Modeling and Predicting Volatility and its Risk Premium: a Bayesian Non-Gaussian State Space Approach

The object of this paper is to model and forecast both objective volatility and its associated risk premium using a non-Gaussian state space approach. Option and spot market information on the unobserved volatility process is captured via nonparametric, ‘model-free’ measures of option-implied and spot price-based volatility, with the two measures used to define a bivariate observation equation in the state space model. The risk premium parameter is specified as a conditionally deterministic dynamic process, driven by past ‘observations’ on the volatility risk premium. The inferential approach adopted is Bayesian, implemented via a Markov chain Monte Carlo (MCMC) algorithm that caters for the non-linearities in the model and for the multimove sampling of the latent volatilities. The simulation output is used to estimate predictive distributions for objective volatility, the instantaneous risk premium and the conditional risk premium associated with a one month option maturity. Linking the volatility risk premium parameter to the risk aversion parameter in a representative agent model, we also produce forecasts of the relative risk aversion of a representative investor. The methodology is applied both to artifically simulated data and to empirical spot and option price data for the S&P500 index over the 2004 to 2006 period.