In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks … traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a …-form and structural models of stochastic volatility …

advantages: i) ensures nonnegative interest rates, ii) easily accommodates unspanned factors affecting volatility and risk …, volatility, and risk premium dynamics — including when interest rates are close to the zero lower bound …

option prices on both markets. We find that including VIX option prices in the model estimation allows better identification … of the parameters driving the risk-neutral conditional distributions and term structure of volatility, thereby enhancing … the estimation of the variance risk premium. We gain new insights on the properties of the premium's term structure and …

information set for the estimation of the empirical pricing kernel and, more in general, for the validity of the fundamental …