The asymmetric relationship between returns and implied higher moments: Evidence from the crude oil market

We investigate the asymmetric relations between returns and changes in implied moments (i.e., volatility, skewness, and kurtosis) in the crude oil market using the United States Oil (USO) Fund option data via a quantile regression model that accounts for investors' heterogeneity. The results show an asymmetric relation between returns and changes in implied moments. With respect to the asymmetric return-volatility and return-kurtosis relation, the impacts of negative returns on changes in implied volatility and kurtosis are stronger than positive returns, especially at the upper quantiles. With respect to the asymmetric return-skewness relation, the impacts of positive returns on changes in implied skewness are more dominant than negative returns, especially at the lower quantiles, and an increase in the contemporaneous positive returns is followed by more implied skewness risk, whereas more negative returns are followed by less implied skewness risk. We argue that the combination of fundamental theories, behavioural theories, investors' heterogeneity theory, and preference higher moments theory support the asymmetric relation between return and implied moments.