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

A 1-year zero-coupon bond with face 100 trades at 97.00. A 2-year bond with face 100 and a 4% annual coupon trades at 97.48. All are default-free. What 2-year discount factor is implied by no-arbitrage pricing from these two bonds?

Value the first coupon with the 1-year factor: 4 x 0.97 = 3.88. Subtract it from 97.48 to get 93.60, then divide by the final payment of 104. The implied 2-year discount factor is 0.9000.

  1. A0.9000Correct
  2. B0.9373
  3. C0.8988
  4. D0.9700

Explanation

The 1-year discount factor is 0.97. Then 97.48 = 4 x 0.97 + 104 x d2, so 104 x d2 = 97.48 - 3.88 = 93.60. This gives d2 = 0.9000. Dividing the whole price by 104 (0.9373) ignores the value of the first coupon. Subtracting the undiscounted coupon of 4 gives 0.8988.

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