Question #28
Reading: Reading 26 The Arbitrage-Free Valuation Framework
PDF File: Reading 26 The Arbitrage-Free Valuation Framework.pdf
Page: 13
Status: Correct
Correct Answer: A
Question
A bond with a 10% annual coupon will mature in two years at par value. The current one- year spot rate is 8.5%. For the second year, the yield volatility model forecasts that the one- year rate will be either 8% or 9%. Using a binomial interest rate tree, what is the current price?
Answer Choices:
A. 101.837
B. 103.572
C. 102.659
Explanation
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 in nodal period 2: V2=100. In nodal period 1, there will be two possible
prices:
V1,U=[(100+10)/1.09+(100+10)/1.09]/2= 100.917
V1,L=[(100+10)/1.08+(100+10)/1.08]/2= 101.852
Thus
V0=[(100.917+10)/1.085+(101.852+10)/1.085]/2= 102.659