{"id":1486,"date":"2020-04-14T17:33:00","date_gmt":"2020-04-14T17:33:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=1486"},"modified":"2026-03-05T20:26:16","modified_gmt":"2026-03-05T20:26:16","slug":"european-options","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/european-options\/","title":{"rendered":"European Options"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"What is the value of a European call option if the spot price at expiration is $110.15?\",\n    \"text\": \"A European call option gives the holder the right to buy 100 shares of company XYZ at a strike price of $100 in three months. If the spot price at expiration is $110.15, what is the value of the call option?\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is A. The payoff of a call option at expiration is calculated as max(0, S \u2212 K) multiplied by the number of shares. Here, max(0, 110.15 \u2212 100) \u00d7 100 = 10.15 \u00d7 100 = $1,015.\"\n    },\n    \"suggestedAnswer\": [\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"$1,015.\"\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"$0.\"\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"-$1,015.\"\n      }\n    ]\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Basics of Derivative Pricing and Valuation (2021 Level I CFA\u00ae Exam \u2013 Reading 49)\",\n  \"description\": \"This video lesson covers the basics of derivative pricing and valuation for CFA Level 1. It explains core concepts like arbitrage, replication, risk neutrality, value vs. price of derivatives, options valuation, and put-call parity. The instructor uses real-world examples and math to simplify key derivative pricing principles and strategies.\",\n  \"uploadDate\": \"2020-12-11T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/vdPgV79RX7E\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=vdPgV79RX7E\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/vdPgV79RX7E\",\n  \"duration\": \"PT45M28S\"\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/vdPgV79RX7E?si=fNf1VM3P6iKoLpU1\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n<p>European options only allow for the exercise of options at the expiry date, while American options allow for early exercise. The terms do not convey any information about where, geographically, the options are traded. The right to exercise is a complex feature of an option, and as such, European options with a fixed exercise date are dealt with first.<\/p>\n<h2><strong>Standard Notation<\/strong><\/h2>\n<p>The following notion is used:<\/p>\n<ul>\n<li>c<sub>T<\/sub> = Price of European call at expiration<\/li>\n<li>S<sub>T<\/sub> = Price of the underlying at time T<\/li>\n<li>X = Exercise price<\/li>\n<li>p<sub>T<\/sub> = Price of a European put option at expiration<\/li>\n<\/ul>\n<h2><strong>Value at Expiration<\/strong><\/h2>\n<h3>European Call Options<\/h3>\n<p>The value of a European call option at expiration is the exercise value, which is the greater of zero or the underlying price at expiration minus the exercise price:<\/p>\n<p>$$ c_T = max(0, S_T &#8211; X) $$<\/p>\n<h3>European Put Options<\/h3>\n<p>The value of a European put option at expiration is simply the opposite \u2013 the greater of zero or the\u00a0exercise price minus the underlying price at expiration:<\/p>\n<p>$$ p_T = max(0, X &#8211; S_T) $$<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>There is a European call option that gives the holder the right to buy 100 shares of company XYZ at $100 in 3 months\u2019 time. What is the value of this call option if the spot price at expiration is $110.15?<\/p>\n<p>A. $1,015<\/p>\n<p>B. $0<\/p>\n<p>C. -$1,015<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is A.<\/p>\n<p>C<sub>T<\/sub>\u00a0= 100 \u00d7 max($0, $110.15-$100) = $100 \u00d7 $10.15 = $1,015<\/p>\n<p>Since we have a call option with a strike price of $100, it makes sense that if the price at expiration is higher than the strike price, our option has gained in value.<\/p>\n<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>European options only allow for the exercise of options at the expiry date, while American options allow for early exercise. The terms do not convey any information about where, geographically, the options are traded. The right to exercise is a&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10],"tags":[],"class_list":["post-1486","post","type-post","status-publish","format-standard","hentry","category-derivatives","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>European Options in Derivatives | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn about European options, their characteristics, pricing formulas, and differences from American options in financial markets.\" \/>\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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