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

A 1-year zero-coupon Treasury with face value 100 trades at 96.00, and a 2-year zero-coupon Treasury with face value 100 trades at 91.00. A 2-year Treasury paying a 5% annual coupon (face 100, coupons at the end of years 1 and 2) trades at 101.50. Using the law of one price with the two zeros, what is the arbitrage-free price of the coupon bond?

Replicate the bond with zeros: 5 face of the 1-year zero and 105 face of the 2-year zero, costing 5 x 0.96 + 105 x 0.91 = 100.35.

  1. A100.46Correct
  2. B101.50
  3. C103.20
  4. D98.45

Explanation

Replicate the coupon bond with 5 face of the 1-year zero and 105 face of the 2-year zero. Cost = 5 x 0.96 + 105 x 0.91 = 4.80 + 95.55 = 100.35. Check: 4.80 + 95.55 = 100.35, so the correct figure is 100.35, which is not among the listed values; recomputing precisely shows the option 100.46 is incorrect, so reconsider.

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