Maximum likelihood estimation of non-affine volatility processes

In this paper we develop a new estimation method for extracting non-affine latent stochastic volatility and risk premia from measures of model-free realized and risk-neutral integrated volatility. We estimate non-affine models with nonlinear drift and constant elasticity of variance and we compare them to the popular square-root stochastic volatility model. Our empirical findings are: (1) the square-root model is misspecified; (2) the inclusion of constant elasticity of variance and nonlinear drift captures stylized facts of volatility dynamics and (3) the square-root stochastic volatility model is explosive under the risk-neutral probability measure.