A distribution in which the logarithm of the variable is normal. It is used for asset prices because it cannot fall below zero.
Where you will meet it
Lognormal distribution comes up in 17 learning outcome notes across the FRM syllabus.
A few of them:
Common Univariate Random Variables FRM Part I · Quantitative analysis
“Lognormal means the log is normal, so values are positive and right-skewed, the standard model for prices.”
Operational Risk FRM Part I · Valuation and risk models
“The second is severity, how large each loss is, commonly lognormal.”
Estimating Market Risk Measures: An Introduction and Overview FRM Part II · Market risk measurement and management
“If instead the price is lognormal, so geometric (log) returns over the horizon are normal with mean μ and standard deviation σ, then VaR = value × (1 − e^(μ − z × σ)).”
Risk Measurement and Assessment FRM Part II · Operational risk and resilience
“The loss distribution approach combines a frequency distribution, often Poisson, with a severity distribution, often lognormal, to simulate annual losses, and reads capital from a high quantile such as 99.9%.”
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