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

In a lognormal model with dr = a r dt + sigma r dw, the annualized lognormal (percentage) volatility is sigma = 20%. The current short rate is 5.00%. What is the approximate annualized basis-point volatility of the short rate?

Basis-point volatility in a lognormal model equals percentage volatility times the rate level. With 20% volatility and a 5% short rate, that is 0.20 times 5%, or 1%, which is 100 basis points per year.

  1. A20 bps
  2. B100 bpsCorrect
  3. C250 bps
  4. D400 bps

Explanation

Basis-point volatility = sigma x r = 0.20 x 5.00% = 1.00% = 100 bps. The 20 bps figure wrongly divides by 5 ... and 400 bps wrongly divides rate by sigma (5/0.2 = 25 gives 2500 bps; 4% confuses the base). 250 bps would come from sigma 50%.

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