A callable bond with an 8.2 percent annual coupon will mature in two years at par value. The current one-year spot rate is 7.9 percent. For the second year, the yield-volatility model forecasts that the one-year rate will be either 6.8 or 7.6 percent. The call price is 101. Using a binomial interest rate tree, what is the current price?
A. 100.99.
B. 100.558.
C. 100.279.
D. 99.759.
Answer:A
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 = (100.795 + 101.205) / 2 = 100.99.