FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
The one-year spot rate is 2%. The one-year forward rate starting in one year is 4%, and the one-year forward rate starting in two years is 6% (all annually compounded). What is the no-arbitrage price of a three-year zero-coupon bond with face value 100?
The three-year zero-coupon bond should price at about 88.93. Compounding the spot and forward rates gives 1.02 × 1.04 × 1.06 = 1.124448, and 100 divided by that figure is 88.93. Adding the rates to 12% would overstate the price.
- A83.96
- B88.93Correct
- C89.29
- D94.23
Explanation
Growth over three years is 1.02 × 1.04 × 1.06 = 1.124448. Price = 100/1.124448 = 88.93. The 89.29 option adds the rates to get 12% (100/1.12), ignoring compounding; 83.96 uses 6% for all years and 94.23 uses 2% for all years.
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