# OAS vs Z-Spread - CFAI Mock wrong??

[original post removed]

Why would you have an “option adjusted spread” on a bond that doesn’t carry an option? OAS just accounts for the change in cash flows that result from an option potentially being exercised. If a bond doesnt have an option, the cash flows won’t adjust

When you create a binomial tree, your assumptions about interest rate volatility will affect the rates at different points in the tree - ie if volatility is higher the forecasted rates will be different than if you assume the volatility of the rates to be lower. If one volatility assumption causes the rate to adjust such that the bond will be called, but another volatility assumption in another model assumes that rates wont adjust that much (ie, fall), then the cash flows from the model will be different and the OAS will be different

I think this Q is all about comparing bonds with embedded options and indeed higher volatility => higher option cost => lower bond price => lower OAS.

I’d select B.

Kwalaw… look at the question… it clearly states for bond with embedded options.

“My understanding is that, for two otherwise identical bonds, one with embedded option and the other without: the two bonds will have the same OAS.”

That statment is incorrect… The OAS is the spread with the option removed. Your statement would be the case if the option had no value… which never happens.

Well, in your original post, you made the statement that " OAS is dependent on the volatility assumption. In other words, the embedded option value affects OAS. But I think this is wrong."

In regard to that statement being wrong: that statement isnt wrong - the volatility assumption will affect the value of the option. Higher volatility will cause the OAS to be lower because the cost of the option is larger. And since I haven’t seen the original question, I can’t comment on the answer key. But, now I can’t tell the difference between the answer key and they question youre asking.

And in regards to this statement:

My understanding is that, for two otherwise identical bonds, one with embedded option and the other without: the two bonds will have the same OAS. For the bond with higher option cost, its Z-spread will be higher (but OAS will not be affected).

That statement is incorrect also - If you have two identical bonds (same coupon, same maturity, same duration, etc), identical except for the fact that one has a call option and one doesn’t, they will have the same z-spread. Z spread in the case of a callable bond makes the assumption that you don’t adjust cash flows in recognition of the option being exercised, therefore it isnt that useful for comparison with a bond with an option.

In the case of the bond with no option, the OAS will = Z spread, because there is no adjustment for any change in cash flows. For the bond with a call option, OAS < Z spread.

All else the same… an embedded and a non embedded bond with have the same ZZZZZ spread. The option adjusted spread will be different, since option affect cashflow and to calculate the spread we use a binominal model. If the spot rates were the same, but the cash flow isn’t (due to options)… how would the two bonds have a same option adjusted spread.