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.

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:

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:

= 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.

There is a mistake in this article. “The clean price itself is calculated as the net present value of its cash flows. “. Actually PV(cashflows)=dirty price.

Suppose, there is a bond nearly issued and today is two months away from its issue date. The buyer would only pay the PV of all its cashflows, so this is the full price. He will not pay another accrued interest.

However, if the seller quoted the price as clean price, he would like to buyer to pay interest as well.

I’ve updated it to make it more clear now. Thanks!

For a treasury bond, don’t we usually use 360 days??

N by the way if coupon is semi annually, we didn’t you take half of 365 days instead of 365 days??

Its a bit confusing!!

Lastly, the clean price should have been discounted to 88 days before adjusting for the accrued coupon

Sanjana,

The day count convention for US Treasury bonds is ACT/ACT. 360 is used for T-bills. the clean price is already exclusive of accrued coupon so there is no adjustment needed.

@admin# I thank for a nice elaboration on the Dirty Price specifically on Accrued Interest.