FIXED INCOME - BOOK QUESTION - SAMUELS & SONS

Hello

i have a question related to this case in the book “SAMUELS & SONS” on fixed income valuation of callable and putable bonds:

3 bonds: free option, callable , putable

4.4 % cupon , callable and putable at par, 3 years to maturity

They provide the 1 year, 2 year, 3 year par rates: 2.25 , 2.75, and 3.1 respectively , and the analyst (ferguson) construct the binomial interest rate tree based on this estimates, which are:

year 0 : 2.5%

year 1 : 3.5930% / 2.9417%

year 2: 4.6470 % / 3.8046% / 3.1150 %

i understand, in the year 0 , the 2.5% is the spot rate, and the rest are the fowards rates.

In the solution (they start with the backward induction etc etc ) and when they get to the year 0 , insted of using the Rate: 2.5% (spot rate) , they use the par rate of 2.25% , WHY DO THEY USE THE PAR RATE INSTED OF USING THE SPOT RATE OF 2.5???

Thank you very much for your help

Shouldnt the 1 year spot & par rates be the same anyway?

i think it shouldnt, the par rate i think is the YTM, what we use to come up with the spot rate, and then the FWD rates.