Fixed Income Derivatives: Bond Futures

In this lesson, we learned how to price futures contracts on bond futures.
This is very similar to pricing bond forwards.

Since the forward price must equal the spot price at the expiration time t=n, we can set up the same equality as for bond futures;

S(n-1)/ B(n-1) = E[S(n)/B(n)] where B(n) is the value of the cash account

With forward contracts as with futures contracts, the "price" paid at time t=0 is equal to 0 and we know what S(n) is, we can change this equation to:

Since both B(n) and F(n-1) are known at t=n-1, we can simplify this to:

And by the law of iterated expectations:

And since F(n) = S(n):

This is different from the forward price G(0):

as it does not depend on the cash account, or short-term interest rate.


We then priced the same bond from the previous lesson, but this time pricing a futures contract instead of a forwards contract:

The reason that the price here is different from the forwards contract is because the futures contract is not discounted by the short-term interest rate, since it does not depend on the interest rate.

The futures contract is worth $103.22 and the forwards contract was worth $103.38.  In this case they are not equal but they can be equal in certain circumstances.