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FRM Part II · FRM Exam Part II · Counterparty Risk and Beyond

A risk manager reports exposure profiles for a 5-year uncollateralized interest rate swap with a fixed notional paying a fixed rate. Which statement best describes the typical shape of the expected exposure profile over the life of the swap and why?

The expected exposure profile is hump-shaped: it rises first and then falls to zero at maturity. Early on, growing uncertainty about rates (diffusion) dominates, but later the shrinking number of remaining cash flows (amortization) dominates.

  1. AIt declines linearly to zero because the notional is amortizing
  2. BIt rises initially then falls toward zero, as the diffusion effect increases uncertainty while the amortization effect reduces remaining cash flowsCorrect
  3. CIt is flat, because the swap has zero value at inception and rates are symmetric
  4. DIt rises continuously until maturity because uncertainty grows with time

Explanation

For a non-amortizing swap, the diffusion effect widens the distribution of future values as time passes, while the amortization effect shrinks the number of remaining payments to exchange. Combined, expected exposure forms a hump, peaking roughly at one-third to one-half of maturity, and goes to zero at maturity.

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