Extremes✓ Mathematical
◆ The PatternExtreme events beyond normal-distribution assumptions
Financial returns exhibit fat tails — extreme moves occur far more often than a Gaussian predicts. Kurtosis > 3 signals leptokurtic behavior. Extreme Value Theory (EVT) models the tail with a Generalized Pareto Distribution (GPD):
P(X > x | X > u) ≈ (1 + ξ · (x−u)/β)−1/ξ
A positive ξ > 0 indicates a heavy (Pareto-type) tail. EVT lets us extrapolate loss quantiles beyond sample extremes.
// Interactive — kurtosis and tail weight visualization
Kurtosis
Black-swan readiness. Stress tests should use EVT-calibrated scenarios, not just historical worst days.
Pattern bridge: Kurtosis and distribution shapes are covered in The Toolkit — Distributions.