Variance of a lognormal

MediumRandom Variables Finance & Derivatives~5m

$\ln X \sim N(\mu,\sigma^2)$ with $\mu = 0$ and $\sigma^2 = 2$ (so $X$ is lognormal). Compute the variance $\mathrm{Var}(X)$ . (to 3 decimals)

Show hints (2)+

Var(X) = E[X²] − (E[X])²; get each from the normal MGF at t = 2 and t = 1.
E[X²] = e^(2μ+2σ²), E[X] = e^(μ+σ²/2); with μ=0, σ²=2 that's e⁴ − e².

Answer

Reveal answer →

47.209 (± 0.01)

Create a free account to see the full worked solution and track your progress.

Create a free account

Interview format: Prop Trading, Systematic & Data-Driven Trading

Related questions