I found a question that I can’t understand well… Can I compare two identical bond but with the only difference that one is callable and the other one is straight? The question said: callable bond OAS 180, straight bond OAS 120, and the answer say Callable bond was undervalue… Is that correct? I know when two bond are identical that would be true but in this case I am not sure…

I encountered the same question, but still can’t understand well.

Why it is possible to compare OAS (straight bond with 15% volatility let say) vs OAS (callable bond with 15% volatility)? Cause i understand that OAS of straight bond (with or without 15% volatility) would also be the same as it’s z-spread. Z-spread of straight bond remain unchanged with interest rate volatility while OAS would decreased in that case.

I mean, except for the case of zero volatility, OAS of a callable bond always greater than OAS of a straight bond.

Then it is correct that z-spread of straight bond (which is OAS 120 in the question) implied zero interest rate volatility, then OAS 180 (also assumed at zero volatility) on a callable bond could be considered as undervalue. Then assumption of the question is zero volatility, right?

Because the methodology of computing the OAS is intended to remove the value of any embedded options. Without the embedded option, the straight bond and the callable bond are identical.

I’m not certain that I understand what you mean by the section I bolded, above. If you mean that the OAS of a callable bond decreases when interest rate volatility increases, then you’re mistaken.

What is true is that, for a given price of a callable bond, the OAS that you compute will decrease as the interest rate volatility that you assume in your model increases. However, if the actual (not the assumed) interest rate volatility increases, the OAS should remain unchanged, because the price of the callable bond will decrease .

If the bonds are priced fairly, you are incorrect. If the bonds are priced fairly, the OAS of a callable bond should always equal the OAS of the otherwise identical straight bond, for any level of interest rate volatility.

No, the assumption is not zero volatility. The volatility is whatever it is. If the model for calculating the OAS is accurate (and that’s a whacking big if), then the callable bond is undervalued relative to the straight bond no matter what the actual volatility is. Because the OAS is comparing a straight bond to a straight bond: the effect of the call option is removed.

Thank you so much I’ve read your answers on other threads. So much grateful for your sharing, that are really helpful.

One more concern, is that correct that the z-spread (added to each spot rate of a spot curve) of a corporate bond would be different to the OAS (added to each node of a interest rate tree)?

I read this in the curriculum “Note that the Z-spread for an option-free bond is simply its OAS at zero volatility” (Book 5, page 146). Then if interest volatility is not zero, Z-spread would not be the same as its OAS. Is it correct? And when compare a bond with option and without, we could only compare its OAS spread (to know if there is any mispricing), we could not compare the OAS (of an option embedded bond) vs z-spread (of an straight bond), rights?

I just got confusing on this by comparing OAS of an bond with option vs z-spread of a straight bond, cause both of them measure the credit risk.

There’s a bit of disagreement in the CFA curriculum. In the reading “The Term Structure and Interest Rate Dynamics”, it defines the z-spread as a constant spread added to each point of the spot curve (which is how I’ve always heard it defined). With that definition, the z-spread is not necessarily equal to the OAS at zero volatility.

In the reading “Valuation and Analysis: Bonds with Embedded Options”, it defines the z-spread as a constant spread added to each point on the forward curve. In that case, it would definitely be the OAS at zero volatility, but that definition is not the usual one.

The assumption for the z-spread is zero volatility (the “z” in z-spread means “zero volatility”; it’s the zero volatility spread). If interest rate volatility is not zero, then the z-spread is meaningless.