I have been reading other threads regarding OAS and I can’t seem to understand this particular thing:

“OAS removes the option: it’s the spread that compensates the bondholder for everything other than the option risk.” (S2000magician).

When we calculate the price of a bond with an embedded option, we assume the bond will be callable/puttable. So, why we would say the option risk is removed if it is called/put when we priced it with the binomial tree? I would think that the risk is still there since it is called/put.

Or is it because we are adding a spread that gives as the market price of an identical bond without the embedded option, we can say the option risk is removed? In another post they write that “the OAS is a constant spread added to every interest rate in the tree so that the model price of the bond is equal to the market price of the bond” Which bond? the bond without the embedded option? an equally likely bond without the embedded option?

Also, why there are two different ways of writing the formula of Z-spread = OAS - option cost?

Intuitively for me the formula would be OAS = Z-spread - option cost (for a call option, and OAS = Z-spread + option cost for a put option). Thanks in advance!

In the binomial tree we explicitly include the effect of the embedded option.

In the market price of the callable/putable bond we include the effect of the embedded option.

Those two effects, being on opposite sides of the equal sign, cancel each other, so the effect of the option is removed.

The price we use is the price of the callable/putable bond, not the price of an option-free bond.

The way to look at it is this:

z-spread − OAS = option cost

The z-spread includes the cost of the option, while the OAS does not; therefore, the difference is the option cost. Algebraically, this is equivalent to:

z-spread = OAS + option cost

The option cost is positive for a call option (i.e., the issuer has to pay a higher yield for a callable bond than for an otherwise identical option-free bond) and negative for a putable bond (i.e., the issuer gets to pay a lower yield for a putable bond than for an otherwise identical option-free bond).

Another question that I stumbled in the EOC. Why if the we have two bonds with similar characteristics, if one has a higher OAS will be undervalued compared with the other? I understand that the higher the spread, the lower the price, but wouldn’t both have the same market price?

Can’t see the intuition around here. Can someone share an example?

Do you want intuition, or do you want understanding?

The understanding is that two very similar assets should generate very similar returns. So, if one is generating a substantially higher return (as evidenced by a higher OAS), it is relatively underpriced.