, N, an asymmetry in the stochastic update of the price ideas of the traders, drift D, and the form of the volatility feedback. An extension of the model to take into account a more realistic distribution of the budgets of different market participants, however, would also need a more realistic modeling of the actual trading process to preserve these properties.