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

In a lognormal short-rate model dr = a·r·dt + σ·r·dw, the current short rate is 5% and annual volatility σ is 20%. What is the approximate one-year standard deviation of the change in the short rate, in basis points?

The basis-point volatility equals the proportional volatility times the rate level, so 20% times 5% gives 1%, or 100 basis points per year. Lognormal models scale absolute volatility with the rate level.

  1. A10 bp
  2. B100 bpCorrect
  3. C20 bp
  4. D200 bp

Explanation

Basis-point volatility = σ × r = 0.20 × 5% = 1.00% = 100 bp per year. Using 20 bp or 200 bp confuses the percentage volatility with a basis-point measure; 10 bp results from multiplying 0.20 by 0.5%.

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