What is a dirty price?
– Dirty price = the market price of a bond including any accrued interest owed to the seller. When a bond trades between coupon (interest) payment dates, the buyer compensates the seller for interest the seller earned since the last coupon date. That added amount is accrued interest; clean price is the same bond price excluding accrued interest.
Key definitions
– Coupon (or coupon payment): the scheduled interest payment a bondholder receives, usually expressed as an annual rate applied to face (par) value.
– Accrued interest: interest that has accumulated on the bond since the last coupon payment but has not yet been paid.
– Clean price: quoted bond price that excludes accrued interest (often what price boards publish).
– Dirty price (also “price plus accrued”): transaction price = clean price + accrued interest.
Why the distinction matters
– Transactions settle with the dirty price because the buyer must pay the seller both the bond’s market value (clean price) and the seller’s earned-but-unpaid interest (accrued interest).
– On a coupon payment date, accrued interest is zero, so clean price = dirty price for that day.
– Quoting conventions differ: many U.S. sources show clean prices; some European markets and interdealer quotes show dirty prices.
How to calculate accrued interest and dirty price
1. Find the coupon payment per period:
– Coupon per period = face value × (annual coupon rate) / (number of coupon periods per year).
2. Determine the day-count fraction for the period:
– fraction = (days since last coupon) / (days in coupon period), using the market’s day-count convention (common conventions include Actual/Actual and 30/360).
3. Compute accrued interest:
– Accrued interest = coupon per period × fraction.
4. Compute dirty price:
– Dirty price = clean price + accrued interest.
Checklist before you buy or price a bond
– Confirm the bond’s coupon schedule (frequency and next coupon date).
– Confirm the bond’s face (par) value and coupon rate.
– Know the quoted price type (clean vs dirty) from your broker or data source.
– Identify the day-count convention used to compute accruals (Actual/Actual,
, Actual/Actual, 30/360, Actual/365, etc.).
– Confirm trade date vs settlement date and calculate days-since-last-coupon to the settlement date (accruals are anchored to settlement, not trade date).
– Check whether the bond is trading ex-dividend (ex-coupon). If the trade settles on or after the ex-dividend date, the buyer may not be entitled to the upcoming coupon; the accrued-interest mechanics and who receives which cashflows can change.
– Verify the quoted price convention: is the quote per 100 of par, per 1,000 of par, and does the data source report clean or dirty prices?
– Be aware of short (odd) first/last coupons or irregular coupon schedules; these require special accrual calculations.
– Confirm rounding rules and currency units used by your broker or data vendor (accrued interest is typically rounded to the nearest cent).
– For taxable considerations, check the issuer and your jurisdiction—accrued interest and coupon income can have different tax treatment.
Worked numeric example (step-by-step)
Assumptions
– Face (par) value = $1,000.
– Annual coupon rate = 5.00% (so annual coupon = $50).
– Coupons paid semiannually (m = 2), so coupon per period = $50 / 2 = $25.
– Clean quoted price = $980.00 (per bond).
– Day-count convention = Actual/Actual.
– Days since last coupon (to settlement) = 60 days.
– Days in coupon period = 182 days.
Steps and arithmetic
1) Fraction of coupon period = 60 / 182 = 0.32967.
2) Accrued interest = coupon per period × fraction = $25 × 0.32967 = $8.24 (rounded to cents).
3) Dirty price = clean price + accrued interest = $980.00 + $8.24 = $988.24.