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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

The discount factors are d(1) = 0.9700, d(2) = 0.9300 and d(3) = 0.8900. A 3-year bond with face value 100 pays an annual coupon of 4%. What is its fair price?

The fair price is 100.16. Each cash flow is multiplied by its own discount factor: 4 times 0.97, 4 times 0.93 and 104 times 0.89, which sum to 3.88 + 3.72 + 92.56. The final payment includes both coupon and principal.

  1. A100.16Correct
  2. B96.60
  3. C104.32
  4. D101.00

Explanation

Price = 4(0.97) + 4(0.93) + 104(0.89) = 3.88 + 3.72 + 92.56 = 100.16. Leaving the final coupon out of the last cash flow gives 96.60. Using d(2) for the final payment gives 104.32. Failing to discount the coupons gives 101.00.

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