# Zero Coupon Bond Forward Price

I'm currently working on the Coursera Financial Engineering and Risk Management course. In one of the questions I was asked to build a binomial pricing model for fixed-income securities. 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

## 1 Answer

Look at slide 3 of Mod 4: Fixed Income Derivatives: Bond Forwards, that's the relevant equation.

$$G_0 = \frac{E_0^\mathbb{Q}[Z^j_t/B_t]}{E_0^\mathbb{Q}[1/B_t]}$$

Where $G_0$ denotes the price of the forward at $t=0$, $E_0^\mathbb{Q}$ is the risk-neutral price at $t=0$, $Z^j_t$ denotes the ex-coupon price of the bond at time $t$ and state $j$, and $B_t$ is the value of the cash account at time $t$.

You need to divide by the risk-neutral price of the reciprocal of the cash account at t=4, which is equal to the t=0 price of a zero-coupon bond with face value of 1 that matures at t=4

*edited for a more complete answer

• Hi user3747260, welcome to Quant.SE! Can you provide a bit more information, this is hard to follow for people that do not have those slides. – Bob Jansen Nov 5 '15 at 21:43