A Pricing Model With Time-varying Risk Aversion And A Parameter Of Contrarians And Empirical Analysis

Besides the heterogeneity of agents’ beliefs, contrary to the traditional ?-nancial models, the risk attitudes for two kinds of investors vary over time due to psychological factors such as prospect theory’s re?ection effect, which refers to the reversing of risk aversion / risk loving in the case of gains / losses. Thus,this paper expands the asset pricing model with homogeneous risk aversion and introduces a time varying risk aversion into the model. At the same time, we introduce an abstract function in [0,1] as the parameter of contrarians, which represents the proportion of contrarians in the chartists, so investors will be divided into fundamentalists, trend chasers and contrarians. Then we develop an asset pricing model with time varying risk aversions and a parameter of contrarians.Using the differential equation theory, we get the equilibrium solution, linearize the model and discuss the stability and bifurcation of the equilibrium solution of the linear model. Then conclude that the stability of the nonlinear system can be described by the linear system when the parameters satisfy certain conditions. Finally, we generalize the abstract function and analyse the stability and bifurcation of nonlinear system with speci?c parameters of wind, indicating that the model generalizes the original model in a way. Through the numerical simulation and statistical test, we compare the return series of this model, the original model and the industrial index and verify the new model is better than before in describing the kurtosis of the return series and so on.