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Energy commodities and calendar spread options

Author

Listed:
  • Frau, Carme
  • Fusai, Gianluca
  • Kyriakou, Ioannis

Abstract

We present a unified framework for pricing calendar spread options on energy commodities under affine models featuring stochastic volatility, jumps, and Samuelson effect. Expressions for the joint characteristic function of log-futures prices are derived, enabling efficient calibration and valuation. An empirical analysis, across WTI crude oil, HH natural gas, and ULSD heating oil shows that stochastic volatility models consistently outperform others. Jumps enhance short-term fit, while volatility dynamics matter more at longer maturities. The Black model remains competitive for short- and mid-term contracts.

Suggested Citation

  • Frau, Carme & Fusai, Gianluca & Kyriakou, Ioannis, 2025. "Energy commodities and calendar spread options," Energy Economics, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:eneeco:v:151:y:2025:i:c:s014098832500636x
    DOI: 10.1016/j.eneco.2025.108809
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    References listed on IDEAS

    as
    1. Crosby, John & Frau, Carme, 2022. "Jumps in commodity prices: New approaches for pricing plain vanilla options," Energy Economics, Elsevier, vol. 114(C).
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    Keywords

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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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