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Dirty Price

The total settlement price paid for a bond, including accrued interest.

Dirty price (also called 'full price' or 'invoice price') is what you actually wire to the seller when you buy a bond. It equals the clean price (the quoted market price) plus accrued interest — the interest that has accumulated since the last coupon payment. Bonds are quoted using clean price so comparisons aren't distorted by coupon payment timing, but you always pay dirty price at settlement. For example, if a bond quotes at 98 (clean) with 0.5 in accrued interest, you pay 98.5 (dirty). The name 'dirty' is market slang reflecting that it includes the 'messy' accrued interest component.

Formula
Pdirty=Pclean+Accrued InterestP_{\text{dirty}} = P_{\text{clean}} + \text{Accrued Interest}
Variables
PDirty price (per 100 par)
CF_iCashflow at time t_i (coupon or principal)
yYield to maturity (annual, decimal)
mCoupon frequency (1, 2, 4, or 12 per year)
t_iTime to cashflow i in years
Assumptions
  • Periodic compounding at coupon frequency (not continuous)
  • ACT/365 Fixed day count for time fractions
  • No business day adjustments applied
  • All cashflows received on scheduled dates
vs. Industry Tools
Excel PRICE()Uses 30/360 by default; specify basis=3 for ACT/365 to match
Bloomberg DPRICEMatches when configured with same day count and compounding