Agent-based Asset Pricing, Learning, and Chaos
The Lucas asset pricing model is one of the most studied model in financial economics in the past decade. In our research, we relax the original assumptions in Lucas model of homogeneous agents and rational expectations. We populate an artificial economy with heterogeneous and boundedly rational agents. By defining a Correct Expectations Equilibrium, agents are able to compute their policy functions and the equilibrium pricing function without perfect information about the market. A natural adaptive learning scheme is given to agents to update their predictions. We examine the convergence of equilibrium with this learning scheme and show that the equilibrium is learnable (convergent) under certain parameter combinations. We also investigate the market dynamics when agents are out of equilibrium, including the cases where prices have excess volatility and the trading volume is high. Numerical simulations show that our system exhibits rich dynamics, including a whole cascade from period doubling bifurcations to chaos.