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

The 3-year spot rate is 4.00% with continuous compounding. What is the 3-year discount factor?

The 3-year discount factor is 0.8869. With continuous compounding it equals e raised to minus the rate times time, so e^-0.12. Annual compounding would give 0.8890, and a linear approximation would give 0.88, both of which are incorrect here.

  1. A0.8869Correct
  2. B0.8890
  3. C0.9608
  4. D0.8800

Explanation

d(3) = exp(-0.04 x 3) = exp(-0.12) = 0.8869. Using annual compounding, 1.04^-3, gives 0.8890. Using only one year gives 0.9608. Linear approximation 1 - 0.12 gives 0.8800, which ignores the exponential.

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