Which bonds are likely putable and why?

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Bonds with embedded put option are putable. In such bonds the option seller is the issuer whereas the option buyer is the bond holder. When interest rates rise and prices fall below a threshold price, bonds with put options can be put by the bond holders by exercising the option.

Yes, and because the benefit of owning the option accrues to the holder, a putable bond will have a lower yield than an otherwise identical option-free, or callable bond.