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Pricing and Hedging of Long-term Futures and Forward Contracts by a Three-Factor Model

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Listed:
  • Kenichiro Shiraya

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

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

This paper shows pricing and hedging efficiency of a three factor stochastic mean reversion Gaussian model of commodity prices using oil and copper futures and forward contracts. The model is estimated using NYMEX WTI (light sweet crude oil) and LME Copper futures prices and is shown to fit the data well. Furthermore, it shows how to hedge based on a three-factor model and confirms that using three different futures contracts to hedge long-term contract outperforms the traditional parallel hedge based on a single futures position by time series data and simulation. It also finds that the three factor model outperforms its two-factor version in replication of actual term structures and that stochastic mean reversion models outperform constant mean reversion models in Out of Sample hedges.

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi, 2009. "Pricing and Hedging of Long-term Futures and Forward Contracts by a Three-Factor Model," CIRJE F-Series CIRJE-F-618, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2009cf618
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    References listed on IDEAS

    as
    1. 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.
    2. 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..
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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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