Mathematical Foundations of Option Pricing Models: A Comparative Analysis

Mathematical Foundations of Option Pricing Models: A Comparative Analysis | 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 Mathematical Foundations of Option Pricing Models: A Comparative Analysis Brandon Yee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6297750/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 This document presents a comprehensive mathematical analysis of three principal option pricing methodologies: Black-Scholes, Binomial Tree, and Monte Carlo simulation. Each section rigorously examines the theoretical underpinnings, derivation procedures, implementation considerations, and comparative advantages of these models. The analysis includes formal mathematical proofs, computational complexity assessments, and convergence properties. This documentation serves as both a theoretical reference and practical implementation guide for financial modeling practitioners. 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. 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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-6297750","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":437456050,"identity":"ce3dc4e4-e87b-4636-bae1-2fe13af7afef","order_by":0,"name":"Brandon Yee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYBACAxDBg+DbADFj4wFStKSBtDSQpOUwmMSrxVz68LMHbyruJPazN7A95qk5b7e2/TDQlhqbaFxaLPvSzA3nnHmWOLPnALsxz7HbydvOJAK1HEvLbcDlsDMMZtK8bYcTN9xIYJPmbbidbHYAqIWx4TAeLezfwFr2338A0nIu2ez8Q0JaeKC2SDCAtBywM7tBwBbLHp4yyTlnDhvPOJPYJjnnWHKC2Q2gLQl4/GLOw75N4k3FYdn+9sPHJN7U2NmbnU9/+OBDjQ1OLTDg2ACMQSZgBCWCVSYQUA4C9iCC8QeUMQpGwSgYBaMAGQAArl5jmspH0ncAAAAASUVORK5CYII=","orcid":"","institution":"Yee Research Company","correspondingAuthor":true,"prefix":"","firstName":"Brandon","middleName":"","lastName":"Yee","suffix":""}],"badges":[],"createdAt":"2025-03-24 18:23:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6297750/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6297750/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79808533,"identity":"50bc75ae-9970-46f9-8636-101545d8701a","added_by":"auto","created_at":"2025-04-03 06:06:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":229980,"visible":true,"origin":"","legend":"","description":"","filename":"opm.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6297750/v1_covered_0907cb48-807b-46a6-b439-84e0bf74ee86.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical Foundations of Option Pricing Models: A Comparative Analysis","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-6297750/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6297750/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This document presents a comprehensive mathematical analysis of three principal option pricing methodologies: Black-Scholes, Binomial Tree, and Monte Carlo simulation. 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