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FRM Part I · FRM Exam Part I · Swaps

A bank pays fixed 5% (semiannual) and receives floating on a $50 million swap. Payments remain in 0.25 years and 0.75 years. The floating payment due in 0.25 years was set at 4.8% per annum. Discount factors are 0.9900 for 0.25 years and 0.9700 for 0.75 years. Using forward rates implied by the discount factors to value the floating leg, what is the swap's value to the bank?

The swap is worth -$0.262 million to the pay-fixed bank. The fixed leg has PV 2.45 million. The floating leg has PV 1.188 million for the known payment plus 1.000 million for the forward-implied payment, totalling 2.188 million. Floating minus fixed equals -0.262 million.

  1. A-$0.262 millionCorrect
  2. B+$0.262 million
  3. C-$0.098 million
  4. D-$0.450 million

Explanation

Fixed payment is 50(0.05)/2=1.25 each date, PV = 1.25(0.99+0.97)=2.45. The first floating payment is 1.20, PV 1.188. The forward rate from 0.25 to 0.75 gives a payment of 50(0.99/0.97-1)=1.0309, PV 1.000. Floating PV is 2.188, so value = 2.188-2.45 = -0.262 million. Assuming the second floating payment also uses 4.8% gives -0.098 million, which is wrong because that rate is not the forward rate.

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