Besides the heterogeneity of agents’ beliefs, we perceive that, contrary to the constant short-term risk attitude of fundamentalists, the risk attitude for chartists varies over time due to psychological factors such as prospect theory’s reflection effect, which refers to the reversing of risk aversion/risk loving in the case of gains/losses. Thus, this paper assumes that complicated dynamics in recent asset markets are attributed to the significant effects of time-varying and heterogeneous risk attitudes as well as agents’ herd behavior, and generalizes an adaptive beliefs system in order to characterize them. This paper also analyzes the existence of stable steady states of the generalized adaptive beliefs system, providing a new psychological insight into excessive and asymmetric volatility. Given the dynamic system, numerical simulations find that, when the chartists are less risk averse than the fundamentalists and their herding propensity increases, time variation in risk attitudes gives rise to large amplitude changes in proportion to agent groups and expand price fluctuations through chaotic dynamics. Along these lines, this paper highlights that psychological factors serve as decisive source of asymmetry in volatility as well as excess volatility, which are observed in the return data.

As a considerable source of asymmetry in return volatility, this paper introduces asymmetric herding and extends the continuous beliefs system to account for its asymmetry and derive the asymmetric herding parameters that are easily estimated by using a maximum likelihood method based on the GARCH-type econometric model. This paper presents new empirical evidence for asymmetry in the exchange rates volatility of major currencies against the US dollar, which have bilateral nature. Interestingly, the asymmetry of Japanese yen is the opposite of that of others and the global financial crisis highlights the opposite asymmetry. Some of traditional hypotheses, such as the leverage effect and the volatility feedback effect, do not adequately explain these findings; however, a significant asymmetric herding effect is observed and appears to be time-varying. Further, the clear link between asymmetric herding and volatility strongly supports the hypothesis of the asymmetric herding effect.