The contract is a 270-day forward on a $100 par treasury bond with ten years remaining to maturity. The bond has a 5% coupon rate, has just made a coupon payment, and will make its next two coupon payment in 182 days and in 365 days. It is currently selling for 98.25. The risk free rate is 4%. What is the no arbitrage price for the forward contract on the treasury bond?
The answer is:
The present value of the next coupon payment is:
2.5/1.04^(182/365)=2.4516
The no-arbitrage forward price is (98.25-2.4516)*1.04^(270/365)=98.62
Why the answer does not consider accrued interest for the second coupon payment period?
The forward price is for the bond; it’s the clean price.
I presume that in the real world when the forward expires and you purchase the bond, you have to pay the dirty price.
But, according to the formula on Cfa book, the bond forward price equals to the FV of bond dirty price minus FV of coupon minus accrued interest at forward expiry. So, I think for the above question, we should also subtract accrued interest at forward expiry which is (2.5*88/365).
I too think that we should factor in the accrued interest. Any idea why we are using clean instead of dirty price?