Skip to content

FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A stock follows geometric Brownian motion with expected return μ = 12% per year and volatility σ = 20% per year. Using the BSM lognormal model, what is the expected continuously compounded return per year (the drift of ln S)?

The expected continuously compounded return is μ − σ²/2, which is 12% − 2% = 10% per year. The volatility drag of half the variance (0.02) is subtracted from the 12% expected return, because ln S has that lower drift.

  1. A12%
  2. B10%Correct
  3. C14%
  4. D8%

Explanation

The drift of ln S is μ − σ²/2 = 0.12 − 0.04/2 = 0.12 − 0.02 = 0.10, or 10%. Option A ignores the volatility adjustment. Option C adds the adjustment instead of subtracting it. Option D subtracts σ² fully (0.12 − 0.04) rather than half of it.

Did you get it right without looking?

One question tells you little. A timed set on The Black-Scholes-Merton Model shows your real accuracy, how long you take and where you lose marks.

Practise The Black-Scholes-Merton ModelFree diagnostic mock

More The Black-Scholes-Merton Model questions