oas option cost

Can anyone please explain me what is option cost?why is option cost less than zero for a putable bond?from what i think a putable bond is an advantage to the hilder therefore its cost should be higher. Need help bit confused. Thank you!

As a put option favors the bondholder, he has to pay for it. He can do so by paying a higher price for the bond, or by accepting a lower coupon payment on the bond, compared to a nonputable bond. In either case, his yield will be lower than the yield on the nonputable bond. The difference in those yields, which is negative, is the cost of the put option (measured in basis points of yield). It’s negative because it’s measuring the additional yield paid by the issuer; for a putable bond, the issuer pays a lower yield.

Thank you so much!

My pleasure.