NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives

Anders B. Trolle, Eduardo S. Schwartz

NBER Working Paper No. 12744
Issued in December 2006
NBER Program(s):   AP

We conduct a comprehensive analysis of unspanned stochastic volatility in commodity markets in general and the crude-oil market in particular. We present model-free results that strongly suggest the presence of unspanned stochastic volatility in the crude-oil market. We then develop a tractable model for pricing commodity derivatives in the presence of unspanned stochastic volatility. The model features correlations between innovations to futures prices and volatility, quasi-analytical prices of options on futures and futures curve dynamics in terms of a low-dimensional affine state vector. The model performs well when estimated on an extensive panel data set of crude-oil futures and options.

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Document Object Identifier (DOI): 10.3386/w12744

Published: Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 22(11), pages 4423-4461, November.

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