This paper models the hump volatility structure of commodity derivatives markets in the rough volatility modelling framework. The model encompasses the stochastic volatility that may be unspanned by futures contracts. A generalized hump-shaped volatility specification is assumed that entails a finite-dimensional affine model for the commodity futures curve and semi-analytical prices for options
on commodity futures. An empirical study of the crude oil futures volatility structure is carried out using a database of futures prices as well as futures option prices spanning 3 years. Implied Hurst parameters inferred from options on Crude Oil future support empirical evidence of rough Crude oil volatility. We show that rough stochastics model provides a much better fit to both futures and options when compared to the model driven by a classical Brownian motion.