Comprehensive Analysis of Option Pricing Methodologies

Comprehensive Analysis of Option Pricing Methodologies | 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PDF Research Article Comprehensive Analysis of Option Pricing Methodologies Brandon Yee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6486777/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 paper conducts a rigorous mathematical and empirical analysis of three foundational option pricing methodologies: Black-Scholes, Binomial Tree, and Monte Carlo simulation. We develop a unified framework to elucidate their theoretical underpinnings, computational complexities, convergence properties, and practical performance across diverse option types and market conditions. Through detailed derivations, complexity assessments, and validations using historical market data, we delineate each model's strengths and limitations. The Black-Scholes model offers closed-form solutions for European options but struggles with volatile markets. The Binomial Tree model excels with American options despite quadratic complexity, while Monte Carlo simulation handles path-dependent options with slower convergence. We extend the analysis to recent innovations, including stochastic volatility, jump-diffusion, and machine learning integrations, providing practitioners with actionable criteria for model selection based on option characteristics, accuracy needs, and computational constraints. GitHub: https://github.com/brandonyee-cs/Option-Pricing-Model 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-6486777","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":460390672,"identity":"4ff28d28-3503-4a8d-9432-8452017ebd18","order_by":0,"name":"Brandon Yee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYBACAxDBg+DbADFj4wFStKSBtDSQpOUwmMSrxVz68LMHbyruJPazN7A95qk5b7e2/TDQlhqbaFxaLPvSzA3nnHmWOLPnALsxz7HbydvOJAK1HEvLbcDlsDMMZtK8bYcTN9xIYJPmbbidbHYAqIWx4TAeLezfwFr2338A0nIu2ez8Q0JaeKC2SDCAtBywM7tBwBbLHp4yyTlnDhvPOJPYJjnnWHKC2Q2gLQl4/GLOw75N4k3FYdn+9sPHJN7U2NmbnU9/+OBDjQ1OLTDg2ACMQSZgBCWCVSYQUA4C9iCC8QeUMQpGwSgYBaMAGQAArl5jmspH0ncAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Brandon","middleName":"","lastName":"Yee","suffix":""}],"badges":[],"createdAt":"2025-04-19 22:53:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6486777/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6486777/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86831530,"identity":"1eefe476-20b9-471e-a5f2-4b6649e7cbf3","added_by":"auto","created_at":"2025-07-16 06:16:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":308805,"visible":true,"origin":"","legend":"","description":"","filename":"OptionPricingModel4.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6486777/v1_covered_eb072465-00f1-4c2d-8876-6e1d508cdfef.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Comprehensive Analysis of Option Pricing Methodologies","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":"","lastPublishedDoi":"10.21203/rs.3.rs-6486777/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6486777/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper conducts a rigorous mathematical and empirical analysis of three foundational option pricing methodologies: Black-Scholes, Binomial Tree, and Monte Carlo simulation. 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