Treasury Bond Futures Formula

[VirtualM]

For pricing Treasury bond futures, the curriculum only gives one “version” of the formula, where the future value of coupon payments is subtracted from the futures price. In contrast, the bond forward formula has two versions, one in which the present value of coupon payments is subtracted from the spot price, and the other version where the future value of coupon payments are subtracted like in the futures formula.
Is there a reason why there is only one version of the formula for T bond futures?

 

[S2000magician]

No.
The two formulae for the bond forward price are equivalent (i.e., give the same price), and both work for T-Bond futures. They were probably just being lazy.

 

[Pompey]

(S0-PV of net cost of carry)*(1+r)T same as S0*(1+r)T - FV of net cost of carry
Since it is a T-bond you can’t call the resultant number as the fair price. you have to take in to account the cheapest to delivery scenario. Hence the resultant number has to be divided by conversion factor. Then that’s the (f0) fair value.