Question #66
Reading: Reading 27 Valuation and Analysis of Bonds With Embedded Options - Anwers
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Question
Using the following interest rate tree, what is the value of a callable bond that has two years remaining to maturity, a call price of 99, and a 2.50% coupon rate? Assume that the call option can be exercised at t=1 year from now. 3.80% 3.18% 2.61%
Answer Choices:
A. 99.21
B. 98.25
C. 98.65. Explanation The callable bond price tree is as follows: 100.00 98.75 98.26 100.00 99.00 100.00 The formula for the price at each node is: Price = min{(prob × (Pup + coupon) + prob × (Pdown + coupon)) / (1 + rate), call price}. Up Node at t = 0.5: min{(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + 0.038), 99} = 98.75. Down Node at t = 0.5: min{(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + 0.026), 99} = 99.00. Node at t = 0.0: min{(0.5 × (98.75 + 2.5) + 0.5 × (99 + 2.5)) / (1 + 0.0318), 99} = 98.25. (Module 27.2, LOS 27.f)
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