Humps in the volatility structure of the crude oil futures market: New evidence

- This paper analyses the volatility structure of commodity derivatives markets.
- 21-years of data on crude oil futures and futures options is used.
- The crude oil futures market has hump-shaped, unspanned stochastic volatility.
- The hump shaped feature is more pronounced when the market is more volatile.
- Hump shape delivers better pricing and hedging compared to exponential decay.

This paper analyses the volatility structure of commodity derivatives markets. The model encompasses hump-shaped, unspanned stochastic volatility, which entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on commodity futures. Using an extensive database of crude oil futures and futures options spanning 21 years, we find the presence of hump-shaped, partially spanned stochastic volatility in the crude oil market. The hump shaped feature is more pronounced when the market is more volatile, and delivers better pricing as well as hedging performance under various dynamic factor hedging schemes.