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

A bank has a 5-year uncollateralised receive-fixed interest rate swap with a counterparty. Which description best fits the shape of its expected exposure profile over time, assuming no collateral and a standard diffusion of rates?

The exposure profile is hump-shaped: it rises at first as rate uncertainty accumulates, then falls toward zero at maturity as fewer remaining payments are left. Diffusion dominates early and amortisation dominates late, so exposure does not keep growing or start at its peak.

  1. AExposure rises monotonically until maturity because uncertainty always grows
  2. BExposure is flat because the notional is constant
  3. CExposure rises initially as uncertainty grows, then declines toward zero as remaining payments shrink (amortisation effect)Correct
  4. DExposure is highest at inception and falls linearly to zero

Explanation

Two effects compete: diffusion increases the spread of possible swap values over time, while amortisation reduces the remaining cash flows that can change in value. The diffusion effect dominates early and amortisation later, giving a hump shape that goes to zero at maturity. A monotonic rise ignores amortisation.

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