Explanation

This is another bond replication problem using the law of one price. We need to find the price of the 4½% coupon bond using the other two bonds.

Given:

• 2 7/8% bond: Price = 94.40
• 6 1/4% bond: Price = 101.30
• Face value: USD 100 (assumed)
• All bonds mature in 1 year with semi-annual coupons

Step 1: Calculate semi-annual coupon payments

• 2 7/8% bond: (2.875%/2) × 100 = 1.4375 per period
• 4 1/2% bond: (4.5%/2) × 100 = 2.25 per period
• 6 1/4% bond: (6.25%/2) × 100 = 3.125 per period

Step 2: Create replicating portfolio

We need to find weights w₁ and w₂ such that: w₁ × (cash flows of 2 7/8% bond) + w₂ × (cash flows of 6 1/4% bond) = cash flows of 4 1/2% bond

At coupon payment: w₁ × 1.4375 + w₂ × 3.125 = 2.25 At maturity: w₁ × (100 + 1.4375) + w₂ × (100 + 3.125) = 100 + 2.25

Step 3: Solve the system

From first equation: w₁ × 1.4375 + w₂ × 3.125 = 2.25 From second equation: w₁ × 101.4375 + w₂ × 103.125 = 102.25

Multiply first equation by 101.4375/1.4375 ≈ 70.57: w₁ × 101.4375 + w₂ × 220.53 = 158.78

Subtract from second equation: (w₁ × 101.4375 + w₂ × 103.125) - (w₁ × 101.4375 + w₂ × 220.53) = 102.25 - 158.78 w₂ × (103.125 - 220.53) = -56.53 w₂ × (-117.405) = -56.53 w₂ = 56.53/117.405 ≈ 0.4815

From first equation: w₁ × 1.4375 + 0.4815 × 3.125 = 2.25 w₁ × 1.4375 + 1.5047 = 2.25 w₁ × 1.4375 = 0.7453 w₁ = 0.5185

Step 4: Calculate price

Price of 4½% bond = w₁ × Price(2 7/8%) + w₂ × Price(6 1/4%) = 0.5185 × 94.40 + 0.4815 × 101.30 = 48.94 + 48.77 = 97.71

Therefore, the correct price is approximately USD 97.71, which corresponds to option C.