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CFA Level I · CFA Level I Exam · Pricing and Valuation of Interest Rate and Other Swaps

A swap with a notional of 10,000,000 has just reset its floating rate to 4.00% (annualized, 180/360 day count) for the next payment, which is due in 180 days. The discount factor for 180 days is 0.9709. The present value of the floating leg, including the notional's par value at that date, is closest to:

The floating leg is worth about 9,900,000. The next floating payment of 10,200,000 (notional plus 2% interest) is discounted back 180 days with a factor of 0.9709. It does not equal par here because the discount rate differs from the rate set at reset.

  1. A9,900,000Correct
  2. B10,000,000
  3. C10,200,000

Explanation

The floating leg is valued as a bond repaying notional plus the next coupon on the next payment date. The payment is 10,000,000 × (1 + 0.04 × 180/360) = 10,200,000. Discounting gives 10,200,000 × 0.9709 = 9,903,180, about 9,900,000. Assuming par at 10,000,000 wrongly assumes the discount rate equals the reset rate, and 10,200,000 is undiscounted.

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