Stochastic volatility models with persistent latent factors: theory and its applications to asset prices

We consider the stochastic volatility model with smooth transition and persistent la-tent factors. We argue that this model has advantages over the conventional stochasticmodel for the persistent volatility factor. Though the linear filtering is widely usedin the state space model, the simulation result, as well as theory, shows that it doesnot work in our model. So we apply the density-based filtering method; in particular,we develop two methods to get solutions. One is the conventional approach usingthe Maximum Likelihood estimation and the other is the Bayesian approach usingGibbs sampling. We do a simulation study to explore their characteristics, and weapply both methods to actual macroeconomic data to extract the volatility generatingprocess and to compare macro fundamentals with them.Next we extend our model into multivariate model extracting common and id-iosyncratic volatility for multivariate processes. We think it is interesting to applythis multivariate model into measuring time-varying uncertainty of macroeconomicvariables and studying the links to market returns via a consumption-based asset pric-ing model. Motivated by Bansal and Yaron (2004), we extract a common volatilityfactor using consumption and dividend growth, and we find that this factor predictspost-war business cycle recessions quite well. Then, we estimate a long-run risk modelof asset prices incorporating this macroeconomic uncertainty. We find that both risk aversion and the intertemporal elasticity of substitution are estimated to be aroundtwo, and our simulation results show that the model can match the first and secondmoments of market return and risk-free rate, hence the equity premium.