Question #32
Reading: Reading 26 The Arbitrage-Free Valuation Framework
PDF File: Reading 26 The Arbitrage-Free Valuation Framework.pdf
Page: 15
Status: Correct
Correct Answer: A
Question
Using the following interest rate tree of semiannual interest rates what is the value of an option free bond that has one year remaining to maturity and has 5% coupon rate with semi-annual coupon payments. Today 6 Months 7.30% 6.20% 5.90%
Answer Choices:
A. 97.53
B. 98.98
C. 98.67
Explanation
The option-free bond price tree is as follows:
100.00
A → 98.89
98.67
100.00
99.56
100.00
As an example, the price at node A is obtained as follows:
PriceA = (prob × (Pup + (coupon / 2)) + prob × (Pdown + (coupon / 2)) / (1 + (rate /
2)) = (0.5 × (100 + 2.5) + 0.5 × (100 + 2.5) / (1 + (0.0730 / 2)) = 98.89. The bond
values at the other nodes are obtained in the same way.
The calculation for node 0 or time 0 is
0.5[(98.89 + 2.5) / (1+ 0.062 / 2) + (99.56 + 2.5) / (1 + 0.062 / 2)] =
0.5(98.3414 + 98.9913) = 98.6663