A non-linear dynamic model of the variance risk premium

We propose a new class of non-linear diffusion processes for modeling financial markets data. Our non-linear diffusions are obtained as transformations of affine processes. We show that asset-pricing and estimation is possible and likelihood estimation is straightforward. We estimate a non-linear diffusion model for the VIX index under both the objective measure and the risk-neutral measure where the latter is obtained from futures prices. We find evidence of significant non-linearity under both measures. We define the difference between the P and Q drift as a measure of the variance risk premium and show that it has strong predictive power for stock returns.