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FRM Part II · FRM Exam Part II · Future Value and Exposure

A bank has a single uncollateralised interest rate swap with a corporate client. Which statement best describes why the expected exposure profile of a single at-the-money, fixed-for-floating interest rate swap typically rises and then falls over its life?

The swap's exposure profile is hump-shaped because the diffusion effect widens the range of possible values over time while the amortisation effect shrinks remaining cash flows as maturity approaches. Early on diffusion dominates, later amortisation dominates, so exposure peaks at an intermediate time.

  1. AInterest rate volatility is highest at inception, so exposure is greatest immediately
  2. BUncertainty in the swap value grows with time, but the number of remaining cash flows to be exchanged declines, producing a hump (amortisation effect dominates later)Correct
  3. CCredit spreads of the counterparty widen steadily, raising exposure until maturity
  4. DMargin requirements rise steadily until maturity, which reduces exposure only at the end

Explanation

The diffusion effect increases the spread of possible swap values as time passes, while the amortisation effect reduces the remaining cash flows and so exposure as maturity nears. The combination yields a hump-shaped profile. Counterparty spreads do not drive exposure; they drive CVA.

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