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more OAS confusion

Please refer to P313 of V5 and P203 of Book 4(schwesernotes). I understand why we need to add a spread to all the 1 year rates in the binomial interest rate tree. This will give us the market value of $102.18. This seems very similiar to what you on P203 of schwesernotes. But on P203-schwesernotes, the spread that is added is called the Z-spread. Why is the spread on P312-V5 referred to as the OAS and not the Z-spread?

If you keep adding small amounts to the binomial interest rate tree without considering options, you get the z-spread... with options, you get the OAS.

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