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Bond forward

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?

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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.

Simplify the complicated side; don't complify the simplicated side.

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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?