An American-style lookback option pricing method based on the jump diffusion model and sentiment factors

An American-style lookback option pricing method based on the jump diffusion model and sentiment factors | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An American-style lookback option pricing method based on the jump diffusion model and sentiment factors Zhe Zhang, Zeyang Feng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6210609/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract With the rapid development of the financial market, the issue of option pricing has also attracted widespread attention. In order to solve the problem of American lookback option pricing, this paper improves the traditional finite element numerical algorithm by introducing the jump diffusion model and emotional factors, combined with the implicit time discrete method. At first, the American lookback option problem is modeled and transformed into a nonlinear parabolic problem suitable for finite element discrete. Then, discrete methods such as hidden BDF2, CNLF, and CNAB were used to solve the numerical problem. By introducing the O-U process model of stock sentiment and option sentiment, the accuracy of option pricing is further improved. Finally, the stability and convergence of the proposed method are verified by numerical experiments, and it has strong practical application potential. American-style look-back options implicit method hop diffusion model finite element method Emotional factors Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6210609","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":433834794,"identity":"404dc5a3-add3-4538-9223-1bab451d1a96","order_by":0,"name":"Zhe Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArUlEQVRIiWNgGAWjYFAC5gMMD8CMBKK1sCUAFRuQpIXHgEQt8v1nPr9IbPvDwM+eY8DwcwcRWhgbzm6zSGwzYJDseWPA2HuGCC3MjL3bDEBaDG7kGDAzthGhhY2Z5xlYiz3RWnjYeJgfgG2RIFaLBA+bGUPCOWMeiTPPCg72EqNFvv/w4w8fyuTk+NuTNz74SYwWIGCTADkQxDpAnAZgoH0gVuUoGAWjYBSMUAAAJ5Qv9ygP7xMAAAAASUVORK5CYII=","orcid":"","institution":"Guilin University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Zhe","middleName":"","lastName":"Zhang","suffix":""},{"id":433834795,"identity":"111e8848-7191-4b5e-8814-0b6483780720","order_by":1,"name":"Zeyang Feng","email":"","orcid":"","institution":"Central China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Zeyang","middleName":"","lastName":"Feng","suffix":""}],"badges":[],"createdAt":"2025-03-12 09:23:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6210609/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6210609/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95553268,"identity":"2ab67c73-c886-4cd4-b9bc-a4190ffb96d8","added_by":"auto","created_at":"2025-11-10 13:53:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":427973,"visible":true,"origin":"","legend":"","description":"","filename":"AnAmericanstylelookbackoptionpricingmethodbasedonthejumpdiffusionmodelandsentimentfactors.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6210609/v1_covered_197cdf4c-418e-4645-98b0-0d895d9d1fb3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An American-style lookback option pricing method based on the jump diffusion model and sentiment factors","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"American-style look-back options, implicit method, hop diffusion model, finite element method, Emotional factors","lastPublishedDoi":"10.21203/rs.3.rs-6210609/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6210609/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWith the rapid development of the financial market, the issue of option pricing has also attracted widespread attention. 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