# Clean and Dirty

Vol. 5 p. 500: the result of the traditional bond calculations is the FULL price, that which the buyer pays the seller. The buyer is in effect paying more than what he should (for he is not entitled to the whole of the forthcoming coupon), but is recompensed on receipt of the next coupon payment.

p. 519 q.18: It appears here than the quoted price of 101 + 12/32 is the CLEAN price.

These two examples seem to contradit each other. What then, does the quoted price actually represent? How does it work in the real world?

Thanks,

M.

The quoted price, as far as I remember, is always going to be the clean price.

Furthermore on p.500 which you mentioned, it clearly states that this is the way to calculate the dirty (full) price. You can see that the exponent of the interest rate is adjusted for the days left until next coupon payment.

Hope this helps

Clean price is more often quoted in the US. Dirty price is more often quoted in Europe.

NO there is no contradiction because Dirty price includes accrual interest which is full price. While clean is the price without accrual interst. Although the second quote appears to be “not clean”, it is because it is simply the quoted price.

Thanks for the replies.

@thegangsterle: I agree that the 2nd quote is clean, as we are asked to compute the full/dirty price thereafter.

I get that dirty means with acc interest and clean means without. I get why this happens.

My confusion lies in the fact that this quoted price is CLEAN (q18) whereas on p. 500 the computed price is DIRTY. If we are given a quoted price, are we to assume that it is clean or dirty? That seems to be the contradiction, or maybe I am not getting something…

krugerkmark, unless I am REALLY missing something here, as I said, p.500 does not contain any quote!.. What I see on p.500 is a way to calculate the dirty price. I think you are confusing yourself for no reason here The QUOTED price is going to be the CLEAN one unless otherwise stated.

Hi Panos,

Yes, I suspected that I was getting in a tangle somehow and think I may have resolved it.

The first paragraph of p. 500 says that the “calculations described earlier [in the chapter]” include acc. interest in the price. I find this a bit misleading as these particular calculations (not those ON p. 500) are made AT coupon payment dates. Thus, there isn´t any acc. interest to worry about!

That sentence could have mentioned that those earlier calculations do NOT include any acc. interest as there isn´t any acc. interest to worry about at coupon dates. If I am correct, the clean and dirty price will be the same at coupon dates.

To me, the passage should read along the lines of “the previous examples don´t address the issues of acc. interest because the settlement dates coincide with coupon dates. We will now factor in acc. interest.”

Does that sound right?

M.

You are right, I read the paragraph and it managed to confuse me as well! If I didn’t know, I too would assume that the previous calculations have included accrued interest, which is not the case. It is redeemed later when it says “Below, we show how the PV formula is modified to compute the full price…”

You are correct in that dirty and clean will be the same at coupon dates as there is no accrued interest to account for.

Essentially, we can simplify I think the way to calculate dirty prices as they are nothing more than clean + accrued interest.

So… take your calculator compute the bond’s price as always and then (assuming you were asked for by the question) just add any accrued interest to that and voila: you have the dirty price !

Example :

The bond’s clean price is 120 today. A coupon of 10 dollars is paid every six months, and it has been 2 months since the last coupon payment. Well, if you want to buy that bond you will have to compensate the seller for the 2 months of interest he has accrued. So the interest is simply 2/6 * 10. So 120 + 3.3 is the dirty price .

As you said at the coupon payment date, the dirty will equal clean since it’s been zero days since the last coupon payment: (0/6 * 10 = 0 accrued interest).