Risk-neutral moments in the crude oil market

In this paper, we provide a comprehensive study on the higher-order risk-neutral moments (RNMs) and differences in RNMs (DRNMs) in the crude oil market, implied by options written on the United States Oil Fund (USO). Based on the t-statistic, the in-sample and the out-of-sample R² statistics, we compare the USO return predictability and USO option return predictability by using RNMs and DRNMs from May 2007 to April 2016. We find that (i) all RNMs have a poor out-of-sample performance of predicting USO returns and simple option returns, while the risk-neutral volatility (VOL) outperforms in terms of both in-sample and out-of-sample predicting delta-hedged option returns; (ii) most of the DRNMs can significantly predict the future USO returns, and (iii) differences in the risk-neutral third cumulant (DTC) and differences in the risk-neutral fourth cumulant (DFC) are two important predictors for the future USO option returns.