Question #48
Reading: Reading 27 Valuation and Analysis of Bonds With Embedded Options - Anwers
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Question
Using the following tree of semiannual interest rates what is the value of a putable semiannual bond that has one year remaining to maturity, a put price of 98 and a 4% coupon rate? The bond is putable today. 7.59% 6.35% 5.33%
Answer Choices:
A. 98.00
B. 98.75
C. 97.92. Explanation The putable bond price tree is as follows: 100.00 A ==> 98.27 98.00 100.00 99.35 100.00 As an example, the price at node A is obtained as follows: PriceA = max{(prob × (Pup + coupon/2) + prob × (Pdown + coupon/2))/(1 + rate/2), putl price} = max{(0.5 × (100 + 2) + 0.5 × (100 + 2))/(1 + 0.0759/2),98} = 98.27. The bond values at the other nodes are obtained in the same way. The price at node 0 = [0.5 × (98.27+2) + 0.5 × (99.35+2)]/ (1 + 0.0635/2) = $97.71 but since this is less than the put price of $98 the bond price will be $98. (Module 27.2, LOS 27.f)
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