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Commodity Spread Option with Cointegration

Author

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  • Katsushi Nakajima

    (Ritsumeikan Asia Pacific University)

  • Kazuhiko Ohashi

    (Graduate School of International Corporate Strategy, Hitotsubashi University)

Abstract

We derive the valuation formula of a European call option on the spread of two cointegrated commodity futures prices, based on the Gibson–Schwartz with cointegration (GSC) model. We also analyze the American commodity spread option including the early exercise premium representation and an analytical approximation valuation formulae with cointegration. In the numerical analysis, we compare the spread option values calculated by the GSC model and the Gibson–Schwartz (GS) model that ignores cointegration. Consistent with the intuition that the cointegration prevents the prices from diverging, the GSC model prices the commodity spread option lower than the GS model which have longer maturity of more than 6 years. In other words, the GS model may overprice the commodity spread options for those with longer maturity without taking account of cointegration. Thus, incorporating cointegration is important for valuation and hedging of long-term commodity spread options such as large scale oil refining plant developments.

Suggested Citation

  • Katsushi Nakajima & Kazuhiko Ohashi, 2016. "Commodity Spread Option with Cointegration," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(1), pages 1-44, March.
    • Handle: RePEc:kap:apfinm:v:23:y:2016:i:1:d:10.1007_s10690-015-9207-1
    DOI: 10.1007/s10690-015-9207-1
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    References listed on IDEAS

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    More about this item

    Keywords

    Cointegration; Commodity prices; Convenience yield; Energy; Spread option;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • 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
    • Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General

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