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Pricing and Hedging of Long-term Futures and Forward Contracts by a Three-Factor Model ( Revised in December 2007; Subsequently published in "Quantitative Finance". )

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  • Kenichiro Shiraya

    (Mizuho-DL Financial Technology Co., Ltd.)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

This paper proposes a new three-factor model with stochastic mean reversions for commodity prices and derives the closed-form solution for the term structure of futures prices. Moreover, it confirms that the prices of crude oil and copper futures prices estimated by our model replicate the observed ones very well. Finally, detailed performance analysis of hedging illiquid long-term futures and forwards with liquid short and medium-term futures shows the validity of our method.

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi, 2007. "Pricing and Hedging of Long-term Futures and Forward Contracts by a Three-Factor Model ( Revised in December 2007; Subsequently published in "Quantitative Finance". )," CARF F-Series CARF-F-113, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf113
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    References listed on IDEAS

    as
    1. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    2. Neuberger, Anthony, 1999. "Hedging Long-Term Exposures with Multiple Short-Term Futures Contracts," The Review of Financial Studies, Society for Financial Studies, vol. 12(3), pages 429-459.
    3. Antonio S. Mello & John E. Parsons, 1995. "Maturity Structure Of A Hedge Matters: Lessons From The Metallgesellschaft Debacle," Journal of Applied Corporate Finance, Morgan Stanley, vol. 8(1), pages 106-121, March.
    4. 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.
    5. 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.
    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, vol. 33(1), pages 33-59, March.
    7. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
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