Callable/putable bond price relation to shift in par rate

CFA Level II Fixed Income
#1

Hi guys,

This is a question for a blue boxed question from Institute, CFA. 2018 CFA Program Level II Volume 5 Fixed Income and Derivatives. CFA Institute, 07/2017:

Given the following details:

  • TTM: 3 years

  • Coupon: 3.5% annually

  • Type of Bond: Callable

The question is:

The price of Bond X is affected:

  1. only by a shift in the one-year par rate.
  2. only by a shift in the three-year par rate.
  3. by all par rate shifts but is most sensitive to shifts in the one-year and three-year par rates.

The answer is:

“The main driver of the call decision is the two-year forward rate one year from now. This rate is most significantly affected by changes in the one-year and three-year par rates.”

What bothers me is how come par rates other than maturity matched rate and the 1 year rate have an impact on the price of the bond though its insignificant?

Thanks in advance for any response!!!