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enter image description hereI'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: $r(0,0) = 5\%, u = 1.1, d = 0.9d, q = 0.5, 1−q = 0.5$

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    $\begingroup$ Not sure why you are using a binomial lattice to price a forward. There is no optionality in a forward. $\endgroup$
    – AlRacoon
    Jan 22, 2020 at 16:48
  • $\begingroup$ This was given to me for an assignment. I've added my calculations from the provided workbooks $\endgroup$
    – jwedmore
    Jan 22, 2020 at 18:38
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    $\begingroup$ 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 $\endgroup$
    – Kevin
    Jan 22, 2020 at 20:32
  • $\begingroup$ @KeSchn you are correct! I have calculated the ZCB price and futures contract price but am stuck on the forward contract $\endgroup$
    – jwedmore
    Jan 22, 2020 at 20:51
  • $\begingroup$ 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 $\endgroup$
    – Josh Ckn
    May 19, 2020 at 18:05

1 Answer 1

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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.

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  • $\begingroup$ Given that the above is basically a no-arbitrage from spot/forward yields (directly linked to ZCB), would you mind expanding briefly if/how this would work for coupon/corporate bonds? $\endgroup$
    – KevinT
    Jan 22, 2021 at 7:31

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