A behavioral asset pricing model with a time-varying second moment

We develop a simple behavioral asset pricing model with fundamentalists and chartists in order to study price behaviorin financial markets when chartists estimate both conditional mean and variance by using a weighted averagingprocess. Through a stability, bifurcation, and normal form analysis, the market impact of the weighting process andtime-varying second moment are examined. It is found that the fundamental price becomes stable (unstable) whenthe activities from both types of traders are balanced (unbalanced). When the fundamental price becomes unstable,the weighting process leads to different price dynamics, depending on whether the chartists act as either trend followersor contrarians. It is also found that a time-varying second moment of the chartists does not change the stability of thefundamental price, but it does influence the stability of the bifurcations. The bifurcation becomes stable (unstable) whenthe chartists are more (less) concerned about the market risk characterized by the time-varying second moment.Different routes to complicated price dynamics are also observed. The analysis provides an analytical foundation forthe statistical analysis of the corresponding stochastic version of this type of behavioral model.