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FRM Part I · FRM Exam Part I · Swaps

A $100 million swap pays floating semiannually. The next floating payment is due in two months and was fixed at a 4% annual rate at the last reset. The discount factor for two months is 0.9950. Ignoring the fixed leg, what is the present value of the floating leg, which consists of that payment and the notional value implied at the next reset?

The floating leg is worth $101.49 million. The next payment is $2.0 million, and at that date the floating bond is worth par, so the total of $102 million is discounted two months at 0.9950. Treating it as exactly par would ignore the known payment.

  1. A$101.49 millionCorrect
  2. B$100.00 million
  3. C$102.00 million
  4. D$99.49 million

Explanation

The next payment is 100(0.04)/2=2.0 million. Right after that payment date, the floating bond is worth par, so the floating leg equals (100+2.0) discounted over two months: 102(0.9950)=101.49 million. $100 million wrongly applies the post-reset par rule today. $102 million ignores discounting.

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