Diff between OAS and Nominal spread

Can anyone explain the difference between OAS and Nominal spread. In exam 4, they have mentioned that as the call gets deferred, call option reduces in value and OAS and Nominal spread come closer. However, doesnt OAS have nothing to do with options. Isnt it the spread of a option free bond?

I thought OAS had to do with Z spread… I guess if the call option reduces value, then the nominal spread and/or z spread (someone correct me if i’m wrong please) will fall, so it’s closer to OAS? I know that OAS = Z spread - Option Value.

The nominal spread is just the difference between a treasury and non-treasury yield. It’s a crude measure that only looks at one point (maturity) and doesn’t break down the components or comment on the entire curve. The z-spread does this. The definition of the z-spread is along the lines of the spread required over the entire curve that would make the pv(non-treasury cash flows) equal to the non-treasury’s price when discounted at the spot + spread. You have to use trial and error to get it. The z-spread is composed of (1) the cost of the option and (2) the OAS. I believe the OAS is model-dependent, so your value for it can vary.

the OAS IS the bond’s spread if it is option free… it takes the option yield out of the z-spread, something like: OAS = z-spread - option yield so, (i think) what they’re doing is comparing OAS to the z-spread, which is then being compared to the nominal yield… somehow…

You will study OAS a lot more in L II so I wouldn’t worry that much about it here. If you understand zeroaffinity’s post, that’s good enough. As zero pointed out the OAS is model-dependent, especially with things like MBS when it is not at all clear in what situations options are exercised. Of course in virtually all of these models there is the question of how interest rates evolve (most people think that interest rates do not evolve like stock prices and the model that says they do actually has a name - Randle Bartleman - that nobody uses for anything) and how volatile they are. The topic is infinitely deep.

i like to think of it like this: Zeroaffinity pointed out that OAS is the spread between the price of the bond without an embedded option and the Risk Free Security => OAS = Non-Callable Bond price - Risk Free Security price For our callable bond, the Nominal Spread is: Nominal Spread = Callable Bond price - Risk Free Security price But, the longer the period to call is, the more the bond will act like a option-free bond (becos it’s years away from being called) => Callable Bond price gets closer to Non-Callable Bond price So now, the Nominal Spread equation can be aproximated by: Nominal Spread = Non-Callable Bond price - Risk Free Security price As you can see, the Nominal Spread is now close/equal to OAS. Please correct me if inaccurate though guys

Yikes. Let’s not get everyone confused the day before the exam! Nominal spread is based on the yield to maturity differences and OAS is based on the spread over the yield curve. That means that OAS and nominal spread can be almost arbitrarily far apart even on option-free bonds (note that OAS on an option free bond is just Z-spread). Also the spread is not a difference in bond price and there is no sense in which “OAS = Non-Callable Bond price - Risk Free Security price” is true. OAS is calculated by finding a spread over a yield curve that makes the the model price of a bond match the market price. Often this is done using interest rate trees, often binomial interest rate trees. "Nominal Spread = Callable Bond price - Risk Free Security price " is only true if price here is ytm not the usual notion of price.

Joey, cheers. So, if I replace the bits where i’ve said “price” with “yield”, doesn’t that make my approach correct?

I think you shouldn’t worry much about this. It’s a hard topic and they will beat you with it on LII. Starting a big discussion on this on Friday before the exam is probably not smart.

I don’t mean to hijack this thread, but after doing a search, this was the first pertinent thread I could find. I have L2 related question: With regard to the OAS and calculating effective duration and effective convexity using a binomial pricing model, one assumption is that the OAS is constant with changes (volatility) in interest rates. However, according to CFAI, they give an example for when volatility is high (say 20%), for a callable bond, the OAS will be relatively smaller. When volatility is low (say 10%), for a callable bond, the OAS will be relatively higher. This part I understand. Or maybe I don’t. In one case the assumption is that OAS is constant. In the other case, OAS is very much dependent upon the volatility of i-rates. I know I’m missing something; perhaps a bunch?

  1. This is level II stuff 2) This is hard L II stuff 3) Even for L II you never have to calculate OAS “OAS is constant with changes (volatility) in interest rates”