FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
A bond pays 50 in one year and 1,050 in two years. The continuously compounded rate is 4% per annum for both maturities. What is the bond's present value?
The present value is 1,017.31. Discount each cash flow by e raised to minus the rate times its own time: 50 for one year and 1,050 for two years at 4% continuous. Using annual compounding, discounting both flows one year, or skipping discounting all give wrong values.
- A1,017.31Correct
- B1,018.90
- C1,056.87
- D1,100.00
Explanation
PV = 50 e^-0.04 + 1,050 e^-0.08 = 50(0.960789) + 1,050(0.923116) = 48.04 + 969.27 = 1,017.31. The 1,018.90 option uses annual compounding at 4% instead of continuous. The 1,056.87 option discounts both cash flows for only one year. The 1,100.00 option applies no discounting.
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