A Non-Linear Dynamic Model of the Variance Risk Premium

Abstract

We estimate a non-linear diffusion model to capture the dynamics of the VIX index. The model is estimated under the risk neutral and the objective probability measures. The risk neutral dynamics are captured through a novel estimation method applied to futures prices. We find that non-linearity is important in capturing the time-series properties of the VIX index. In particular, we document that the VIX mean reverts more quickly from high levels than from low levels, suggesting that financial crisis regimes are less persistent than predicted by a linear model. The nonlinearity can explain the VIX risk premium outliers, especially the peak in the financial crisis in 2008.