FI - option and interest risk interest, following, only, decrease, practice

busprof

I would like to discuss this practice question

Which of the following bonds has the greatest interest rate risk ?
A- 5% 10Y callable bond
B- 5% 10Y putable bond
C- 5% 10Y option free bond

The answer given by the book is : C, saying that options are reducing interest rate risk

For me, I would have responsed A. A bondholder holding an option free bond is subject to increase and decrease in interest rate. She could win or lose
But with a callable bond, she is only subject to increase in interest rate (then decrease in bond price). If there is a decrease in interest rate (then increase in bond price), the bond issuer is likely to call the bond.
For me it's risker for a bondholder to have a callable bond than an option free bond.

thanks for your help on this matter