Explanation:
To calculate the arbitrage-free value of the bond, we need to discount each cash flow using the appropriate spot rates derived from the par rates.
Step 1: Calculate spot rates from par rates
For 1-year bond: Par rate = 3.00%, so 1-year spot rate (z₁) = 3.00%
For 2-year bond: Par rate = 5.00% Using the formula: 100 = 5/(1+z₁) + 105/(1+z₂)² Where z₁ = 3.00% 100 = 5/(1.03) + 105/(1+z₂)² 100 = 4.8544 + 105/(1+z₂)² 95.1456 = 105/(1+z₂)² (1+z₂)² = 105/95.1456 = 1.1036 1+z₂ = √1.1036 = 1.0505 z₂ = 5.05%
Step 2: Calculate bond value using spot rates
The bond has:
Value = 6/(1.03) + 106/(1.0505)² = 5.8252 + 106/1.1036 = 5.8252 + 96.0548 = 101.88
Therefore, the arbitrage-free value is closest to 101.88.
Ultimate access to all questions.
An analyst gathers the following information about two annual coupon benchmark bonds:
| Maturity (Years) | Par Rate |
|---|---|
| 1 | 3.00% |
| 2 | 5.00% |
The arbitrage-free value of an option-free, 2-year, 6% annual coupon bond with the same risk and liquidity as the benchmark bonds is closest to:
A
101.57.
B
101.88.
C
101.97.
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