FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
Annually compounded spot rates are 2.00% for one year and 3.00% for two years. What is the two-year par yield, paying an annual coupon, closest to?
The two-year par yield is about 2.99%. It equals one minus the two-year discount factor, divided by the sum of the one- and two-year discount factors. It sits slightly below the 3.00% spot rate because the earlier coupon is discounted at the lower one-year spot rate.
- A2.00%
- B2.50%
- C2.99%Correct
- D3.50%
Explanation
Discount factors: d1 = 1/1.02 = 0.980392, d2 = 1/1.0609 = 0.942596. Par coupon c = (1 − d2)/(d1 + d2) = 0.057404/1.922988 = 2.985%, about 2.99%. It is below the 3.00% two-year spot rate because the coupon payment at year 1 is discounted at the lower one-year rate.
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