Modeling Variance Risk Premia Dynamics

This paper proposes a flexible approach for retrieving the VRP which delivers more refined, precise and realistic estimates of the market price of risk. We define a class of structural time series models that isolates as structural components the dynamics of the physical variance and, by embedding its expectations into the model, the price attached by the market to the variance risk (i.e. the VRP). In fact, by doing this we deconstruct the mechanism of formation of the variance expectations under the risk neutral measure. Given the latent nature of the variables of interest of which only imprecise approximations are observable (i.e., high frequency return based variance measures and option implied risk neutral variance expectations), we advocate the use of methodologies based or signal extraction techniques. These techniques allow us to obtain measurement error free estimates of the VRP, and thus to disentangle, with a high degree of precision, its underlying time series properties as well as possible dependencies with the state of the economy. We advocate the inclusion of interactions and discontinuities, with emphasis on structural breaks, extreme events, uncertainty due to heteroskedasticity, correlations and spillovers, as being essential to replicate complex dynamics and interdependencies between the physical variance and its risk neutral expectation. In an empirical application to the SP500, we address the excess return puzzle by disentangling the predictability stemming from the part of the variance risk premium associated with normal sized price fluctuation from that associated with extreme tail events, i.e. tail risk. We also provide wide international evidence with respect to eight major markets. We find that excess returns are to a large extent explained by extreme tail events and only marginally, if any at all, by the premium associated to normal price fluctuations.