The dirty price is the price of a bond including any interest that has accrued since issue of the most recent coupon payment. Whereas the clean price is the price of a bond excluding the accrued interest.
Before discussing the Clean and dirty prices, let us first know about Accrued Interest.
ACCRUED INTEREST:
The interest a bond will pay out builds every day until the payment date. The time between interest payments is the accrual period. Many U.S bonds pay interest semi-annually. One can figure the amount of accrued interest on a bond by multiplying the number of days since the last payment by the daily interest rate and the bond face value. On the interest payments date, bonds accrued interest resets to zero. Some bond markets include accrued interest in the trading price and others add it explicitily after trading. The price including accrued interest is known as the “flat” or “dirty price”. The price excluding accrued interest is sometimes known as the “clean price”.
DIRTY PRICE:
- A bonds dirty price is its clean price plus accrued interest. If you were to graph the bonds dirty price minus clean price each day, you would see it rise during the accrual period from zero to the periods coupon amount.
- Unless you happen to buy a bond on the payment date, you will pay a dirty price that reflects accrued interest as of the purchase date. That accrued interest goes into the bonds sellers pocket. When the bond reaches its next payment date, you will receive the full coupon amount. Because you paid the accrued interest up front, your net interest for the period is the coupon amount minus the initial accrued interest.
CLEAN PRICE:
- Clean price is the price of a coupon bond not including any accrued interest.
- A clean price is the discounted future cash flows, not including any interest accruing on the next coupon payment date, and immediately following each coupon payment, the clean price will equal the dirty price.
- Clean price = Dirty Price – Accrued Interest
The country in which the coupon paying bond is traded will influence how the bond is quoted. In the United States, it is the market convention to quote a bond in terms of its clean price; in other markets, bonds are more commonly quoted in terms of their dirty price.
