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Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives

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  • Anders B. Trolle
  • Eduardo S. Schwartz

Abstract

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.

Suggested Citation

  • Anders B. Trolle & Eduardo S. Schwartz, 2006. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," NBER Working Papers 12744, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:12744
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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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