Clean and Dirty Bond Prices: How Accrued Interest Is Shared
Summary
The document clarifies the distinction between a bond’s clean price and dirty price when the bond changes hands between coupon dates. A quoted market price is generally the clean price, which excludes accrued interest. At settlement, the buyer pays the clean price plus accrued interest; this total is the dirty price. The distinction explains why a buyer’s invoice can exceed the quoted price without implying that the seller receives the next coupon.
Accrued interest allocates the upcoming coupon between seller and buyer according to the portion of the coupon period each held the bond. The buyer receives the full coupon when it is paid, while the seller is compensated at purchase for the interest accrued during the seller’s holding period. The response offers an everyday billing analogy and a simple half-period example, rather than a pricing formula. It focuses on conventional accrual and does not address differences in day-count conventions, settlement rules, or bond-specific market practices.
Key ideas
- A bond’s clean price excludes accrued interest, while its dirty price includes it.
- At settlement, the buyer typically pays the clean price plus accrued interest.
- Accrued interest compensates the seller for the share of the coupon period before the sale.
- The buyer receives the coupon payment, with the purchase settlement allocating value between buyer and seller.
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Full text
# Why we need compute the clean price # Why we need compute the clean price First, is the yield of `dirty price` is same as the yield of this bond at beginning? If they are same, then the `dirty price` is already the current price of this bond, why do we again minus the `arraccrued interest`? It seems the seller received extra percentage of the next coupon, but actually he didn't get any of next coupon? So I really confuse here. We have the `jump condition` for the discrete coupon paying bond: $V(t_i^-, r) = V(t_i^+,r) - C_i,$ here $t_i$ is the $i$-th coupon paying, so this $V(t,r)$ should correspond which price? ## Answer by nbbo2 (score 2, accepted) https://quant.stackexchange.com/a/33123 When you read a Bond price in the newspaper, on a web site, in a database of bond prices it is always the Clean Price. [You don't have to compute anything! The clean price is there!]. When you actually buy the bond you receive an invoice asking you to pay the Clean Price plus the Accrued Interest, which are added together for your convenience and are called the Dirty Price. It is similar to a restaurant, where a hamburger is listed for 1,99 EUR but when you get the bill at the end of the meal there is is a service charge,a tax, and maybe other unexpected items which bring the bill to 2,07 EUR. The service charge compensates the waiter who brought the meal to you, the accrued interest compensates the seller of the bond who is ethically entitled to a portion of the next coupon you will receive (if he held the bond for a part of the coupon period, for example if he held for 1/2 the coupon period he is entitled to half the next coupon under accounting "accrual" principles). Essentially the accrued interest is a mechanism for sharing the value of the next coupon (which the buyer will receive) in a fair way between buyer and seller based on when in the coupon period the bond changed hands.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.