Arbitrage, speculation and futures price fluctuations with boundedly rational and heterogeneous agents

This paper proposes a dynamic model for the futures market with three types of investors. The bounded rationality and heterogeneity of investors are taken into consideration. The equilibrium of the system and its stability conditions are derived with mathematical analysis. In the equilibrium, the futures price and the spot price converge to the equilibrium simultaneously. The equilibrium is determined by many factors, including the risk appetite and the rationality of investors, the trading costs, the arbitrage basis price and the fundamental price. When the stability conditions are violated, complex dynamics will emerge in the market. As shown by the simulations, the arbitrage is likely to destabilize the market. Moreover, when investors have the high degree of rationality, the equilibrium will become unstable and the futures market is inefficient. Statistical analysis indicates that the model can reproduce the stylized facts observed in the futures market, such as long memory, volatility clustering and fat tail of returns.