Dirty Price

A dirty price for a bond is the price that includes the accrued interest on the bond since the last coupon payment.

For example, consider a bond with a face value of $1,000, a coupon rate of 5%, and semi-annual coupon payments. The coupon payment dates are June 30 and December 31 each year.

If today’s date is December 1, 2010, the last coupon payment was made on June 30, 2010. So for the period between June 30, 2010 and December 1, 2010, interest has accrued on the bond but has not yet been paid out.

Assume the current market price for this bond is $980. This market price of $980 is called the clean price, as it does not include accrued interest.

To calculate the dirty price, we first need to calculate the accrued interest. There are 182 days between June 30 and December 1. As this is a semi-annual coupon bond, the full year would have 2 coupon periods of 6 months each, i.e. 2 * 182 = 364 days.

The annual coupon amount is 5% of $1,000 which is $50.

So the accrued interest is calculated as:

Accrued Interest = (Coupon Amount / Total Days in Coupon Period) * Days since last coupon

Accrued Interest = ($50 / 364 days) * 182 days = $25

Therefore, the dirty price = Clean Price + Accrued Interest = $980 + $25 = $1,005

So on December 1, 2010, the dirty price for this bond is $1,005. This includes the clean market price of $980 plus the accrued interest of $25 since the last coupon payment on June 30, 2010.