We show that the prices of risk for factors that are nonlinear in the market return are readily obtained using index option prices. The price of co-skewness risk corresponds to the market variance risk premium, and the price of co-kurtosis risk corresponds to the market skewness risk premium....

Observable covariates are useful for predicting default under the natural measure, but several findings question their value for explaining credit spreads under the pricing measure. We introduce a discrete time no-arbitrage model with observable covariates, which allows for a closed form...

A substantial portion of the variation in the market variance risk premium can be explained by the conditional covariance between the market return and its variance, which we refer to as the leverage effect. This finding holds at different data frequencies and for various sample periods, and it...