Lognormal distribution

The distribution of a variable whose natural logarithm is normally distributed. Bounded below at zero and skewed right, it suits asset prices, which cannot go negative but have no upper limit.

Where you will meet it

Lognormal distribution appears in 3 learning outcomes on the CFA syllabus. A few of them:

• Explain continuous compounding and the lognormal distribution
  CFA Level I · Quantitative Methods

  “A variable is lognormally distributed when its natural logarithm is normally distributed.”

• Explain the framework of a binomial tree for interest rates
  CFA Level II · Fixed Income

  “In the standard lognormal model, neighbouring rates at the same date differ by the factor e raised to 2σ, where σ is the annual volatility of rates, so the lower rate equals the upper rate × e raised to −2σ.”

• Name the assumptions behind the Black–Scholes–Merton model for valuing options
  CFA Level II · Derivatives and Risk Management

  “In Black–Scholes–Merton the underlying follows geometric Brownian motion, so prices are lognormally distributed and continuously compounded returns are normal.”

Practise it

• Today's practice question One question, with every wrong option explained.
• Free Level I diagnostic test Twelve questions that show which topics to start with.
• Free finance calculators Check your arithmetic on the exam's core formulas.

All terms beginning with L · Glossary