Agent-based simulations of toy market models. - Lye, Ribin. (2010)
A simple deterministic model of the financial market has been constructed. The traders in this model make their trading decisions based on utility functions which can be controlled to contain different degree of fundamentalist mentality and chartist mentality. In spite of the simplicity, our market produced price distributions of stocks that are dynamical which we see in the real world. A phase diagram was mapped out based on critical parameter settings which change the price distribution of the market between three phases – “dead market”, “boom market” and “jammed market”. We quantified the phase transition in the form of order parameters and the determination of a critical exponent. Three refined models were also constructed based on this deterministic model – Stochastic Sell Model (incorporation of random selling traders), Stochastic Buy Model (incorporation of random buying traders) and Coupling to Stock Index Models (utility functions containing information from a stock index). The Stochastic Sell and Stochastic Buy Models produced a phase diagram that is similar to the deterministic model, and we found a general expansion of the phase “boom market” with increase in the number of random trading traders. The critical exponent defining the phase transition has changed value, suggesting a different universality class. The Coupling to Stock Index Model produced the same phase diagram as the deterministic model and has the same critical exponent value. We also offered possible explanations to the observations in the phase diagrams and future refinements that can be made to bring the model closer to reality.