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FRM Part II · FRM Exam Part II · Credit Value Adjustment

For an uncollateralised interest rate swap with a bullet notional and no margin, which describes the typical shape of the expected exposure profile over the life of the swap, and why?

The profile rises then falls. Early on, growing rate uncertainty increases potential positive value, but as payments are exchanged fewer cash flows remain, so exposure shrinks toward zero at maturity, producing a hump-shaped profile.

  1. AIt declines linearly because the notional amortises
  2. BIt rises then falls, as diffusion increases uncertainty initially while the remaining payments shrink toward maturityCorrect
  3. CIt is flat because the notional is constant
  4. DIt rises monotonically until maturity because volatility keeps growing

Explanation

Two effects compete: rising uncertainty in rates (diffusion effect) and fewer remaining cash flows (amortisation effect). The result is a hump-shaped profile peaking at around one-third to one-half of the life. A monotonic rise ignores the roll-off of cash flows, which drives exposure to zero at maturity.

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