Asset Pricings Under Correlations Between The Model Uncertainty And Time-varying Fear

Equity premium is an important factor for investors to determine asset allocation and predict stock prices.Studying the way equity premium changes is not only an important content of asset pricing theory,but also an important subject in finance research.As the representative of higher order index,variance risk premium has a good prediction function in asset market.Investors' model uncertainty and time-varying fear are two main factors to change asset pricing.Drechelser(2013)first quantified the model uncertainty and investors' time-varying fear and analyzed them as independent volatility components.However,model uncertainty affects investor confidence,and vice versa.Therefore,it is necessary to improve the assumption that the model uncertainty and investors' time-varying fear are independent of each other.The main of this paper is to develop and improve Drechelser's model.This paper improve his work by hypothesising that model uncertainty associated with time-varying fear of investors,and discuss the relevance of model uncertainty and investors time-varying fear.Also,this paper discusses the influence of correlation on equity premium and variance risk premium.First of all,this paper establishes the affine jump diffusion model with covariance matrix which is non-diagonalized,and does the diagonal transformation by finding the eigenroots and the eigenvectors and the Gram-Schmidt method.In the special case of two-dimensional diffusion covariance matrix,this paper use the two submatrix to take the partial derivative of the correlation coefficient.In this way,this paper discusses how model uncertainty and investors' time-varing fear changes with the correlation coefficient.Then,this paper discusses the reference model and alternative models in affine jump diffusion process,and set a ceiling for relative entropy rate of the alternative model,which constraints the scope of alternative model set.By using a recursive utility function about representative investor's preference and solving it,the expressions of pricing kernel,risk-free rate,the equity premium and the variance risk premia are obtained.This paper also gives a logarithmic linear representation of equity.Finally,this paper analyses how investors' model uncertainty and the correlation coefficient between the model uncertainty and time-varying fear of investors influence the equity premium and the the variance risk premia.