FRA Question confusion, difference, reasonable, discounts

king_kong

Schweser Vol 4 pg. 90 Example 1a. This calculation doesn't make any sense.

The first step calculates the payoff of the FRA as the difference between LIBOR and the reference rate. This seems reasonable.

The second step discounts the payoff to the FRA maturity (also makes sense). However, it discounts the payoff at LIBOR + 200bps.

It seems inconsistent (read as incorrect) to calculate the payoff at LIBOR flat and then discount it at LIBOR +.

To add to my confusion, see question 10 on pg 115. This is the same problem which it solves as follows:

Calculate payoff of FRA as (Reference - LIBOR + BPS). It then discounts to PV at LIBOR + BPS.

At least the solution is consistent? Obviously I am confused with this deal. Is their a problem here, or have I gotten dumber since Level 2?

nannan66

Hmm.....wrong level question.

pennyless

Just read through and I share your opinion. Additionally I couldn't find any related calculations in the CFAI books...

Market standard for the FRA-payment at maturity is to discount the FV with the LIBOR (matching the loan-period) obtained 2 days before the loan starts. The FV of the FRA is (which is right in Schweser) the difference between the FRA-rate and the obtained LIBOR fixing.

IAmNeil

It is customary to discount at LIBOR/Euribor rate since the assumption is that both party has the same credit worthiness of big banks thus can borrow at those rates.

If one party has higher credit risk, then it can be argued that you need to discount at a more appriopiate rate. However, I believe it is definitely not standard to do so, not in CFAI cirriculum anyway.

dyga

As it is an OTC-instrument you could change the contract to different discounting, but it makes no sense even if counterpartys would have totally different credit ratings. This is because the payment due flows 2 days after LIBOR fixing - so there is only a settlement risk, no credit issue here. This makes it different to the loan where the repayment flow occurs at the end.

However when you mark a FRA to market (before maturity) you could apply risk-adjusted discounting when your NPV is positive because the flow is at risk until the contract settles. You would essentially discount (like Schweser is doing) via the risk-free rate to get the exposure which is at risk. For a AAA customer you would leave it there and for worse ratings you shift the dicount curve upwards to reflect credit costs in the NPV. But this is only internal credit pricing and has nothing to do with the actual flow occuring when the contract settles!