A volatility model based on adaptive expectations: An improvement on the rational expectations model

Investment expectations affect stock price volatility, making asset pricing more difficult. Correctly capturing investment expectations can help alleviate this problem. In this paper, we analyze the rational expectations properties of existing volatility models. Second, we explore a volatility model based on adaptive expectations by using mathematical methods and the applicable conditions and continuity feature of the adaptive expectations volatility model. Third, under the assumption of adaptive expectations, we construct adaptive expectations GARCH (ADGARCH) and LSTM-ADGARCH models. Using daily trading data from the Shanghai stock index and SPX500 for the period 2015-2021, we find that the volatility model based on adaptive expectations has more explanatory power than one based on rational expectations.