First, is the yield of dirty price is same as the yield of this bond at beginning?

If they are same, then the dirty price is already the current price of this bond, why do we again minus the arraccrued interest?

It seems the seller received extra percentage of the next coupon, but actually he didn't get any of next coupon? So I really confuse here.

We have the jump condition for the discrete coupon paying bond: $V(t_i^-, r) = V(t_i^+,r) - C_i,$ here $t_i$ is the $i$-th coupon paying, so this $V(t,r)$ should correspond which price?

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    $\begingroup$ to compare apples to apples. dirty price includes the interest components. so the dirty price would be higher than the clean price. if you want to compare bond price today to that yesterday, you must exclude interest from both make them compareable $\endgroup$ – nimbus3000 Mar 20 '17 at 5:41
  • $\begingroup$ The point is to reduce fluctuations. Traders only want to see the change due to interest rate, economic factors etc. They don't want to see the change due to accrued interests, which is known and not interesting. $\endgroup$ – HelloWorld Mar 20 '17 at 6:10
  • $\begingroup$ @nimbus3000 OK, I may ask more clear, what's the difference between the current bond price $B(t,T)$ and the dirty price at time $t$? $\endgroup$ – A.Oreo Mar 20 '17 at 6:50
  • $\begingroup$ at a time t, clean price of the bond is the dirty price - accrud interest. $\endgroup$ – nimbus3000 Mar 20 '17 at 6:53
  • $\begingroup$ @nimbus3000 yeah I know this formula, but I want to know the relation between the most initial bond price $B(t,T)$ and dirty price, only clearing their relation, I can know the meaning of dirty price. Are they the same concept? Since, generally we will sell the bond as price $B(t,T).$ $\endgroup$ – A.Oreo Mar 20 '17 at 6:57

When you read a Bond price in the newspaper, on a web site, in a database of bond prices it is always the Clean Price. [You don't have to compute anything! The clean price is there!]. When you actually buy the bond you receive an invoice asking you to pay the Clean Price plus the Accrued Interest, which are added together for your convenience and are called the Dirty Price.

It is similar to a restaurant, where a hamburger is listed for 1,99 EUR but when you get the bill at the end of the meal there is is a service charge,a tax, and maybe other unexpected items which bring the bill to 2,07 EUR.

The service charge compensates the waiter who brought the meal to you, the accrued interest compensates the seller of the bond who is ethically entitled to a portion of the next coupon you will receive (if he held the bond for a part of the coupon period, for example if he held for 1/2 the coupon period he is entitled to half the next coupon under accounting "accrual" principles). Essentially the accrued interest is a mechanism for sharing the value of the next coupon (which the buyer will receive) in a fair way between buyer and seller based on when in the coupon period the bond changed hands.

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  • $\begingroup$ I think this solution is very clear. But one thing I still confuse is that we have the jump condition for the discrete coupon paying bond: $V(t_i^-, r) = V(t_i^+,r) - C_i,$ here $t_i$ is the $i$-th coupon paying, so this $V(t,r)$ should correspond which price? $\endgroup$ – A.Oreo Mar 21 '17 at 6:13
  • $\begingroup$ I think for the continuous coupon paying case $C(t)dt$ this $V(t,r)$ is clean price and the discrete coupon paying case this $V(t,r)$ is dirty price? $\endgroup$ – A.Oreo Mar 21 '17 at 6:19
  • $\begingroup$ so can we think of the clean price as the discounted cashflows of the future excluding the current coupon? Nevertheless the yield of the bond should be based on the dirty price. $\endgroup$ – Ric Mar 21 '17 at 8:46

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