{"title":"一个有节制的亚扩散布莱克-斯科尔斯模型","authors":"Grzegorz Krzyżanowski, Marcin Magdziarz","doi":"10.1007/s13540-024-00276-2","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we focus on the tempered subdiffusive Black–Scholes model. The main part of our work consists of the finite difference method as a numerical approach to option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has an accuracy order <span>\\(2-\\alpha \\)</span> with respect to time, where <span>\\(\\alpha \\in (0,1)\\)</span> is the subdiffusion parameter and 2 with respect to space. Furthermore, we provide stability and convergence analysis. Finally, we present some numerical results.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A tempered subdiffusive Black–Scholes model\",\"authors\":\"Grzegorz Krzyżanowski, Marcin Magdziarz\",\"doi\":\"10.1007/s13540-024-00276-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we focus on the tempered subdiffusive Black–Scholes model. The main part of our work consists of the finite difference method as a numerical approach to option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has an accuracy order <span>\\\\(2-\\\\alpha \\\\)</span> with respect to time, where <span>\\\\(\\\\alpha \\\\in (0,1)\\\\)</span> is the subdiffusion parameter and 2 with respect to space. Furthermore, we provide stability and convergence analysis. Finally, we present some numerical results.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13540-024-00276-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00276-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
In this paper, we focus on the tempered subdiffusive Black–Scholes model. The main part of our work consists of the finite difference method as a numerical approach to option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has an accuracy order \(2-\alpha \) with respect to time, where \(\alpha \in (0,1)\) is the subdiffusion parameter and 2 with respect to space. Furthermore, we provide stability and convergence analysis. Finally, we present some numerical results.
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