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Pricing commodity futures and determining risk premia in a three factor model with stochastic volatility: the case of Brent crude oil

Author

Listed:
  • Jilong Chen

    (Zhejiang Gongshang University)

  • Christian Ewald

    (University of Glasgow
    Inland University of Applied Sciences)

  • Ruolan Ouyang

    (Jinan University)

  • Sjur Westgaard

    (Norwegian University of Science and Technology)

  • Xiaoxia Xiao

    (Jinan University)

Abstract

In this paper we introduce a three factor model to price commodity futures contracts. This model allows both the spot price volatility and convenience yield to be stochastic, nevertheless futures prices can be obtained conveniently in closed form. Further, we use Brent crude oil futures prices to calibrate the model using the extended Kalman filter. In comparison to the benchmark model for commodity futures pricing, the Schwartz two-factor model, our three factor model shows a superior fit for contracts that have longer maturities. We further assess risk premia in Brent crude oil through the two models and observe that the Schwartz two-factor model over-predicts risk premia in comparison to the new model.

Suggested Citation

  • Jilong Chen & Christian Ewald & Ruolan Ouyang & Sjur Westgaard & Xiaoxia Xiao, 2022. "Pricing commodity futures and determining risk premia in a three factor model with stochastic volatility: the case of Brent crude oil," Annals of Operations Research, Springer, vol. 313(1), pages 29-46, June.
    • Handle: RePEc:spr:annopr:v:313:y:2022:i:1:d:10.1007_s10479-021-04198-7
    DOI: 10.1007/s10479-021-04198-7
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    References listed on IDEAS

    as
    1. Date, Paresh & Mamon, Rogemar & Tenyakov, Anton, 2013. "Filtering and forecasting commodity futures prices under an HMM framework," Energy Economics, Elsevier, vol. 40(C), pages 1001-1013.
    2. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    3. Kang, Wensheng & Ratti, Ronald A. & Yoon, Kyung Hwan, 2015. "Time-varying effect of oil market shocks on the stock market," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 150-163.
    4. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    5. Cassese, Gianluca & Guidolin, Massimo, 2006. "Modelling the implied volatility surface: Does market efficiency matter?: An application to MIB30 index options," International Review of Financial Analysis, Elsevier, vol. 15(2), pages 145-178.
    6. Pasricha, Gurnain Kaur, 2006. "Kalman Filter and its Economic Applications," MPRA Paper 22734, University Library of Munich, Germany.
    7. Eugene F. Fama & Kenneth R. French, 2015. "Commodity Futures Prices: Some Evidence on Forecast Power, Premiums, and the Theory of Storage," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 4, pages 79-102, World Scientific Publishing Co. Pte. Ltd..
    8. Jaime Casassus & Pierre Collin‐Dufresne, 2005. "Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates," Journal of Finance, American Finance Association, vol. 60(5), pages 2283-2331, October.
    9. Gary B. Gorton & Fumio Hayashi & K. Geert Rouwenhorst, 2013. "The Fundamentals of Commodity Futures Returns," Review of Finance, European Finance Association, vol. 17(1), pages 35-105.
    10. Scheitrum, Daniel P. & Carter, Colin A. & Revoredo-Giha, Cesar, 2018. "WTI and Brent futures pricing structure," Energy Economics, Elsevier, vol. 72(C), pages 462-469.
    11. Huiming Zhu & Yawei Guo & Wanhai You, 2015. "An empirical research of crude oil price changes and stock market in China: evidence from the structural breaks and quantile regression," Applied Economics, Taylor & Francis Journals, vol. 47(56), pages 6055-6074, December.
    12. Robert S. Pindyck, 2001. "The Dynamics of Commodity Spot and Futures Markets: A Primer," The Energy Journal, , vol. 22(3), pages 1-29, July.
    13. Hamilton, James D. & Wu, Jing Cynthia, 2014. "Risk premia in crude oil futures prices," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 9-37.
    14. Christian-Oliver Ewald & Ruolan Ouyang, 2017. "An Analysis of the Fish Pool Market in the Context of Seasonality and Stochastic Convenience Yield," Marine Resource Economics, University of Chicago Press, vol. 32(4), pages 431-449.
    15. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    16. Gurdip Bakshi & Xiaohui Gao & Alberto G. Rossi, 2019. "Understanding the Sources of Risk Underlying the Cross Section of Commodity Returns," Management Science, INFORMS, vol. 65(2), pages 619-641, February.
    17. Steven D. Baker, 2021. "The Financialization of Storable Commodities," Management Science, INFORMS, vol. 67(1), pages 471-499, January.
    18. Brooks, Chris & Prokopczuk, Marcel & Wu, Yingying, 2013. "Commodity futures prices: More evidence on forecast power, risk premia and the theory of storage," The Quarterly Review of Economics and Finance, Elsevier, vol. 53(1), pages 73-85.
    19. Ewald, Christian & Zou, Yihan, 2021. "Analytic formulas for futures and options for a linear quadratic jump diffusion model with seasonal stochastic volatility and convenience yield: Do fish jump?," European Journal of Operational Research, Elsevier, vol. 294(2), pages 801-815.
    20. Basu, Devraj & Miffre, Joëlle, 2013. "Capturing the risk premium of commodity futures: The role of hedging pressure," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2652-2664.
    21. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    22. 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, vol. 33(1), pages 33-59, March.
    23. Cifuentes, Sebastián & Cortazar, Gonzalo & Ortega, Hector & Schwartz, Eduardo S., 2020. "Expected prices, futures prices and time-varying risk premiums: The case of copper," Resources Policy, Elsevier, vol. 69(C).
    24. Carl Chiarella & Boda Kang & Christina Sklibosios Nikitopoulos & Thuy‐Duong Tô, 2016. "The Return–Volatility Relation in Commodity Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(2), pages 127-152, February.
    25. Sakkas, Athanasios & Tessaromatis, Nikolaos, 2020. "Factor based commodity investing," Journal of Banking & Finance, Elsevier, vol. 115(C).
    26. Hahn, Warren J. & DiLellio, James A. & Dyer, James S., 2018. "Risk premia in commodity price forecasts and their impact on valuation," Energy Economics, Elsevier, vol. 72(C), pages 393-403.
    27. Yao, Can-Zhong & Kuang, Peng-Cheng, 2019. "A study of lead–lag structure between international crude oil price and several financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    28. repec:bla:jfinan:v:59:y:2004:i:4:p:1877-1900 is not listed on IDEAS
    29. Marta Szymanowska & Frans Roon & Theo Nijman & Rob Goorbergh, 2014. "An Anatomy of Commodity Futures Risk Premia," Journal of Finance, American Finance Association, vol. 69(1), pages 453-482, February.
    30. 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, vol. 33(1), pages 61-86, March.
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    More about this item

    Keywords

    Commodity futures; Stochastic volatility; Multi-factor models;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q02 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Commodity Market

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