Zero Coupon Binomial Model Forward

[Tom Sun]

I'm building a binomial pricing model for fixed-income securities for a MOOC. Specifically a 10-period model with 5% initial short rate, u=1.1, d=0.9, q=1-q=0.5.

One of the questions asked for the bond forward price with maturity at t=4. And the forward price I got was exactly the same as the bond price. Is that correct for zero coupon bonds?

Here's my spreadsheet: https://goo.gl/5e7JSp

 

[Dmitri M.]

I'm building a binomial pricing model for fixed-income securities for a MOOC. Specifically a 10-period model with 5% initial short rate, u=1.1, d=0.9, q=1-q=0.5.

One of the questions asked for the bond forward price with maturity at t=4. And the forward price I got was exactly the same as the bond price. Is that correct for zero coupon bonds?

Here's my spreadsheet: https://goo.gl/5e7JSp

It depends on what you mean by bond forward price. Suppose you have a forward bond that starts at T1 and matures and T2. Its price today (at t=0) will be the same as the price of a zero coupon bond that starts today and matures at T2 by a simple replication argument - the forward bond pays par at T2 and the spot bond pays the same amount at the same time, therefore their prices must be equal. But this price does not hold a lot of meaning. What you are usually interested in is the price you want to pay for the forward bond at T1, or its discount rate, which is the same thing. And that price will certainly be different from the spot bond price, unless you interest rates are zero. This blog has detailed explanation of froward discount rate.