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Abstract

We present a unified framework for pricing calendar spread options on energy commodities under affine models featuring stochastic volatility, jumps, and Samuelson effects. Expressions for the joint characteristic function of log-futures prices are derived, enabling efficient calibration and valuation. An empirical analysis, across WTI crude oil, Henry Hub 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.

Publication Type:	Article
Additional Information:	© 2025. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Energy commodities, bivariate models, joint characteristic function, estimation, calendar spread option
Subjects:	H Social Sciences > HD Industries. Land use. Labor H Social Sciences > HF Commerce
Departments:	Bayes Business School Bayes Business School > Faculty of Actuarial Science & Insurance Bayes Business School > Faculty of Finance
SWORD Depositor:	Symplectic Administrator

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