Fixed Income- Reading 47 EOC- #9, #15

Just wanted to clarify the following:

So on Page- 351 of the official curriculum (Reading 47) as well as in Level I, if Treasury market is the benchmark:

then Nominal Spread is based on Treasury yield curve, while Z-spread and OAS are based on Treasury spot rate curve

However as per explanation of EOC #9, #15, they seem to suggest that for OAS, Treasury yield curve can also be used as the benchmark…can somebody explain?

Inasmuch as there is a one-to-one correspondence between spot yield curves and par yield curves – given a spot curve there is a unique corresponding par curve, and given a par curve there is a unique corresponding spot curve – saying that a par curve is a benchmark for OAS, while not a particularly well-reasoned description, is not strictly wrong.

Thst said, I haven’t read the particular explanation you cite, so there may be more to it than what I’ve written. If they’re suggesting that the OAS is added to the rates on the par curve, they’re obviously wrong.

I agree. Based on my read what I believe they are getting at is that the benchmark used to construct the spot curve is the yield curve. The spot curve then provides the forward rates which are the rates used in the binomial intererest rate tree which you can calculate OAS from.

It does seem to imply that you add the OAS to the spot par curve, which is incorrect as s2000magician notes. Not particularly well written.

EDIT: good catch s2000magician, it’s getting late on the East Coast smiley

I hope you meant that it implies that you add the OAS to the _ par _ curve (which is incorrect); implying that you add the OAS to the (non-zero volatility) spot curve _ is _ correct.