Explaining intraday crude oil returns with higher order risk-neutral moments

High frequency crude oil option data is used to extract the higher order risk-neutral moments from the crude oil market. These risk-neutral moments include the variance, third central moment and the recently developed tail risk variation measures. We find it is beneficial to disaggregate these risk-neutral moments into their semi-moments, and to work with their log differences instead of the level. The log differences of the second and third semi-moments, and to a lesser extent, the log differences of the tail risk measures, are found to explain returns in the crude oil and S & P 500 futures at high frequency. We also provide evidence that the efficient market hypothesis holds at high frequency in these markets.