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 …

effects, i.e., it is possible that the structure of the volatility surface changes without a change in the volatility level … state, I show that this superior performance is directly linked to a third volatility factor which is unrelated to the … volatility level. The second chapter studies the price of the smile, which is defined as the premia for individual option risk …