{"title":"Energy commodities and calendar spread options","authors":"Carme Frau , Gianluca Fusai , Ioannis Kyriakou","doi":"10.1016/j.eneco.2025.108809","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":11665,"journal":{"name":"Energy Economics","volume":"151 ","pages":"Article 108809"},"PeriodicalIF":14.2000,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Energy Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S014098832500636X","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Energy Economics is a field journal that focuses on energy economics and energy finance. It covers various themes including the exploitation, conversion, and use of energy, markets for energy commodities and derivatives, regulation and taxation, forecasting, environment and climate, international trade, development, and monetary policy. The journal welcomes contributions that utilize diverse methods such as experiments, surveys, econometrics, decomposition, simulation models, equilibrium models, optimization models, and analytical models. It publishes a combination of papers employing different methods to explore a wide range of topics. The journal's replication policy encourages the submission of replication studies, wherein researchers reproduce and extend the key results of original studies while explaining any differences. Energy Economics is indexed and abstracted in several databases including Environmental Abstracts, Fuel and Energy Abstracts, Social Sciences Citation Index, GEOBASE, Social & Behavioral Sciences, Journal of Economic Literature, INSPEC, and more.