Value of a call within a callable bond

CFA Level II Fixed Income
#1

I would like to compute the value of a call within a callable bond

  • The callable bond is a 3-year bond, coupon is 1,5%
  • Available rates in the exercice are par rate, spot rate, and one-year forward

The formula in the book states : value of a call = value of a bond straight – value of a callable bond. So we should compute both the value of the bond straight and value of callable to find the value of the call

But my question is : in the answer, spot rates are used to compute the value of the bond straight and one-year forward are used to compute the value of the callable : why do not we use the same rates for the straight and callable bond?

NB: also, I am wondering on a related issue: when should we use par rate to compute the value of a bond ? and why par rates are not the same as spot rates here in the table ?

Thank you very much!

#2

"one-year forward" can be translated from “spot rates”.

You may be use the method that you prefer.

#3

So you mean to compute both callable and straight bond I can indifferently choose 1-year forward or spot rates, and will get the same result ? Sorry, I think I might miss something because it is not very clear for me…

#4

Arbitrage Free Framework shows that the value will be same regardless of using Spot Rates or Forward Rates, because one can be derived from the other.

#5

It’s always just as easy to use forward rates as it is to use spot rates, and it’s often easier to use forward rates (e.g., when you have callable or putable bonds and you have to decide whether the option will be exercised or not).