{"id":43622,"date":"2022-12-19T12:18:23","date_gmt":"2022-12-19T12:18:23","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=43622"},"modified":"2026-03-25T10:50:36","modified_gmt":"2026-03-25T10:50:36","slug":"price-and-value-of-swaps","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/price-and-value-of-swaps\/","title":{"rendered":"Price and Value of Swaps"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Pricing and Valuation of Interest Rates and Other Swaps (2024\/25 LI CFA\u00ae Exam \u2013 Derivatives \u2013 M7)\",\n  \"description\": \"This video lesson covers the pricing and valuation of interest rate and other swaps, focusing on forward and futures contracts. It explains the differences in their pricing, valuation methods, and market applications, including why forward and futures prices may diverge due to margining, interest rate movements, and market conditions.\",\n  \"uploadDate\": \"2022-12-11T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/4BtaPfEd2Ao\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/4BtaPfEd2Ao\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/4BtaPfEd2Ao\",\n  \"duration\": \"PT28M50S\"\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"What are the possible values of a one-year constant-maturity treasury (CMT) swap?\",\n    \"text\": \"A $10 million face value of a stylized constant-maturity treasury (CMT) swap is struck at 10%. It is a one-year CMT swap on the six-month yield in 0.5% increments. Calculate the possible values of the CMT swap after one year.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The possible values of the CMT swap after one year are $50,000, $0, and \u2212$50,000.\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/study-notes\/frm\/part-2\/market-risk-measurement-and-management\/the-science-of-term-structure-models\/\"\n    },\n    \"suggestedAnswer\": [\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"$25,000, $0, and \u2212$25,000.\",\n        \"upvoteCount\": 0\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"$100,000, $0, and \u2212$100,000.\",\n        \"upvoteCount\": 0\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"None of the above.\",\n        \"upvoteCount\": 0\n      }\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\/4BtaPfEd2Ao\"\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<p>Remember that a swap contract involves a series of periodic settlements with a final settlement at maturity. <strong>Swap price<\/strong> (or <strong>par swap rate)<\/strong> is a periodic fixed rate that equates the present value (PV) of all future expected floating cash flows to the PV of fixed cash flows.<\/p>\n<p>The swap rate is equivalent to the forward rate, \\(F_0(T)\\); it satisfies no-arbitrage conditions. On the other hand, the current market reference rate (MRR) is the \u201cspot\u201d price. Therefore, from the fixed-rate payer perspective, the periodic value is given by:<\/p>\n<p>$$\\text{Periodic settlement value}=(\\text{MRR}-\\text{S}_{\\text{N}})\\times\\text{Notional amount}\\times\\text{Period}$$<\/p>\n<p>The swap value on any settlement date is calculated as the current settlement value using the above formula plus the present value of all the remaining future swap settlements.<\/p>\n<p>Like all other forward commitments, the value of a swap contract at initiation is zero.<\/p>\n<p>Note that it\u2019s our assumption that MRR is set at the beginning of each interest period and has the same periodicity and day count as the swap rate. In addition, the net of fixed and floating differences is exchanged at the end of each period.<\/p>\n<div style=\"text-align: center; margin: 25px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 10px 18px; border: 2px solid #1a73e8; border-radius: 999px; color: #1a73e8; text-decoration: none; font-weight: 500; background-color: #f5f9ff; white-space: nowrap;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Value swaps across settlement periods <\/a><\/div>\n<h3>Examples: Calculating the Swap Value and Effect of Varying MRRs<\/h3>\n<p>FinnLay LTD has entered a 4-year interest rate swap with a financial institution with a notional amount of USD 100 million. The contract states that FinnLay signed to receive a semiannual USD fixed rate of 2.5% and, in turn, pay a semiannual market reference rate (MRR).<\/p>\n<p>The MRR is expected to equal the respective implied forward rates (IFRs).<\/p>\n<h4>Scenario 1<\/h4>\n<p>If at the beginning of the sixth month, the MRR is 0.85%, the first swap settlement value from Finnlay\u2019s perspective is <em>closest to<\/em>:<\/p>\n<h4>Solution<\/h4>\n<p>$$\\begin{align*}\\text{Periodic settlement value}&amp;=(\\text{MRR}-\\text{S}_{\\text{N}})\\times\\text{Notional Amount}\\times\\text{Period}\\\\&amp;=(2.5\\%-0.85\\%)\\times\\text{USD 100m}\\times0.5\\\\&amp;=\\text{USD 0.825m}\\end{align*}$$<\/p>\n<h4>Scenario 2<\/h4>\n<p>If implied forward rates <strong>remain constant<\/strong> as set at trade inception, how will this affect the MTM value from Finnlay\u2019s perspective immediately after the first settlement?<\/p>\n<h4>Solution<\/h4>\n<p>The swap price (or fixed swap rate) of 2.5% is set at the initiation of the trade, which equates to the PV of fixed versus floating payments.<\/p>\n<p>If there is no change in interest rate expectations, the PV of remaining floating payments rises above the PV of fixed payments.<\/p>\n<p>As such, Finnlay, as a fixed receiver, realizes an MTM loss on the swap because:<\/p>\n<p>$$\\sum\\text{PV}(\\text{Floating payments paid})&gt;\\sum\\text{PV}(\\text{Fixed payments received})$$<\/p>\n<h4>Scenario 2<\/h4>\n<p>If implied forward rates <strong>decline <\/strong>just after initiation, how will this affect the MTM value from Finnlay\u2019s perspective ?<\/p>\n<h4>Solution<\/h4>\n<p>A decrease in expected forward rates just after initiation will reduce the PV of floating payments while the fixed swap rate will remain constant.<\/p>\n<p>Since FinnLay is the fixed-rate receiver, it will realize an MTM gain because:<\/p>\n<p>$$\\sum\\text{PV}(\\text{Floating payments paid})&lt;\\sum\\text{PV}(\\text{Fixed payments received})$$<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>Invest Capital Inc has signed a three-year swap contract to receive a fixed interest rate of 2.5% on a semiannual basis and pay a 6-month USD MRR. The notional amount of the swap contract is USD 100,000.<\/p>\n<p>Assume that the initial 6-month MRR sets at 0.56%, and MRR is expected to be upward sloping. The first settlement value in six months from Invest Capital is <em>closest<\/em> to:<\/p>\n<p>A. $970.<\/p>\n<p>B. $1,940.<\/p>\n<p>C. $2,500.<\/p>\n<h3>Solution<\/h3>\n<p>The correct answer is <strong>A<\/strong>.<\/p>\n<p>From the fixed-rate payer perspective, the periodic value is given by:<\/p>\n<p>$$\\begin{align*}\\text{Periodic settlement value}&amp;=(\\text{S}_{\\text{N}}-\\text{MRR})\\times\\text{Notional Amount}\\times\\text{Period}\\\\&amp;=(2.5\\%-0.56\\%)\\times\\text{USD 100,000}\\times0.5\\\\&amp;=$970\\end{align*}$$<\/p>\n<p><strong>B is incorrect<\/strong>. It is calculated as \\(=2.5\\%-0.56\\%\\times\\text{USD 100,000}\\). It omits the period in the formula.<\/p>\n<p><strong>C is incorrect<\/strong>. It is the amount of the fixed interest amount after six months.<\/p>\n<\/blockquote>\n<div style=\"text-align: center; margin: 40px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 20px; border-radius: 999px; background-color: #1a73e8; color: #ffffff; text-decoration: none; font-weight: 600;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Start Free Trial \u2192 <\/a>\n<p style=\"font-size: 15px; margin-top: 12px; color: #555;\">Learn how swap values are calculated using the present value of future cash flows, why swaps typically have zero value at initiation, and how changes in market reference rates affect valuation in CFA Level I derivatives.<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Remember that a swap contract involves a series of periodic settlements with a final settlement at maturity. Swap price (or par swap rate) is a periodic fixed rate that equates the present value (PV) of all future expected floating cash&#8230;<\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10],"tags":[44],"class_list":["post-43622","post","type-post","status-publish","format-standard","hentry","category-derivatives","tag-price-and-value-swaps","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>Price and Value of Swaps | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Learn how swap pricing works, including the par swap rate, present value calculations, and factors influencing fixed and floating cash flows.\" \/>\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\/price-and-value-of-swaps\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Price and Value of Swaps | CFA Level 1 - 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