Abstract
This paper analyzes the volatility structure of the commodity derivatives markets. The model encompasses stochastic volatility that may be unspanned by the futures contracts. A generalized hump-shaped volatility specification is assumed that entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on commodity futures. An empirical study of the crude oil futures volatility structure is carried out using an extensive database of futures prices as well as futures option prices spanning 21 years. The study supports hump-shaped, partially spanned stochastic volatility specification. Factor hedging, which takes into account shocks to both the volatility processes and the futures curve, depicts the out-performance of the hump-shaped volatility in comparison to the more popular exponential decaying volatility and the presence of unspanned components in the volatility of commodity futures.
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