Forward Contract on Zero-Coupon Bond

[giosach]

Hi all, new member here. Long time lurker however :P

I'm currently studying the Financial Engineering & Risk Management course by Columbia University on Coursera. I'm seriously stuck on the second question of the week 5 quiz. I have built an n=10 period binomial model, and we know that r=5%, u=1.1, d=0.9 and q=1-q=1/2. On question 1, I computed the price of a zero-coupon bond that matures at t=10 to be $61.62. Question 2 asks to compute the price of a forward contract on the same bond that matures at t=4. I have seriously tried everything I could think of for the last 3 days and it's still the only question from the whole quiz that I can't come up with an answer. Any help would be much appreciated. Thanks in advance

 

[Qui-Gon]

Since d < 1+r < u, your binomial model is arbitrage free. Computing the price of the forward is thus reduced to finding a replicating portfolio comprised of some number of units of the underlying zero-coupon bond and some number of units of the money market account, and then finding the price of this portfolio. The construction should parallel the one given in Shreve 1 (or any intro book on pricing in discrete time) for European options, only now your underlying is a bond not a stock and your derivative is a forward not an option.