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Pricing of forwards and other derivatives in cointegrated commodity markets

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  • Benth, Fred Espen
  • Koekebakker, Steen

Abstract

We analyze cointegration in commodity markets, and propose a parametric class of pricing measures which preserves cointegration for forward prices with fixed time to maturity. We present explicit expressions for the term structure of volatility and correlation in the context of our spot price models based on continuous-time autoregressive moving average dynamics for the stationary components. The term structures have many interesting shapes, and we provide some empirical evidence from refined oil future prices at NYMEX defending our modeling idea. Motivated from these results, we present a cointegrated forward price dynamics using the Heath–Jarrow–Morton approach. In this setting, the concept of cointegration is extended to what we call cointegration in the limit, which is an asymptotic form of the notion. The Margrabe formula for spread option prices is shown to hold, with an explicit plug-in volatility. We present several numerical examples showing that cointegration leads to significantly cheaper spread options compared to the complete market case, where cointegration disappears with respect to the pricing measure.

Suggested Citation

  • Benth, Fred Espen & Koekebakker, Steen, 2015. "Pricing of forwards and other derivatives in cointegrated commodity markets," Energy Economics, Elsevier, vol. 52(PA), pages 104-117.
    • Handle: RePEc:eee:eneeco:v:52:y:2015:i:pa:p:104-117
    DOI: 10.1016/j.eneco.2015.09.009
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    References listed on IDEAS

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    Cited by:

    1. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
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    3. Daniel Leonhardt & Antony Ware & Rudi Zagst, 2017. "A Cointegrated Regime-Switching Model Approach with Jumps Applied to Natural Gas Futures Prices," Risks, MDPI, vol. 5(3), pages 1-19, September.
    4. Adland, Roar & Benth, Fred Espen & Koekebakker, Steen, 2018. "Multivariate modeling and analysis of regional ocean freight rates," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 113(C), pages 194-221.

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    More about this item

    Keywords

    Cointegration; Risk premium; CARMA processes; Commodity markets; Spot and forward relationship; Heath–Jarrow–Morton modeling;
    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q14 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Agricultural Finance
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting

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