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FRM Part I · FRM Exam Part I · Properties of Interest Rates

A 2-year bond with face value 100 pays an annual coupon of 6, with the next coupon in one year. Continuously compounded zero rates are 4% for 1 year and 5% for 2 years. What is the bond price?

The bond price is about 101.68. Discount the year-1 coupon of 6 at the 4% zero rate (5.76) and the year-2 cash flow of 106 at the 5% zero rate (95.91). Each cash flow must use the zero rate matching its own maturity.

  1. A101.68Correct
  2. B101.62
  3. C103.61
  4. D96.25

Explanation

Discount each cash flow at its own zero rate. 6e^(-0.04) = 5.7647 and 106e^(-0.10) = 95.9127, giving 101.68. Discounting everything at 5% gives 101.62, which is wrong because the year-1 coupon must use the 1-year rate. The 96.25 distractor drops the 6 coupon at year 2.

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