The clean price of a security/derivative is the price excluding any interest that has accrued since issue or the most recent coupon payment. This is to be compared to the dirty price, which is the price of a security/derivative including the accrued interest.

Clean Price = Dirty Price - Accrued Interest

The Bank of England Handbook 20 - Basic Bond Analysis states:

When a bond is bought or sold midway through a coupon period, a certain amount of coupon interest will have accrued. The coupon payment is always received by the person holding the bond at the time of the coupon payment (as the bond will then be registered in his name). Because he may not have held the bond throughout the coupon period, he will need to pay the previous holder some ‘compensation’ for the amount of interest which accrued during his ownership. In order to calculate the accrued interest, we need to know the number of days in the accrued interest period, the number of days in the coupon period, and the money amount of the coupon payment. In most bond markets, accrued interest is calculated on the following basis:-

((Coupon interest) x (no. of days that have passed in coupon period))/(total no of days in the coupon period)

Prices in the market are usually quoted on a clean basis (i.e. without accrued) but settled on a dirty basis (i.e. with accrued).

See also mtm_dirty.