Finance:Clean price

Short description: Price of a bond excluding interest accrued

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

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

where $\text{AI}$ 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.

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

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

where $C$ is the coupon for the period and $\alpha$ is the accrual fraction from the last coupon date under the applicable day count convention.

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 $$\text{AI}=0.05\times 100\times \frac{90}{360}=1.25.$$ If the quoted clean price is 98.40, then the dirty price is $$P_{\text{dirty}}=P_{\text{clean}}+\text{AI}=98.40+1.25=99.65.$$

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 $179/360$, so $$\text{AI}=0.05\times 100\times \frac{179}{360}=2.49.$$ If the clean price is unchanged at 98.40, the dirty price on 30 Nov is $$P_{\text{dirty}}=98.40+2.49=100.89.$$

On the coupon date 1 Dec 2025 the accrued interest resets to zero and the coupon is paid, so immediately after payment $$P_{\text{dirty}}=P_{\text{clean}},$$ 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

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