# Calculate Clean and Dirty Price of a Bond

We know that the clean price of the bond is the offered price of the bond excluding the accrued interest, while the dirty price is clean price plus the accrued interest.

In most bond markets, the general convention is to quote the clean price. However, since the bond may have accrued interest at the time of sale since the last coupon payment, the actual price paid will be the dirty price.

Dirty Price = Clean Price + Accrued Interest

The dirty price is calculated as the net present value of its cash flows, and this includes the accrued interest. The accrued interest is calculated keeping in mind that the interest accrues on a daily basis.

The accrued interest is calculated as follows:

Accrued Interest = C x No. of days since the last coupon payment / Day count base

The calculation of accrued interest includes the last coupon date but excludes the value date (which is most often the settlement date).

While calculating the accrued interest, the appropriate day-count convention for the bond in question should be used.

A UK Treasury gilt pays a coupon of 7% and matures in 2015. The coupon is paid semi-annually on 1st January, and 1st July. The bond is sold for 96.5 value on 30th March, 2011.

Assume Actual/Actual day-count convention.

Since the last coupon date, 88 days have passed. The accrued interest will be calculated as:

Accrued Interest = 7 * 88/365 * 0.5

\= 0.843836

The dirty price of the bond = 96.5 + 0.843836 = 97.343836

This is the normal case for cum-dividend bonds (bonds where the purchaser receives the next coupon payment).

If the bond is trading ex-dividend (the purchaser does not get the next coupon payment), then the accrued interest will actually be deducted from the clean price.