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We show that the prices of risk for factors that are nonlinear in the market return are readily obtained using index option prices. We apply this insight to the price of co-skewness and co-kurtosis risk. The price of co-skewness risk corresponds to the spread between the physical and the risk-neutral second moments, and the price of co-kurtosis risk corresponds to the spread between the physical and the risk-neutral third moments. The option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An out-of-sample analysis of factor models with co-skewness and co-kurtosis risk indicates that the new estimates of the price of risk improve the models performance. Models with higher-order market moments also robustly outperform standard competitors such as the CAPM and the Fama-French model.

Option-Based Estimation of the Price of Co-Skewness and Co-Kurtosis Risk