A multifactor stochastic volatility model of commodity price

Abstract

We propose a novel representation of commodity spot prices in which the cost-of-carry and the spot price volatility are both driven by an arbitrary number of risk factors, nesting many existing specifications. The model exhibits unspanned stochastic volatility, provides simple closed-form expressions of commodity futures, and yields analytic formulas of European options on futures. We estimate the model using oil futures and options data, and find that the pricing of traded contracts is accurate for a wide range of maturities and strike prices. The results suggest that at least three risk factors in the spot price volatility are needed to accurately fit the volatility surface of options on oil futures, highlighting the importance of using general multifactor models in pricing commodity contingent claims.