# Dirty price

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Dirty price

The dirty price of a bond represents the value of a bond, exclusive of any commissions or fees. The dirty price is also called the "full price" or the "all in price."

## Bond Pricing

Bonds, as well as a variety of other fixed income securities, provide for coupon payments to be made to bond holders on a fixed schedule. The dirty price of a bond will decrease on the days coupons are paid, resulting in a saw-tooth pattern for the bond value.[1] This is because there will be one fewer future cash flow (i.e., the coupon payment just received) at that point.

To separate out the effect of the coupon payments, the accrued interest between coupon dates is subtracted from the value determined by the dirty price to arrive at the clean price.[2] The accrued interest is based on the day count convention, coupon rate, and number of days from the preceding coupon payment date.[3]

The clean price more closely reflects changes in value due to issuer risk and changes in the structure of interest rates. Its graph is smoother than that of the dirty price. Use of the clean price also serves to differentiate interest income (based on the coupon rate) from trading profit and loss.

It is market practice in US to quote bonds on a clean-price basis. When a bond settles the accrued interest is added to the value based on the clean price to reflect the full market value.

## Example

A corporate bond has a coupon rate of 7.2% and pays 4 times a year, on the 15th of January, April, July, and October. It uses the 30/360 US day count convention.

A trade for 1,000 par value of the bond settles on January 25. The prior coupon date was January 15. The accrued interest reflects ten days' interest, or \$2.00 (7.2% of 1,000 * (10 days/360 days)).

The full value of these bonds is set by the market at \$985.50. The following table illustrates the values of these terms.

The market convention for bond prices assigns a dirty price of 98.55 to the trade, not 0.9855. This is sometimes referred to as the price for 100 par value.

Bond Pricing Example
Term Value
Par value 1,000.00
Full market value \$985.50
Dirty price 98.55
Accrued interest \$2.00
Flat market value \$983.50
Clean price 98.35

## Footnotes

1. ^ see the figure in Bond Accrued Interest.
2. ^ see Clean and Dirty Prices.
3. ^ see Trade Interest Bought/Sold.

## References

• Bond Accrued Interest, 2008, retrieved 2008-07-06 . Discussion of dirty price, clean price, and accrued interest, including diagrams illustrating the relationships.
• Coupon Interest, 2008, retrieved 2008-07-06 . Discussion of coupon interest, including trade interest figuration.
• Bond Pricing in the Market, 2008, retrieved 2008-07-06 . Explanation of how bonds are priced, including valuation, coupon interest, and clean and dirty pricing, with diagrams.

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