{"id":1501,"date":"2020-04-14T17:33:00","date_gmt":"2020-04-14T17:33:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=1501"},"modified":"2026-03-30T18:50:16","modified_gmt":"2026-03-30T18:50:16","slug":"put-call-forward-parity-european-options","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/","title":{"rendered":"Put-Call-Forward Parity for European Options"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Basics of Derivative Pricing and Valuation (2025 Level I CFA\u00ae Exam \u2013 Derivative \u2013 Module 2)\",\n  \"description\": \"This video lesson covers the fundamentals of derivative pricing and valuation, including arbitrage, replication, and risk-neutral pricing. Key topics include forward and futures pricing, cost of carry, swap valuation, and options pricing models. Concepts like put\u2013call parity, factors affecting options value, and differences between European and American options are explained in detail.\",\n  \"uploadDate\": \"2022-06-29T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/04\/derivative-pricing-thumbnail.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/0Geaej45v7w\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/0Geaej45v7w\",\n  \"duration\": \"PT1H8M27S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"A European put has an exercise price of $58 that expires in 120 days. The long forward is priced at $55 (also expires in 120 days) and makes no cash payments during the life of the options. The risk-free rate is 4.5% and the put is selling for $3.00. According to the put-call-forward parity, what is the price of a call option with the same strike price and expiration date as the put option?\",\n    \"text\": \"A European put has an exercise price of $58 that expires in 120 days. The long forward is priced at $55 (also expires in 120 days) and makes no cash payments during the life of the options. The risk-free rate is 4.5% and the put is selling for $3.00. According to the put-call-forward parity, what is the price of a call option with the same strike price and expiration date as the put option?\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C. Using put-call-forward parity, c\u2080 = p\u2080 + F\u2080\/(1 + r)^T \u2212 X\/(1 + r)^T. Substituting the values gives c\u2080 = 3.00 + 55\/(1.045)^(120\/365) \u2212 58\/(1.045)^(120\/365) \u2248 0.83.\"\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\"\n  width=\"611\"\n  height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/0Geaej45v7w\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  referrerpolicy=\"strict-origin-when-cross-origin\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n<p>Another important concept in the pricing of options has to do with put-call-forward parity for European options. This involves buying a call and bond (fiduciary call) and a synthetic protective put, which requires buying a put option and a forward contract on the underlying that expires at the same time as the put option.<\/p>\n\n\n\n<div style=\"text-align: center; margin: 24px 0;\">\n  <div style=\"max-width: 680px; margin: 0 auto;\">\n    <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n       style=\"display: inline-flex; align-items: center; justify-content: center;\n       width: 100%; padding: 12px 20px;\n       border: 2px solid #1a73e8; border-radius: 999px;\n       color: #1a73e8; text-decoration: none;\n       font-size: 15px; font-weight: 600;\n       line-height: 1.2; white-space: nowrap;\">\n      Apply put-call-forward parity relationships through our free trial.\n    <\/a>\n  <\/div>\n<\/div>\n\n\n<h2>Put-Call-Forward Parity<\/h2>\n<p>An alternative structure for a protective put is to buy a forward contract and a risk-free bond in which the face value is the forward price rather than purchasing the underlying asset. As we have established that a fiduciary call is equivalent to a &#8220;regular&#8221; protective put, it holds that a fiduciary call must also be equivalent to a protective put with a forward contract.<\/p>\n<p>The fiduciary call consists of a long call and a long position in a zero-coupon bond:<\/p>\n<p>$$ \\text{Value at inception} = c_0 + \\frac{X}{(1+r)^T} $$<\/p>\n<p>The synthetic protective put is made up of a long put and a long forward:<\/p>\n<p>$$ \\text{Value at inception} = p_0 + \\frac{F_0(T)}{(1+r)^T} $$<\/p>\n<p>As the two portfolios have precisely the same payoff, their original investments should be the same as well. By setting the fiduciary call equal to the synthetic protective put, we establish\u00a0the <strong>put-call parity for options on forward contracts<\/strong>.<\/p>\n<p>$$ c_0 + \\frac{X}{(1+r)^T} = p_0 + \\frac{F_0(T)}{(1+r)^T} $$<\/p>\n<p>Solving for \\(F_0(T)\\), we acquire the equation for the forward price in terms of the call, put, and riskless bond.<\/p>\n<p>$$\u00a0\\frac{F_0(T)}{(1+r)^T} =\u00a0c_0 + \\frac{X}{(1+r)^T} &#8211;\u00a0p_0 $$<\/p>\n<p>Where\u00a0\\(\\frac{F_0(T)}{(1+r)^T}\\) is the value of the forward today multiplied by \\((1+r)^T\\) to get its value at expiration.<\/p>\n<p>Therefore, a synthetic forward combines a long call, a short put, and a zero-coupon bond with a face value of \\(X &#8211; F_0(T)\\).<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>A European put has an exercise price of $58 that expires in 120 days. The long forward is priced at $55 (also expires in 120 days) and makes no cash payments during the life of the options. The risk-free rate is 4.5% and the put is selling for $3.00. According to the put-call-forward parity, what is the price of a call option with the same strike price and expiration date as the put option?<\/p>\n<p>A. $50.43<\/p>\n<p>B. $3.31<\/p>\n<p>C. $0.83<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is C.<\/p>\n<p>c<sub>0<\/sub>\u00a0= p<sub>0<\/sub>\u00a0+ F<sub>o<\/sub>\/(1 + r)<sup>T<\/sup>\u00a0&#8211; X\/(1 + r)<sup>T<\/sup><\/p>\n<p>c<sub>0 <\/sub>= 3.00 + 55\/(1.045)<sup>120\/365<\/sup>\u00a0&#8211; 58\/(1.045)<sup>120\/365<\/sup><\/p>\n<p>c<sub>0 <\/sub>= 0.043<\/p>\n<\/blockquote>\n<div style=\"text-align: center; margin: 30px 0;\"><a style=\"display: inline-block; padding: 12px 24px; 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>\n<p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">Build confidence in CFA derivatives with exam-style practice on option pricing, synthetic positions, and arbitrage relationships.<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Another important concept in the pricing of options has to do with put-call-forward parity for European options. This involves buying a call and bond (fiduciary call) and a synthetic protective put, which requires buying a put option and a forward&#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-1501","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>Put-Call-Forward Parity Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Put-call-forward parity defines the relationship between European options, forward contracts, &amp; their pricing. Learn how this principle applies to derivatives.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Put-Call-Forward Parity Explained | CFA Level 1\" \/>\n<meta property=\"og:description\" content=\"Put-call-forward parity defines the relationship between European options, forward contracts, &amp; their pricing. Learn how this principle applies to derivatives.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/\" \/>\n<meta property=\"og:site_name\" content=\"AnalystPrep | CFA\u00ae Exam Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2020-04-14T17:33:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-30T18:50:16+00:00\" \/>\n<meta name=\"author\" content=\"Simon\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Simon\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/\"},\"author\":{\"name\":\"Simon\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/8d6352b658ba58a707920fba950b3687\"},\"headline\":\"Put-Call-Forward Parity for European Options\",\"datePublished\":\"2020-04-14T17:33:00+00:00\",\"dateModified\":\"2026-03-30T18:50:16+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/\"},\"wordCount\":423,\"articleSection\":[\"Derivatives\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/\",\"name\":\"Put-Call-Forward Parity Explained | CFA Level 1\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#website\"},\"datePublished\":\"2020-04-14T17:33:00+00:00\",\"dateModified\":\"2026-03-30T18:50:16+00:00\",\"author\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/8d6352b658ba58a707920fba950b3687\"},\"description\":\"Put-call-forward parity defines the relationship between European options, forward contracts, & their pricing. Learn how this principle applies to derivatives.\",\"breadcrumb\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Put-Call-Forward Parity for European Options\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#website\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/\",\"name\":\"AnalystPrep | CFA\u00ae Exam Study Notes\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/8d6352b658ba58a707920fba950b3687\",\"name\":\"Simon\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/09\/analystprep-150x150.png\",\"contentUrl\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/09\/analystprep-150x150.png\",\"caption\":\"Simon\"},\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/author\/analystprep\/\"}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/0Geaej45v7w\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"4108\" \/>\n<meta property=\"og:video:width\" content=\"480\" \/>\n<meta property=\"og:video:height\" content=\"270\" \/>\n<meta property=\"ya:ovs:adult\" content=\"false\" \/>\n<meta property=\"ya:ovs:upload_date\" content=\"2020-04-14T17:33:00+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Put-Call-Forward Parity Explained | CFA Level 1","description":"Put-call-forward parity defines the relationship between European options, forward contracts, & their pricing. Learn how this principle applies to derivatives.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/","og_locale":"en_US","og_type":"article","og_title":"Put-Call-Forward Parity Explained | CFA Level 1","og_description":"Put-call-forward parity defines the relationship between European options, forward contracts, & their pricing. Learn how this principle applies to derivatives.","og_url":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/","og_site_name":"AnalystPrep | CFA\u00ae Exam Study Notes","article_published_time":"2020-04-14T17:33:00+00:00","article_modified_time":"2026-03-30T18:50:16+00:00","author":"Simon","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Simon","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/"},"author":{"name":"Simon","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/8d6352b658ba58a707920fba950b3687"},"headline":"Put-Call-Forward Parity for European Options","datePublished":"2020-04-14T17:33:00+00:00","dateModified":"2026-03-30T18:50:16+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/"},"wordCount":423,"articleSection":["Derivatives"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/","name":"Put-Call-Forward Parity Explained | CFA Level 1","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website"},"datePublished":"2020-04-14T17:33:00+00:00","dateModified":"2026-03-30T18:50:16+00:00","author":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/8d6352b658ba58a707920fba950b3687"},"description":"Put-call-forward parity defines the relationship between European options, forward contracts, & their pricing. Learn how this principle applies to derivatives.","breadcrumb":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/put-call-forward-parity-european-options\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/cfa-level-1-exam\/"},{"@type":"ListItem","position":2,"name":"Put-Call-Forward Parity for European Options"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/","name":"AnalystPrep | CFA\u00ae Exam Study Notes","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/cfa-level-1-exam\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/8d6352b658ba58a707920fba950b3687","name":"Simon","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/image\/","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/09\/analystprep-150x150.png","contentUrl":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/09\/analystprep-150x150.png","caption":"Simon"},"url":"https:\/\/analystprep.com\/cfa-level-1-exam\/author\/analystprep\/"}]},"og_video":"https:\/\/www.youtube.com\/embed\/0Geaej45v7w","og_video_type":"text\/html","og_video_duration":"4108","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2020-04-14T17:33:00+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/1501","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/comments?post=1501"}],"version-history":[{"count":24,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/1501\/revisions"}],"predecessor-version":[{"id":60118,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/1501\/revisions\/60118"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/media?parent=1501"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/categories?post=1501"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/tags?post=1501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}