# what is the difference in calculating OAS vs. Z ?

differences in calculation Z spread added to treasury spot curve OAS spread added to forward rates on tree right? Z price used is an option free bond OAS price used is a bond with option what else? what is the difference, technically, when calculating OAS and Z? I know that the difference is option cost obviously, but TECHNICALLY in calculations what is the difference???/ Thank you

If my thought process is correct, the way in calculating the spreads are the same. You add a certain number of bps to the interest rates from which you discount each CF until you reach an arbitrage free value.

thats what I was thinking, and if this is true, the only difference in calculations (given the same benchmark) is just the price then, so I am on a quest to find out if this is true lol

Calculating the Z-spread is something you can do really easily in Excel by trial-and-error (and of course better ways). It’s just the spread over the spot curve that gives you the current price (do one or two this way to get the feel is really useful). Calculating the OAS is much more difficult. For example, on an MBS you have to generate your interest rate tree and then decide what happens at each node (interest rates drop x%, what percentage refinance?). This will be part of your model which is why the OAS that you calculate and the one I calculate might be different. Now when I have some massive tree I can start calculating my OAS by working backwards in the tree and then discounting by a spread over treasuries. It’s a ton more work and not something you should know how to do for the exam.

thank you JDV, I was hoping that you would contribute, I felt that the difference in calculations could not be simply the price, and I just needed some justification for it, even though we do not need it for the exam I feel the need to satisfy my curiosity and feed the intuition so that I have a sound foundation, so to say a lot of the time you have to take things as given in the CFAI, which is what makes notes valuable. But I wish i actually knew the bottom of all calculations, that would actually make my day easier. lol anyways thank you

I missed the boat the first way around, let me explain, I just realized that the underlying CASHFLOWS will be ALSO DIFFERENT , this is the reason that OAS and Z will be different (if the cashflows are same, z = oas). so the technical process is as such : Given the rates at each node, the cfs must be predicted, the price is set to market price at the beginning node and this way we find what rates are priced in (even though we have the rates at each node, we must also add rates to these nodes in order to get the OAS) might be obvious to a lot of you, but I finally caught on

^Right! Good job.

So, does that mean that to calculate z-spread we assume deterministic interest rates but to calculate the OAS spread we assume stochastic rates? And if so, is this a problem?