Final answer:
To value a three-year, 6% annual pay bond with a face value of £100, discount the future cash flows (coupon payments and the principal) using the given spot rates. The present value of each year's cash flow is calculated and summed to obtain the bond's total present value, which represents the bond's arbitrage-free value.
Step-by-step explanation:
The valuation of a three-year, 6% annual pay bond requires discounting its future cash flows by the current spot rates that correspond to the bond's risk and liquidity characteristics. The bond has a face value of £100 and pays a 6% coupon on an annual basis. To find the arbitrage-free value of the bond, we need to calculate the present value (PV) of all future coupon payments and the face value using the given spot rates.
The present value formula for each cash flow is:
PV = Cash Flow / (1 + Spot Rate)^Time
Calculating each year:
- Year 1: £100 x 6% = £6; PV = £6 / (1 + 0.03)^1 = £5.83
- Year 2: £100 x 6% = £6; PV = £6 / (1 + 0.0375)^2 = £5.56
- Year 3: £100 x 6% + £100 (principal) = £106; PV = £106 / (1 + 0.04)^3 = £92.54
Summing up all the present values gives us the bond's total value:
Total PV = £5.83 + £5.56 + £92.54 = £103.93
Therefore, the arbitrage-free value of the bond is £103.93.