1rst: we add OAS because in the binomial tree is taking into account the fact that the callable bond will follow the ‘call rule’ and its value at certain nodes will reflect the fact that it will be called at the given interest rates… if there was no possibility that the bond will be called then z-spread would be appropriate because the cash flows would be the same and OAS = Z spread 2nd: we use OAS so that different securities (with different option costs) can be compared, and the relative credit and liquidity can be evaluated. If we use z-spread a security with an z-spread of 250 bps will appear to a security (with similar credit and liq) with a z-spread of 200 bps, however is the first security’s has a prepayment option worth 150 bps and the second security has a prepayment option worth only 50 bps then the first security will actually be overvalued relative to the second

Thanks, Marty3 but I am still confused. In several places in CFAI and kaplan the OAS as defined as the “spread with the option cost removed” But if the OAS is calculated using the tree while accounting for the call rules, how is does this NOT include the option cost?! Its certainly not the same spread as you’d get on an otherwise identical bond WITHOUT the options. If you calculate the spread on the tree and fully incorporate the call rules, how does this NOT reflect the option cost? This has been REALLY bothering me. The two treatments of the OAS seem to conflict: if z spread = OAS + cost of call option but OAS is calculated in a way that reflects the option, how does this work!?

Just as an example CMBS valuation is done with z-spread. Virtually no prepayment risks. Plain MBS valuation done with OAS using a binomial i-r- model because prepayment risk is heavy

z spread = OAS + cost of call option cost of option could be positive or negative, so the above is correct.

But if the OAS is derived using a tree that reflects the call rules, how can we say that the OAS does NOT reflect the option cost??