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

soddy1979

surely this is just a duration question...?

mnieman

My understanding:

Callable bond- Bond issuer is at a better position.
Putable bond- Bond holder is at a better position.
Option free bond- both are not in a better position- since they are locked in the bond interest rate until the bond matures. the bond is not sensitive to interest rate change. hence is more risky.
So the answer is C.

Buzz