This paper investigates the effect of heterogeneity and bounded rationality on market anomalies in price formation. We establish a heterogeneous agent model under prospect theory, where asset price fluctuation is determined by evolutionary dynamics system embedded in the model. Specifically, our model includes three types of expectation schemes related to different decision-making progresses: the rational scheme, the emotional scheme and the noise scheme. Agents under emotional scheme make decisions based on the cumulative prospect theory framework, which makes psychological factor tractable. By analyzing the distribution of return rate under selected parameters, we show that the model return shares the same pattern as those of SSE 50 Index. Furthermore, we investigate the factors of option implied volatility smile based on dynamic system, and the results suggest that the smile anomaly may be associated with the tail risk of the underlying asset's return distribution, which is effected by market stability and psychological factors.

The dataset is generated by the ABM simulation. We construct an artificial market based on the heterogeneous agents model via python. Under the selected parameters, we run the model for n rounds with each value of parameter, and each round contains thousands of time series values. By calculating the average to guarantee robust simulation results, we get the statistic analysis of daily return shown in the paper.