Distribution whose logarithm follows a normal law, widely used to model heavy-tailed losses and strictly positive amounts.
A random variable X follows a lognormal distribution with parameters μ and σ if ln(X) follows a normal distribution N(μ, σ²). The lognormal is right-skewed (heavy right tail), making it suited to insurance loss modeling: small claims are frequent, large ones are rare but possible. It is fully characterized by two parameters: μ (log-scale parameter) and σ (shape parameter). VaR and TVaR have closed-form expressions. It is notably used in solvency models (Solvency II standard formula) for non-life underwriting risk and cyber loss modeling. Its heavy tail is more realistic than the normal for extreme losses.
Cyber losses modeled as lognormal μ = 12, σ = 1.2. VaR at 99.5% (Solvency II SCR level) ≈ e^(12 + 1.2 × 2.576) ≈ 1.15 M EUR.
lognormal distribution, distribution log-normale, log-normal, loi lognormale