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Simple OAS question

Hi everybody, I find it difficult to get the logic here:
We know putable options benefit us therefore the option value is negative, i.e. we pay for the option. So far so good but why is OAS  Z-spread? This means an increased spread for considering the option, right? Shouldn’t the option reduce the value of the bond? How does the spread increase? To me an increased spread means higher returns, no?
Thank!

The OAS is what the spread would be without the option!

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Where have you been all my life mattmania… i tried to wrap my brain around why that was happening for atleast an hour and I settled on just accepting it and moving on. With one sentence you’ve provided me one of those “OHHHHHHH” moments that feel so good.

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