why use the call price if the call price is less than the discount value in the example below.
thank you so much for your time.
A callable bond with an 8.2% annual coupon will mature in two years at par value. The current one-year spot rate is 7.9%. For the second year, the yield-volatility model forecasts that the one-year rate will be either 6.8% or 7.6%. The call price is 101. Using a binomial interest rate tree, what is the current price?
Your answer: A was incorrect. The correct answer was B) 101.000.
The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value for all the nodes in nodal period 2: V2=100. In nodal period 1, there will be two possible prices:
V1,U =[(100+8.2)/1.076+(100+8.2)/1.076]/2 = 100.558
V1,L =[(100+8.2)/1.068+(100+8.2)/1.068]/2= 101.311
Since V1,L is greater than the call price, the call price is entered into the formula below:
V0=[(100.558+8.2)/1.079)+(101+8.2)/1.079)]/2 = 101.000.