
Explanation:
The 1-year discount factor is . Assuming semiannual compounding, the 1-year semiannual spot rate is found by $1 / (1 + r_1/2)^2 = 0.9831(1 + r_1/2)^2 = 1.01719r_1 \approx 1.71%$.
The bond price is the present value of its cash flows (semiannual coupon of $2.5 and principal of $100):
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Q.28 A trader wants to price a bond with a 5% coupon rate and a maturity of 1.5 years. The coupon payment is semiannual. Due to a bug in the system, the trader was not able to download the complete structure of the market spot rates. The table below shows the data the trader was able to gather.
| Term in years | Spot rates |
|---|---|
| 0.5 | 1.10% |
| 1.0 | n/a |
| 1.5 | 3.00% |
Which of the following are the missing spot rate and the bond price if the 1-year discount factor is 0.9831?
A
1-year spot rate = 1.71%; Bond price = 102.967
B
1-year spot rate = 2.10%; Bond price = 102.957
C
1-year spot rate = 2.50%; Bond price = 102.947
D
1-year spot rate = 2.65%; Bond price = 104.944
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