spot rate curve and binomial interest rate tree confusion

Annisquam then develops a model that compares the value of a bond determined using a binomial interest rate tree to its value determined using spot rates. The bond he selects for the comparison is non-benchmark, option-free, and has five years to maturity and an annual-pay coupon rate of 3%. The coupon rate is below the coupon rate of the benchmark bond. The yield curve is currently downward sloping. The output of Annisquam’s model shows that the spot rates generate a value equal to the market price of the bond, but the interest rate tree methodology produces a higher value. Assuming Annisquam’s spot rate valuation is correct, why does his model most likely produce a different result?

  1. He is valuing a non-benchmark bond.
  2. The model is incorrect because both methodologies should value the bonds equally.
  3. The yield curve is downward sloping.

Answer is 2. Why is the answer not 3. the interest rates used in the binomial tree comes from the spot curve which they just said is downward sloping- isn’t this going to affect the valuation? I understand why its 2 so please explain why its not 3.

For an option-free bond you should get the same value in a properly calibrated tree as you do from the spot curve _ irrespective of _:

  • The shape of the curve
  • The assumed interest rate volatility

but why? could you please elaborate?