Expected LIBOR and forward rates

[Alpha9]

Should I just accept that the market's best guess at LIBOR in n years' time is the n-year forward rate?

Page 28 of the notes suggests that an (n-year) FRA ( paying LIBOR and receiving fixed 6%) will have zero value if the forward rate is 6%. I think the value will actually be (6% less expected LIBOR) discounted for n years. So the only way this can be zero is if I expect LIBOR to be equal to the n-year forward rate.

Is that about the size of it?

But then I'm not sure where any credit risk of the banks comes in: actual LIBOR tends to be higher than equivalent Treasury Bill rates because of banks' credit risk, according to the solution of 3.13 ("What is LIBOR?") on page 36. Meanwhile we can work out forward rates from spot rates, which don't seem to involve credit risk...

 

[TheOke]

I guess for consistency, the FRA is priced and discounted with the interbank swap curve [ie the zero curve derived from the money-market, FRAs and SWAPS (not government bills)].

This seems to imply a circularity in that the swap curve is itself derived from the FRA. In reality (again I guess), the derivative market is identical to any market. You have buyers and sellers and where they agree is the correct and fair price. So you have short and long parties to FRAs, Swaps etc, and the rate at which both sides are prepared to enter into the agreements (at zero cost) is the fair rate. From these rates, the swap curve is derived (which has the credit risk premium in it). And from the swap curve (which is derived from zero-cost agreements), you can price older and existing FRA agreements.

In the exam, the curve is probably assumed known and you just have to price another agreement with the given curve, such that the price is arbitrage-free with reference to the pre-existing contracts.