Unspanned stochastic volatility and the pricing of commodity derivatives

Abstract

Commodity derivatives are becoming an increasingly important part of the global derivatives market. Here we develop a tractable stochastic volatility model for pricing commodity derivatives. The model features unspanned stochastic volatility, quasi-analytical prices of options on futures contracts, and dynamics of the futures curve in terms of a low-dimensional affine state vector. We estimate the model on NYMEX crude oil derivatives using an extensive panel data set of 45,517 futures prices and 233,104 option prices, spanning 4082 business days. We find strong evidence for two predominantly unspanned volatility factors.