Explanation:
This question involves bond replication using the law of one price. We need to find the price of an 8% coupon bond using the given zero-coupon bond and 10% coupon bond.
Given:
Step 1: Create a replicating portfolio
Let's create a portfolio that replicates the 8% coupon bond using the other two bonds:
We need to find weights w₁ and w₂ such that: w₁ × (cash flows of zero-coupon) + w₂ × (cash flows of 10% coupon) = cash flows of 8% coupon
Step 2: Set up equations
Zero-coupon bond: Pays USD 100 at maturity (1 year) 10% coupon bond: Pays 5% × 100 = USD 5 at 6 months, and 5% × 100 + 100 = USD 105 at 1 year
At 6 months: w₁ × 0 + w₂ × 5 = 4 At 1 year: w₁ × 100 + w₂ × 105 = 104
Step 3: Solve the system
From first equation: w₂ = 4/5 = 0.8 Substitute into second equation: w₁ × 100 + 0.8 × 105 = 104 w₁ × 100 + 84 = 104 w₁ × 100 = 20 w₁ = 0.2
Step 4: Calculate price
Price of 8% coupon bond = w₁ × Price(zero) + w₂ × Price(10% coupon) = 0.2 × 96.12 + 0.8 × 106.20 = 19.224 + 84.96 = 104.184 ≈ USD 104.18
Therefore, the correct price is USD 104.18, which corresponds to option D.
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You have been asked to check for arbitrage opportunities in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. If a 1-year zero-coupon bond is priced at USD 96.12 and a 1-year bond paying a 10% coupon semi-annually is priced at USD 106.20, what should be the price of a 1-year Treasury bond that pays a coupon of 8% semiannually?
A
USD 98.10
B
USD 101.23
C
USD 103.35
D
USD 104.18
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