“For a given bond price, the higher the interest rate volatility assumed, the lower the OAS for a callable bond.” pg351
I thought that higher IR vol -> higher option cost -> lower bond price (since long callable bond = short option) -> higher yield -> higher OAS
What gives?
That means, the option is even more expensive. Thus, when you strip out the option, the lower the spread.
Are you saying:
*option is stripped* -> value of bond increases by the value of the option; higher option cost -> higher bond price increase -> lower yield
?
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Yes, that is correct. If you stripped the value of the call option the value of the callable bond would have to increase to be equal to a bond without the call provision. The way to look at this from a yield stand point is the higher yield of a bond with an embedded option would decrease until it equals that of the yield without the option.
I think you are probably still hung on the OAS concept. Find a spot rate curve image with z-spread, oas, and treasury rates and it will make more sense.
Remember, OAS means the spread with the effect of the option removed; the OAS is the Z-spread minus the option value.
If interest rate volatility increases, the value of the embedded option increases. Thus, the OAS decreases (subtracting a bigger value gives a smaller difference).