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OAS and Z-Spread

I just wanted to confirm something.

If bond has call option, the investor needs to be compensated so: Z-Spread > OAS
If bond has put option, the investor pays for this right so: OAS > Z-Spread

Is this correct?

Thanks in advance

yup, and remember bonds with options where interest rates are not path dependent (like a callable corporate) need the OAS spread from the binomial model

bonds with options where interest rates are path dependent (MBS, certain ABS) need the OAS spread from Monte Carlo simulation ...

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