# Forward Contract Price on Zero Coupon Bond

I'm trying to calculate the forward contract on a zero coupon bond where the forward contract matures at t=4. The zero coupon bond matures at t=10 and has a face value of 100. The price of that bond is 61.62

$$n=10-period$$ binomial model for the short-rate The lattice parameters are: $$r(0,0) = 5\%, u = 1.1, d = 0.9d, q = 0.5, 1−q = 0.5$$

• Not sure why you are using a binomial lattice to price a forward. There is no optionality in a forward. – AlRacoon Jan 22 '20 at 16:48
• This was given to me for an assignment. I've added my calculations from the provided workbooks – jwedmore Jan 22 '20 at 18:38
• Looks very much like the coursera course on financial engineering by Haugh and Iyengar. :) @AlRacoon the tree is needed to model the stochastic short rate – Kevin Jan 22 '20 at 20:32
• @KeSchn you are correct! I have calculated the ZCB price and futures contract price but am stuck on the forward contract – jwedmore Jan 22 '20 at 20:51
• i'm stuck too, did you find the answer? i find at T=0 F=90,85 So the forward price should be 147,43 because the Face value of the Bond is 100 or am i missing something? thanks – Josh Ckn May 19 '20 at 18:05

To calculate the forward price $$F$$ of a zero coupon bond at t=4, note that arbitrage considerations imply that $$Z(0,10)= Z(0,4) F$$. This essentially means that investing in a 4 year zero coupon bond together with a forward contract to invest from year 4 to year 10 must be the same as investing in a 10 year bond. So you need to first calculate Z(0,4) from your lattice.