Does the value of risky debt equals the value of risk free debt minus a put option?

Yes, the value of risky debt can be understood as the value of risk-free debt minus the value of a put option. This is based on the idea that a bondholder has the right, but not the obligation, to sell the bond back at a predetermined price if the issuer defaults. The put option reflects the potential loss due to default risk, thus reducing the overall value of the risky debt relative to risk-free debt.