{"id":17604,"date":"2021-07-12T14:45:37","date_gmt":"2021-07-12T14:45:37","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=17604"},"modified":"2026-03-06T11:48:39","modified_gmt":"2026-03-06T11:48:39","slug":"calculate-the-value-of-a-capped-or-floored-floating-rate-bond","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/calculate-the-value-of-a-capped-or-floored-floating-rate-bond\/","title":{"rendered":"Capped or Floored Floating-Rate Bonds"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"VideoObject\",\r\n  \"name\": \"Valuation and Analysis of Bonds with Embedded Options (2025 Level II CFA\u00ae Exam \u2013 Fixed Income \u2013 Learning Module 3)\",\r\n  \"description\": \"CFA Level II Fixed Income lesson on Bonds with Embedded Options covering callable and putable bonds, arbitrage-free valuation using interest rate trees, option-adjusted spreads (OAS), effective duration and convexity, key rate durations, interest rate volatility effects, capped and floored floaters, and valuation of convertible bonds.\",\r\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/5zZuTYmjxW8\/maxresdefault.jpg\",\r\n  \"uploadDate\": \"2021-09-09\",\r\n  \"duration\": \"PT1H8M58S\",\r\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=5zZuTYmjxW8\",\r\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/5zZuTYmjxW8\"\r\n}\r\n<\/script><\/p>\r\n\r\n<p><script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"QAPage\",\r\n  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"What is the value of the capped three-year floating-rate bond?\",\r\n    \"text\": \"A three-year floating rate bond pays coupons of one-year LIBOR annually, set in arrears and capped at 5%. The LIBOR swap curve is given in the binomial lattice provided, and interest rate volatility is assumed to be 10%. The value of the capped floater is closest to: 99.44, 99.77, or 100.00.\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is 99.44. The cap at 5% limits the coupon payments in high-rate states, reducing the expected value of the floater when discounting through the interest-rate lattice.\"\r\n    }\r\n  }\r\n}\r\n<\/script> <script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@graph\": [\r\n    {\r\n      \"@type\": \"ImageObject\",\r\n      \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree.jpg\",\r\n      \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree.jpg\",\r\n      \"caption\": \"Euribor swap curve tree\",\r\n      \"width\": 1590,\r\n      \"height\": 1344,\r\n      \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n      \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n      \"creditText\": \"AnalystPrep Design Team\",\r\n      \"creator\": {\r\n        \"@type\": \"Organization\",\r\n        \"name\": \"AnalystPrep\",\r\n        \"url\": \"https:\/\/analystprep.com\/\"\r\n      }\r\n    },\r\n    {\r\n      \"@type\": \"ImageObject\",\r\n      \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-scaled.jpg\",\r\n      \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-scaled.jpg\",\r\n      \"caption\": \"Euribor swap curve tree solution\",\r\n      \"width\": 2048,\r\n      \"height\": 1229,\r\n      \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n      \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n      \"creditText\": \"AnalystPrep Design Team\",\r\n      \"creator\": {\r\n        \"@type\": \"Organization\",\r\n        \"name\": \"AnalystPrep\",\r\n        \"url\": \"https:\/\/analystprep.com\/\"\r\n      }\r\n    },\r\n    {\r\n      \"@type\": \"ImageObject\",\r\n      \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-1024x615.jpg\",\r\n      \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-1024x615.jpg\",\r\n      \"caption\": \"Euribor swap curve tree example 2\",\r\n      \"width\": 1024,\r\n      \"height\": 615,\r\n      \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n      \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n      \"creditText\": \"AnalystPrep Design Team\",\r\n      \"creator\": {\r\n        \"@type\": \"Organization\",\r\n        \"name\": \"AnalystPrep\",\r\n        \"url\": \"https:\/\/analystprep.com\/\"\r\n      }\r\n    },\r\n    {\r\n      \"@type\": \"ImageObject\",\r\n      \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree-768x649.jpg\",\r\n      \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree-768x649.jpg\",\r\n      \"caption\": \"LIBOR swap curve tree\",\r\n      \"width\": 768,\r\n      \"height\": 649,\r\n      \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n      \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n      \"creditText\": \"AnalystPrep Design Team\",\r\n      \"creator\": {\r\n        \"@type\": \"Organization\",\r\n        \"name\": \"AnalystPrep\",\r\n        \"url\": \"https:\/\/analystprep.com\/\"\r\n      }\r\n    },\r\n    {\r\n      \"@type\": \"ImageObject\",\r\n      \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-768x461.jpg\",\r\n      \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-768x461.jpg\",\r\n      \"caption\": \"LIBOR swap curve tree solution\",\r\n      \"width\": 768,\r\n      \"height\": 461,\r\n      \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n      \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n      \"creditText\": \"AnalystPrep Design Team\",\r\n      \"creator\": {\r\n        \"@type\": \"Organization\",\r\n        \"name\": \"AnalystPrep\",\r\n        \"url\": \"https:\/\/analystprep.com\/\"\r\n      }\r\n    }\r\n  ]\r\n}\r\n<\/script><\/p>\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/5zZuTYmjxW8\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p>Capped and floored floaters can be valued using the arbitrage-free framework.<\/p>\r\n<h2>Valuation of a Capped Floater<\/h2>\r\n<p>A <em><strong>capped floater<\/strong><\/em> (floating rate loan) is a bond that pays a coupon that resets every period based on the reference rate. Reference rates can be EURIBOR or LIBOR.<\/p>\r\n<p>The coupon is determined at the beginning of each period and is paid at the end of each period.<\/p>\r\n<p>Thus, a capped floater protects the issuer against rising interest rates above a certain maximum rate. This makes it an issuer option.<\/p>\r\n<p>$$ \\text{Value of capped floater} = \\text{Value of straight bond}\u00a0 &#8211; \\text{Value of embedded cap} $$<\/p>\r\n<div style=\"text-align: center; margin: 18px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 10px 18px; border: 2px solid #1e5bd8; color: #1e5bd8; background: #f5f7fb; border-radius: 9999px; text-decoration: none; font-weight: 600; white-space: nowrap;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Practice capped and floored floating-rate bond valuation questions <\/a><\/div>\r\n<h4>Example: Capped Floater<\/h4>\r\n<p>A three-year floating rate bond pays annual coupons of one-year Euribor at the end of each year and is capped at 6.00%. The Euribor swap curve is given in the binomial lattice below. The interest rate volatility is assumed to be 15%.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26631\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree.jpg\" alt=\"1 - Euribor Swap Curve Tree\" width=\"1590\" height=\"1344\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree-300x254.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree-1024x866.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree-768x649.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree-1536x1298.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/1-Euribor-Swap-Curve-Tree-400x338.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>The value of the capped floater and embedded cap are <em>closest to<\/em>:<\/p>\r\n<p><strong>Solution<\/strong><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26632\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-scaled.jpg\" alt=\"2 - Euribor Swap Curve Tree - Solution\" width=\"2048\" height=\"1229\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-scaled.jpg 2048w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-300x180.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-1024x615.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-768x461.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-1536x922.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/2-Euribor-Swap-Curve-Tree-Solution-400x240.jpg 400w\" sizes=\"auto, (max-width: 2048px) 100vw, 2048px\" \/>Therefore, the value of the capped floater is 99.89.<\/p>\r\n<p>$$ \\text{Value of embedded cap} = 100-99.89 = 0.11 $$<\/p>\r\n<h2>Valuation of a\u00a0Floored Floater<\/h2>\r\n<p>A<em><strong> floored floater<\/strong><\/em> is a floating rate bond whose coupon rate cannot fall below a specified minimum rate, which is known as the floor.<\/p>\r\n<p>The investor is long an embedded option that offers protection against falling interest rates. Thus, it is referred to as an investor option.<\/p>\r\n<p>$$ \\text{Value floored floater} = \\text{Value of straight bond}\u00a0 + \\text{Value of embedded floor} $$<\/p>\r\n<h4>Example: Floored Floater<\/h4>\r\n<p>A three-year floating rate bond pays annual coupons of one-year Euribor at the end of each year and is floored at 2.0%. The Euribor swap curve is given in the interest rate tree below. The interest rate volatility is assumed to be 15%.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26633\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-scaled.jpg\" alt=\"3 - Euribor Swap Curve Tree - Example 2\" width=\"2048\" height=\"1229\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-scaled.jpg 2048w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-300x180.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-1024x615.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-768x461.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-1536x922.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/3-Euribor-Swap-Curve-Tree-Example-2-400x240.jpg 400w\" sizes=\"auto, (max-width: 2048px) 100vw, 2048px\" \/>The value of the floored floater is <em>closest to<\/em>:<\/p>\r\n<p><strong>Solution<\/strong><\/p>\r\n<p>From the above binomial tree, the value of the floored floater has been calculated to be $100.49.<\/p>\r\n<p>The floor adds 0.49 in value to the straight bond. Had the floor been 1.5%, the floored floater and the straight bond would be worth par.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>A three-year floating rate bond pays coupons of one-year LIBOR annually, set in arrears and capped at 5%. The Libor swap curve is as given in the binomial lattice below. The interest rate volatility is assumed to be 10%.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26634\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree.jpg\" alt=\"4 - Libor Swap Curve Tree\" width=\"1590\" height=\"1344\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree-300x254.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree-1024x866.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree-768x649.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree-1536x1298.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/4-Libor-Swap-Curve-Tree-400x338.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>The value of the capped floater is <em>closest to<\/em>:<\/p>\r\n<ol type=\"A\">\r\n\t<li>99.44.<\/li>\r\n\t<li>99.77.<\/li>\r\n\t<li>100.00.<\/li>\r\n<\/ol>\r\n<h4><strong>Solution<\/strong><\/h4>\r\n<p><strong>The correct aswer is A.<\/strong><\/p>\r\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26635\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-scaled.jpg\" alt=\"5 - Libor Swap Curve Tree - Solution\" width=\"2048\" height=\"1229\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-scaled.jpg 2048w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-300x180.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-1024x615.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-768x461.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-1536x922.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/5-Libor-Swap-Curve-Tree-Solution-400x240.jpg 400w\" sizes=\"auto, (max-width: 2048px) 100vw, 2048px\" \/><\/strong><\/p>\r\n<\/blockquote>\r\n<p>Reading 30: Valuation and Analysis of Bonds with Embedded Options<\/p>\r\n<p><em>LOS 30 (m) Calculate the value of a capped or floored floating-rate bond.<\/em><\/p>\r\n\n            <div \n                class=\"elfsight-widget-pricing-table elfsight-widget\" \n                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\n                data-elfsight-pricing-table-version=\"2.6.1\"\n                data-elfsight-widget-id=\"elfsight-pricing-table-3\">\n            <\/div>\n            \r\n\r\n<div style=\"text-align: center; margin: 32px 0 10px;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; 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>\r\n<p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">Strengthen your fixed income valuation skills by solving CFA exam-style questions on capped floaters, floored floaters, and embedded option bond pricing.<\/p>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Capped and floored floaters can be valued using the arbitrage-free framework. Valuation of a Capped Floater A capped floater (floating rate loan) is a bond that pays a coupon that resets every period based on the reference rate. Reference rates&#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":[102,472],"tags":[],"class_list":["post-17604","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-fixed-income","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>Valuing Capped and Floored Floaters | CFA II<\/title>\n<meta name=\"description\" content=\"Learn how to calculate the value of capped and floored floating-rate bonds using the arbitrage-free framework.\" \/>\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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