Skip to content

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

A risk analyst at a bank compares a normal short-rate model (constant absolute volatility) with a lognormal short-rate model in which the volatility of the rate is proportional to its level. Which statement best describes a key property of the lognormal model?

In a lognormal short-rate model the rate's basis-point volatility is proportional to its level, so it increases as rates rise, and the rate is always positive because its logarithm is normally distributed. Negative rates and constant basis-point volatility are features of normal models.

  1. AThe short rate can become negative when volatility is high
  2. BThe basis-point volatility of the rate rises as the level of the rate rises, and the rate stays positiveCorrect
  3. CThe basis-point volatility is independent of the rate level
  4. DRates are mean-reverting only when volatility is constant

Explanation

In a lognormal model dr = a r dt + sigma r dw, the absolute (basis-point) volatility equals sigma times r, so it rises with the rate level. The log of the rate is normally distributed, so the rate cannot go negative. Constant basis-point volatility and possible negative rates describe the normal model.

Did you get it right without looking?

One question tells you little. A timed set on The Art of Term Structure Models: Volatility and Distribution shows your real accuracy, how long you take and where you lose marks.

Practise The Art of Term Structure Models: Volatility and DistributionFree diagnostic mock

More The Art of Term Structure Models: Volatility and Distribution questions