# Why we need compute the clean price

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?

• 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 – nimbus3000 Mar 20 '17 at 5:41
• 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. – HelloWorld Mar 20 '17 at 6:10
• @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 $t$? – A.Oreo Mar 20 '17 at 6:50
• at a time t, clean price of the bond is the dirty price - accrud interest. – nimbus3000 Mar 20 '17 at 6:53
• @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 $B(t,T).$ – A.Oreo Mar 20 '17 at 6:57

• 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? – A.Oreo Mar 21 '17 at 6:13
• 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? – A.Oreo Mar 21 '17 at 6:19