Skip to content

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

A lognormal short-rate model is specified as dr = a·r·dt + σ·r·dw (no mean reversion), with σ = 20% and a constant a. A trader notes that the rate is currently 5%. Which conclusion about this model is most appropriate?

In a lognormal model volatility is σ times the rate, so at a 5% rate and σ of 20% the basis point volatility is 1%, or 100 bps. Percentage volatility is constant and rates cannot become negative.

  1. ARates can become negative since the Brownian shock is normally distributed
  2. BPercentage volatility is constant at 20%, so basis point volatility is 100 bps at a 5% rate, and rates remain positiveCorrect
  3. CBasis point volatility is constant at 20 bps regardless of the rate level
  4. DBasis point volatility is 20% × √5% = 447 bps, and rates remain positive

Explanation

In the lognormal model, volatility of the rate is σr, so percentage volatility is constant at 20%. Basis point volatility = 0.20 × 5% = 1% = 100 bps. Because the process is multiplicative, r stays positive. The 447 bps figure mistakenly applies a CIR square-root form.

Did you get it right without looking?

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

Practise The Art of Term Structure Models: DriftFree diagnostic mock

More The Art of Term Structure Models: Drift questions