Explanation

To calculate the price of a 3-year 0.2% annual coupon bond using forward rates, we need to discount each cash flow using the appropriate forward rates.

Given:

• Forward rates:
  • f(0,1) = 0.1% = 0.001 (for year 1)
  • f(1,1) = 0.3% = 0.003 (for year 2)
  • f(2,1) = 0.6% = 0.006 (for year 3)
• Coupon rate: 0.2% = 0.002
• Par value: 100

Cash flows:

• Year 1: Coupon = 100 × 0.002 = 0.2
• Year 2: Coupon = 100 × 0.002 = 0.2
• Year 3: Coupon + Principal = 0.2 + 100 = 100.2

Discount factors calculation:

1. Year 1 discount factor: DF₁ = 1 / (1 + f(0,1)) = 1 / (1 + 0.001) = 1 / 1.001 = 0.999000999

2. Year 2 discount factor: DF₂ = 1 / [(1 + f(0,1)) × (1 + f(1,1))] = 1 / (1.001 × 1.003) = 1 / (1.001 × 1.003) = 1 / 1.004003 = 0.99601396

3. Year 3 discount factor: DF₃ = 1 / [(1 + f(0,1)) × (1 + f(1,1)) × (1 + f(2,1))] = 1 / (1.001 × 1.003 × 1.006) = 1 / (1.001 × 1.003 × 1.006) = 1 / 1.010018018 = 0.990079

Present value of cash flows:

• PV₁ = 0.2 × DF₁ = 0.2 × 0.999000999 = 0.1998002
• PV₂ = 0.2 × DF₂ = 0.2 × 0.99601396 = 0.199202792
• PV₃ = 100.2 × DF₃ = 100.2 × 0.990079 = 99.2059158

Total price: Price = PV₁ + PV₂ + PV₃ = 0.1998002 + 0.199202792 + 99.2059158 = 99.604918792 ≈ 99.60

Verification with spot rates: We can also calculate spot rates from forward rates:

• s₁ = f(0,1) = 0.1%
• s₂ = [(1 + f(0,1)) × (1 + f(1,1))]^(1/2) - 1 = (1.001 × 1.003)^(1/2) - 1 = 1.004003^(0.5) - 1 = 0.0020005 = 0.20005%
• s₃ = [(1 + f(0,1)) × (1 + f(1,1)) × (1 + f(2,1))]^(1/3) - 1 = (1.001 × 1.003 × 1.006)^(1/3) - 1 = 1.010018018^(1/3) - 1 = 0.003333 = 0.3333%

Using spot rates: Price = 0.2/(1.001) + 0.2/(1.0020005)² + 100.2/(1.003333)³ = 0.1998 + 0.1992 + 99.2059 = 99.6049 ≈ 99.60

Therefore, the price is closest to 99.60, which corresponds to option C.