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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift

A trader calibrates Model 1 (zero drift) to the current term structure by matching a single volatility to an option price. Later, the trader sees the model produce a one-year-ahead 95% range for the short rate of 2.00% ± 1.96σ, with σ = 90 bp. Which range is closest?

The range is 2.00% ± 1.96 × 0.90%, or about 0.24% to 3.76%. With zero drift, the expected rate stays at 2.00% and one-year standard deviation equals σ, 90 basis points, so the 95% band is ±176 basis points.

  1. A0.24% to 3.76%Correct
  2. B0.20% to 3.80%
  3. C1.10% to 2.90%
  4. D−0.10% to 4.10%

Explanation

With zero drift and T = 1 year, the standard deviation is 90 bp. 1.96 × 90 = 176.4 bp, giving 2.00% ± 1.764%, i.e. 0.236% to 3.764%, rounded to 0.24% to 3.76%. The 0.20 to 3.80 range uses a rounded multiplier of 2.0 (180 bp), which is less accurate.

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