Clean price

In finance the clean price is the price of a bond excluding accrued interest since the previous coupon date. The dirty price (full price) includes accrued interest. They are related by

$${\displaystyle P_{\text{clean}}\;=\;P_{\text{dirty}}\;-\;{\text{AI}},}$$

where ${\displaystyle {\text{AI}}}$ is the accrued interest for the current coupon period.

In many markets bonds are quoted on a clean-price basis. At settlement the accrued interest is added to the quoted clean price to obtain the amount paid. ^{[1] [2]}

Clean prices are more stable through time than dirty prices. Dirty prices rise between coupons as interest accrues, then drop when the coupon is paid, creating a saw-tooth pattern. A common calculation for accrued interest is

${\displaystyle {\text{AI}}\;=\;C\times \alpha ,}$

where ${\displaystyle C}$ is the coupon for the period and ${\displaystyle \alpha }$ is the accrual fraction from the last coupon date under the applicable day count convention. ^[3]

Example

A bond has par 100 and a coupon rate of 5% paid semi-annually on 1 Jun and 1 Dec. It uses the 30/360 US day count convention.

Suppose settlement is 1 Sep 2025. The prior coupon date was 1 Jun 2025. The accrued interest is $${\displaystyle {\text{AI}}\;=\;0.05\times 100\times {\frac {90}{360}}\;=\;1.25.}$$ If the quoted clean price is 98.40, then the dirty price is $${\displaystyle P_{\text{dirty}}\;=\;P_{\text{clean}}+{\text{AI}}\;=\;98.40+1.25\;=\;99.65.}$$

Second example. Same bond, one day before the next coupon.

Settlement is 30 Nov 2025. The prior coupon date was 1 Jun 2025. Under 30/360 US the accrual fraction from 1 Jun to 30 Nov is ${\displaystyle 179/360}$, so $${\displaystyle {\text{AI}}\;=\;0.05\times 100\times {\frac {179}{360}}\;=\;2.49.}$$ If the clean price is unchanged at 98.40, the dirty price on 30 Nov is $${\displaystyle P_{\text{dirty}}\;=\;98.40+2.49\;=\;100.89.}$$

On the coupon date 1 Dec 2025 the accrued interest resets to zero and the coupon is paid, so immediately after payment $${\displaystyle P_{\text{dirty}}\;=\;P_{\text{clean}},}$$ showing the saw-tooth drop in dirty price around coupon dates while the clean price is unchanged (ignoring yield moves).

See also

• Accrued interest
• Bond
• Dirty price

References

1. Tuckman, Bruce; Serrat, Angel (2022). "1: Prices, Discount Factors, and Arbitrage". Fixed Income Securities: Tools for Today’s Markets (4th ed.). Wiley. ISBN   978-1-119-83555-4.
2. "Accrued Interest". MSRB Glossary. Municipal Securities Rulemaking Board. Retrieved 4 October 2025.
3. "Accrued Interest". MSRB Glossary. MSRB. Retrieved 4 October 2025.

Further reading

• Calculation of the clean price of a bond in a cash management bond repurchase operation, Bank of Canada. Retrieved 2015-11-10.

External links

• Clean price By Investopedia
• Calculate clean and dirty price of a bond by Financetrain