Dirty price

The price of a bond includes the value of interest that has accrued since the previous coupon date. This is the dirty price or full price. The clean price excludes accrued interest. The two are related by

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

where ${\displaystyle {\text{AI}}}$ is 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]}

Bond pricing

Coupon-paying bonds accrue interest between coupon dates, so the dirty price rises between coupons and then drops when the coupon is paid. This produces a saw-tooth pattern over time.

Accrued interest is commonly calculated as $${\displaystyle {\text{AI}}\;=\;C\times \alpha ,}$$ where ${\displaystyle C}$ is the coupon for the period and ${\displaystyle \alpha }$ is the accrual fraction from the last coupon to the valuation date under the applicable day count convention. ^[3]

Clean prices track changes in value due to credit and the shape of the yield curve more smoothly than dirty prices. They also separate interest income from trading gains and losses.

Example

A corporate bond has a coupon rate of 7.2% on par 100 and pays quarterly on 15 January, 15 April, 15 July, and 15 October. It uses the 30/360 US day count convention.

A trade for 100 par settles on 25 January 2025. The prior coupon date was 15 January 2025. The accrued interest reflects ten days: $${\displaystyle {\text{AI}}=0.072\times 100\times {\frac {10}{360}}=0.20.}$$

If the dirty price is 98.55, the clean price is 98.35: $${\displaystyle P_{\text{clean}}=P_{\text{dirty}}-{\text{AI}}=98.55-0.20=98.35.}$$

Dirty and clean price at settlement

Term	Value
Par value	100.00
Dirty price (amount paid)	$98.55
Accrued interest	$0.20
Clean price (quoted)	$98.35

Looking at the same bond, one day before the next coupon date.

Settlement is 14 Apr 2025. The prior coupon date was 15 Jan 2025. Under 30/360 US the accrual fraction from 15 Jan to 14 Apr is ${\displaystyle 89/360}$. The accrued interest is $${\displaystyle {\text{AI}}=0.072\times 100\times {\frac {89}{360}}=1.78.}$$ If the quoted clean price is unchanged at 98.35, then the dirty price on 14 Apr is $${\displaystyle P_{\text{dirty}}=P_{\text{clean}}+{\text{AI}}=98.35+1.78=100.13.}$$

On the coupon date 15 Apr 2025 the accrued interest resets to zero and the coupon ${\displaystyle C=0.072\times 100/4=1.80}$ is paid. Immediately after payment, $${\displaystyle P_{\text{dirty}}=P_{\text{clean}}=98.35,}$$ illustrating the saw-tooth drop in dirty price around coupon dates while the clean price is unchanged (ignoring yield moves).

See also

• Accrued interest
• Bond valuation
• Clean price
• Day count convention

Footnotes

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.

References

• Coupon Interest, 2008, archived from the original on 2008-05-23, retrieved 2008-07-06. Discussion of coupon interest, including trade interest figuration.

• Accrued Interest Defined, 2014, retrieved 2014-03-04. Glossary entry with examples of calculations.

• Bond Pricing in the Market, 2008, archived from the original on 2008-08-04, retrieved 2008-07-06. Explanation of how bonds are priced, including valuation, coupon interest, and clean and dirty pricing, with diagrams.