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Instead of heuristical heterogeneity assumption in the current heterogeneous agent models (HAMs), we derive the trading heterogeneity by introducing information uncertainty about the fundamental value to a HAM. Conditional on their private information about the fundamental value, agents choose different trading strategies when optimizing their expected utilities. This provides a micro-foundation to heterogeneity and switching behavior of agents. We show that the HAM with trading heterogeneity originating from the incomplete information performs equally well, if not better than existing HAMs, in generating bubbles, crashes, and mean-reverting prices. The simulated time series matches with the S&P 500 in terms of power law distribution in returns, volatility clustering and long memory in volatility. [ABSTRACT FROM AUTHOR]

Abstract: Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used in discrete-time HAMs. The time delay represents a memory length of a moving average rule in discrete-time HAMs. Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents’ behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize an otherwise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized facts observed in financial markets. [ABSTRACT FROM AUTHOR]