{"id":18658,"date":"2021-07-28T16:01:45","date_gmt":"2021-07-28T16:01:45","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=18658"},"modified":"2026-03-12T06:51:50","modified_gmt":"2026-03-12T06:51:50","slug":"identify-assumptions-of-the-black-scholes-merton-option-valuation-model","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/identify-assumptions-of-the-black-scholes-merton-option-valuation-model\/","title":{"rendered":"Assumptions of the Black-Scholes-Merton Option Valuation Model"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Which assumption of the Black-Scholes-Merton model is least accurate?\",\n    \"text\": \"Which of the assumptions of the Black-Scholes-Merton (BSM) option valuation model is least accurate?\\n\\nA. There are no taxes or transaction costs.\\nB. The risk-free rate of interest is known and constant for all maturities, borrowing, and lending.\\nC. Unlimited short selling is not allowed.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C. The Black-Scholes-Merton model assumes that unlimited short selling is permitted. This assumption is necessary for dynamic hedging strategies, such as delta hedging, which may require holding negative positions in the underlying asset. Assumptions A and B are standard assumptions of the BSM model.\",\n      \"dateCreated\": \"2026-01-21\",\n      \"upvoteCount\": 0\n    }\n  }\n}\n<\/script><\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/rnMud0L9-g0\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>The Black-Scholes-Merton (BSM) model is an optional pricing model. Under this model, the underlying share prices evolve in continuous time and are characterized at any point in time by a continuous distribution rather than a discrete distribution.<\/p>\n<p>The following key assumptions underpin the BSM model:<\/p>\n<ol>\n<li>The price of the underlying share follows a geometric Brownian motion. This implies that there are no jumps in share prices.<\/li>\n<li>There are no risk-free arbitrage opportunities.<\/li>\n<li>The risk-free rate of interest is constant, equal for all maturities, and identical for borrowing or lending.<\/li>\n<li>The volatility of the return of the underlying is known and constant.<\/li>\n<li>Unlimited short selling of the underlying is permitted.<\/li>\n<li>No taxes or transaction costs are payable.<\/li>\n<li>The underlying share can be traded continuously and in very small numbers of units.<\/li>\n<li>Early exercise of the options is not allowed (BSM, therefore, can only be used to value European options).<\/li>\n<\/ol>\n<p>These assumptions result in a complete market.<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>Which of the assumptions of the Black-Scholes-Merton Model is least accurate:<\/p>\n<ol type=\"A\">\n<li>There are no taxes or transaction costs.<\/li>\n<li>The risk-free rate of interest is known and constant. It is the same for all maturities, borrowing, and lending.<\/li>\n<li>Unlimited short selling is not allowed.<\/li>\n<\/ol>\n<h4>Solution<\/h4>\n<p><strong>The correct answer is C.<\/strong><\/p>\n<p>Unlimited short selling is permitted. This means that we can sell securities that we do not own. This is a necessary assumption because to hedge a derivative whose price is positively correlated with that of the underlying asset \u2013 e.g., a call option, which will have a positive delta \u2013 we need to hold a negative quantity of the underlying asset.<\/p>\n<p>A and B are assumptions of the BSM model.\u2003<\/p>\n<\/blockquote>\n<p>Reading 34: Valuation of Contingent Claims<\/p>\n<p><em>LOS 34 (f) Identify assumptions of the Black\u2013Scholes\u2013Merton option valuation model.<\/em><\/p>\n<div style=\"text-align: center; margin: 30px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 26px; border-radius: 9999px; background: #1e5bd8; color: #ffffff; font-weight: bold; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a><\/p>\n<p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">Practice CFA Level II derivatives questions covering the Black-Scholes-Merton model, option valuation assumptions, risk-neutral pricing, and delta-hedging concepts.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The Black-Scholes-Merton (BSM) model is an optional pricing model. Under this model, the underlying share prices evolve in continuous time and are characterized at any point in time by a continuous distribution rather than a discrete distribution. The following key&#8230;<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[102,302],"tags":[216,304],"class_list":["post-18658","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-derivatives","tag-cfa-level-2","tag-derivatives","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Black-Scholes Model Assumptions<\/title>\n<meta name=\"description\" content=\"Learn the key assumptions of the Black-Scholes-Merton model, including constant volatility, risk-free rates, and continuous price movements.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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