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FRM Part I · FRM Exam Part I · Swaps

A swap pays a floating LIBOR payment for the period from 6 to 12 months, with a notional of USD 50 million and semiannual compounding for the payment. Continuously compounded LIBOR zero rates are 3.0% for 6 months and 3.5% for 12 months. The 12-month OIS discount factor is 0.9650. Using LIBOR forwards and OIS discounting, what is the present value of this floating payment?

The present value is about USD 0.9747 million. The continuously compounded forward rate of 4.0% converts to 4.04% semiannual, giving a payment of 1.0101 million. Discounting it with the OIS factor of 0.9650 gives 0.9747 million. Using LIBOR discounting or skipping the conversion gives different, incorrect values.

  1. AUSD 0.9747 millionCorrect
  2. BUSD 0.9650 million
  3. CUSD 1.0101 million
  4. DUSD 0.9753 million

Explanation

Forward rate (continuous) = (3.5% x 1 - 3.0% x 0.5)/0.5 = 4.0%. Converted to semiannual compounding: 2 x (e^0.02 - 1) = 4.0402%. Payment = 50 x 0.040402 x 0.5 = 1.0101m. PV at OIS = 1.0101 x 0.9650 = 0.9747m. Discounting at the LIBOR factor e^-0.035 gives 0.9753, which is the wrong curve.

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