具有多尺度随机波动的均值回归现货价格模型下期货价差期权定价的封闭逼近

IF 0.7 3区工程技术 Q4 ENGINEERING, INDUSTRIAL

Probability in the Engineering and Informational Sciences Pub Date : 2023-02-20 DOI:10.1017/s0269964823000049

Seung-Yong Baek, Jeong‐Hoon Kim

{"title":"具有多尺度随机波动的均值回归现货价格模型下期货价差期权定价的封闭逼近","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":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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

摘要

大宗商品现货价格往往会回归到某种长期平均水平，而且大多数大宗商品衍生品都是基于期货价格，而不是现货价格。因此，我们考虑期货的价差期权，而不是现货或现货指数，其中对数现货价格遵循均值回归过程。均值回归过程的波动性是由两个不同的(快和慢)尺度因子驱动的。我们利用渐近分析方法得到了期货价格的近似封闭形式和期货价差期权的近似封闭形式公式。通过数值实验讨论了我们的解析公式相对于经典的KBS公式的全面改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A closed-form approximation for pricing spread options on futures under a mean-reverting spot price model with multiscale stochastic volatility

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Probability in the Engineering and Informational Sciences 数学-工程：工业

CiteScore

2.20

自引率

18.20%

发文量

审稿时长

>12 weeks

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.