Question #89
Reading: Reading 27 Valuation and Analysis of Bonds With Embedded Options - Anwers
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Question
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?
Answer Choices:
A. 100.279
B. 100.558
C. 101.000. 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 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. (Module 27.2, LOS 27.f)
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