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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

    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. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

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    Bibliographic Info

    Article provided by Society for Financial Studies in its journal The Review of Financial Studies.

    Volume (Year): 22 (2009)
    Issue (Month): 11 (November)
    Pages: 4423-4461

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    Handle: RePEc:oup:rfinst:v:22:y:2009:i:11:p:4423-4461

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    Cited by:
    1. Peter Christoffersen & Bruno Feunou & Kris Jacobs & Nour Meddahi, 2012. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Working Papers 12-34, Bank of Canada.
    2. Jaime Casassus & Peng Liu & Ke Tang, 2011. "Relative Scarcity of Commodities with a Long-Term Economic Relationship and the Correlation of Futures Returns," Documentos de Trabajo 404, Instituto de Economia. Pontificia Universidad Católica de Chile..
    3. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, School of Economics and Management, University of Aarhus.
    4. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
    5. Prokopczuk, Marcel & Wese Simen, Chardin, 2014. "The importance of the volatility risk premium for volatility forecasting," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 303-320.
    6. Eduardo Schwartz, 2013. "The Real Options Approach to Valuation: Challenges and Opportunities," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 50(2), pages 163-177, November.
    7. Yang, Fan, 2013. "Investment shocks and the commodity basis spread," Journal of Financial Economics, Elsevier, vol. 110(1), pages 164-184.
    8. Gonzalo Cortazar & Ivo Kovacevic & Eduardo S. Schwartz, 2013. "Commodity and Asset Pricing Models: An Integration," NBER Working Papers 19167, National Bureau of Economic Research, Inc.
    9. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.
    10. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    11. Peter Christoffersen & Mathieu Fournier & Kris Jacobs, 2013. "The Factor Structure in Equity Options," CREATES Research Papers 2013-47, School of Economics and Management, University of Aarhus.
    12. I. Halperin & A. Itkin, 2012. "Pricing Illiquid Options with $N+1$ Liquid Proxies Using Mixed Dynamic-Static Hedging," Papers 1209.3503, arXiv.org.
    13. Fink, Jason D. & Fink, Kristin E. & Russell, Allison, 2010. "When and how do tropical storms affect markets? The case of refined petroleum," Energy Economics, Elsevier, vol. 32(6), pages 1283-1290, November.
    14. Larsson, Karl & Nossman, Marcus, 2011. "Jumps and stochastic volatility in oil prices: Time series evidence," Energy Economics, Elsevier, vol. 33(3), pages 504-514, May.
    15. Kanniainen, Juho & Lin, Binghuan & Yang, Hanxue, 2014. "Estimating and using GARCH models with VIX data for option valuation," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 200-211.
    16. Lorenz Schneider, 2014. "A Stochastic Volatility Model for Crude Oil Futures Curves and the Pricing of Calendar Spread Options," Papers 1401.7913, arXiv.org.
    17. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    18. Daskalaki, Charoula & Skiadopoulos, George, 2011. "Should investors include commodities in their portfolios after all? New evidence," Journal of Banking & Finance, Elsevier, vol. 35(10), pages 2606-2626, October.

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