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Commodity derivatives pricing with cointegration and stochastic covariances

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  • Chiu, Mei Choi
  • Wong, Hoi Ying
  • Zhao, Jing

Abstract

Empirically, cointegration and stochastic covariances, including stochastic volatilities, are statistically significant for commodity prices and energy products. To capture such market phenomena, we develop a continuous-time dynamics of cointegrated assets with a stochastic covariance matrix and derive the joint characteristic function of asset returns in closed-form. The proposed model offers an endogenous explanation for the stochastic mean-reverting convenience yield. The time series of spot and futures prices of WTI crude oil and gasoline shows cointegration relationship under both physical and risk-neutral measures. The proposed model also allows us to fit the observed term structure of futures prices and calibrate the market-implied cointegration relationship. We apply it to value options on a single commodity and on multiple commodities.

Suggested Citation

  • Chiu, Mei Choi & Wong, Hoi Ying & Zhao, Jing, 2015. "Commodity derivatives pricing with cointegration and stochastic covariances," European Journal of Operational Research, Elsevier, vol. 246(2), pages 476-486.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:2:p:476-486
    DOI: 10.1016/j.ejor.2015.05.012
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    7. Hyun Jin Jang & Kiseop Lee & Kyungsub Lee, 2020. "Systemic risk in market microstructure of crude oil and gasoline futures prices: A Hawkes flocking model approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(2), pages 247-275, February.
    8. Philippe Raimbourg & Paul Zimmermann, 2022. "Is normal backwardation normal? Valuing financial futures with a local index-rate covariance," Post-Print hal-04011013, HAL.
    9. Raimbourg, Philippe & Zimmermann, Paul, 2022. "Is normal backwardation normal? Valuing financial futures with a local index-rate covariance," European Journal of Operational Research, Elsevier, vol. 298(1), pages 351-367.
    10. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.

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