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Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives

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  • Anders B. Trolle
  • Eduardo S. Schwartz
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    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.

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    Bibliographic Info

    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12744.

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    Date of creation: Dec 2006
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    Publication status: published as 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.
    Handle: RePEc:nbr:nberwo:12744

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    1. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 60(4), pages 473-89, October.
    2. Anders B. Trolle & Eduardo S. Schwartz, 2006. "A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives," NBER Working Papers 12337, National Bureau of Economic Research, Inc.
    3. Hilliard, Jimmy E. & Reis, Jorge, 1998. "Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 33(01), pages 61-86, March.
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    6. Miltersen, Kristian R. & Schwartz, Eduardo S., 1998. "Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 33(01), pages 33-59, March.
    7. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Estimating and Testing Exponential Affine Term Structure Models by Kalman Filter," CIRANO Working Papers, CIRANO 95s-44, CIRANO.
    8. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, American Finance Association, vol. 52(3), pages 923-73, July.
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    17. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
    18. Richter, Martin & Sørensen, Carsten, 2002. "Stochastic Volatility and Seasonality in Commodity Futures and Options: The Case of Soybeans," Working Papers, Copenhagen Business School, Department of Finance 2002-4, Copenhagen Business School, Department of Finance.
    19. K. R. Miltersen, 2003. "Commodity price modelling that matches current observables: a new approach," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 3(1), pages 51-58.
    20. Gibson, Rajna & Schwartz, Eduardo S, 1990. " Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, American Finance Association, vol. 45(3), pages 959-76, July.
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