{"title":"A closed-form approximation for pricing spread options on futures under a mean-reverting spot price model with multiscale stochastic volatility","authors":"Seung-Yong Baek, Jeong‐Hoon Kim","doi":"10.1017/s0269964823000049","DOIUrl":null,"url":null,"abstract":"\n Commodity spot prices tend to revert to some long-term mean level and most commodity derivatives are based on futures prices, not on spot prices. So, we consider spread options on futures instead of spot or spot index, where the log spot price follows a mean-reverting process. The volatility of the mean-reverting process is driven by two different (fast and slow) scale factors. We use asymptotic analysis to obtain a closed-form approximation of the futures prices and a closed-form formula for the approximate prices of spread options on the futures. The overall improvement of our analytic formula over the classical Kirk–Bjerksund–Sternsland (KBS) formula is discussed via numerical experiments.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"30 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability in the Engineering and Informational Sciences","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1017/s0269964823000049","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
引用次数: 0
Abstract
Commodity spot prices tend to revert to some long-term mean level and most commodity derivatives are based on futures prices, not on spot prices. So, we consider spread options on futures instead of spot or spot index, where the log spot price follows a mean-reverting process. The volatility of the mean-reverting process is driven by two different (fast and slow) scale factors. We use asymptotic analysis to obtain a closed-form approximation of the futures prices and a closed-form formula for the approximate prices of spread options on the futures. The overall improvement of our analytic formula over the classical Kirk–Bjerksund–Sternsland (KBS) formula is discussed via numerical experiments.
期刊介绍：
The primary focus of the journal is on stochastic modelling in the physical and engineering sciences, with particular emphasis on queueing theory, reliability theory, inventory theory, simulation, mathematical finance and probabilistic networks and graphs. Papers on analytic properties and related disciplines are also considered, as well as more general papers on applied and computational probability, if appropriate. Readers include academics working in statistics, operations research, computer science, engineering, management science and physical sciences as well as industrial practitioners engaged in telecommunications, computer science, financial engineering, operations research and management science.
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