Coupon Accrual and Valuation for Bonds Paying Interest at Maturity
Summary
The document addresses how to interpret and value a bond whose interest is paid only at maturity. Its example asks whether a stated annual coupon rate should accrue simply over the bond’s life, be compounded, or represent the total interest paid at maturity. These interpretations lead to different coupon cash flows and accrued values, so the quoted rate alone is insufficient to calculate present value reliably.
The response outlines several market conventions: simple interest accumulated from issue to maturity, a rate quoted as the actual total return at maturity, and compounding at a specified frequency. It recommends identifying the convention assigned to the particular bond and comparing its projected cash flows and prices across settlement dates with a market reference. The source notes that vendor classifications can be wrong and that a specific bond may not be covered, so the convention should be verified rather than assumed from a descriptive label.
Key ideas
- A bond that pays all interest at maturity can follow different accrual and compounding conventions.
- A quoted coupon may be an annual rate or the total rate paid at maturity.
- Simple accumulation and compound accumulation produce different cash flows and present values.
- Verify the bond’s convention against its market classification and cash flow calculations, since vendor data may be erroneous.
Tags
Full text
# Bonds with coupon "pay only at maturity" - coupon fraction calculation # Bonds with coupon "pay only at maturity" - coupon fraction calculation How is coupon fraction calculated for bonds that pay coupon only once at maturity? How those coupons work. Example: Face Value 100$ Coupon: 10% Frequncy : Fixed pay only at maturity Issue Date 01/01/2024 Maturity 01/01/2026 Today 01/07/2024 What is the bond fraction as of Today 0.75 ( or 7.5usd) or 1.5 ( or 15usd)? And how much does it pay at maturity 10USD or 20USD? I am trying to calculate pv of a bond with such CF structure, but unsure how to treat the coupon EDIT I pulled the CF from reuters (although it may be errneous)(it is not covered by bbg); the bond was issued 15 Aug 2024, so to me it seems "Fixed: pay only at maturity" to be Annual Rate % * time to maturity for clean and Annual Rate % * full time for dirty price. ## Answer by Dimitri Vulis (score 2) https://quant.stackexchange.com/a/81957 The key question is - is the quoted "10%" an annual rate, or is it paid once at maturity, and is it compounded. Looking at Bloomberg's calc types, all of these seem to be possible: > 7: CD/Interest at Maturity Used for zero coupon bonds or bonds that pay all interest at maturity. Yields are calculated on simple interest basis. For bonds that pay interest at maturity the coupon rate is stated as an annual rate. The coupon value is accumulated over the period from issue to maturity $\cdots$ > 269: Coupon Rate Paid at Maturity Used for zero coupon bonds or bonds that pay all interest at maturity. Yields are calculated on annual compound basis. For bonds that pay interest at maturity the coupon rate is stated as be the real rate paid, not the annualized rate $\cdots$ > 1489: Compound Interest Used for bonds that pay coupons at maturity on a compounded basis and bonds that compound interest for a period of time, then pay cash on a regular schedule until maturity The coupon rate can be compounded on an annual, semi-annual, quarterly or monthly basis depending on coupon frequency as well as a few others. If you have a particular bond in mind, find it on Bloomberg terminal and see what calc type was assigned by Bloomberg, and hope it is correct. Then you look at Bloomberg CSHF (cash flows) and BXT for different settlement dates, and try to match Bloomberg.
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