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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution

In a normal model with dr = λ dt + σ dw, the short rate is 4.00%, and annual basis-point volatility is 120 bps. A trader wants to rescale to a lognormal model that gives the same volatility at the current rate level. What percentage (lognormal) volatility should be used?

The equivalent lognormal volatility is 30%. Normal volatility of 1.20% divided by the current rate of 4.00% gives 0.30, because lognormal volatility times the rate level must equal the absolute basis-point volatility at that point.

  1. A3.0%
  2. B30.0%Correct
  3. C4.8%
  4. D12.0%

Explanation

Lognormal volatility times the rate equals the basis-point volatility: σ_LN × 4% = 1.20%. So σ_LN = 1.20/4.00 = 30%. Using 120/4 without unit conversion gives 30 expressed wrongly, and multiplying 1.2% by 4 gives 4.8%, which is the wrong operation.

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