Value at Risk (VaR)

Quantitative Finance Glossary

Loss threshold not exceeded with confidence α over horizon h: VaR_α = -infx : F_L(x) ≥ α — the α-quantile of the loss distribution. Three computation methods: parametric (delta-normal, Gaussian assumption), historical simulation (empirical quantile of h-day P&L over the lookback), and Monte Carlo. Not subadditive (Artzner et al. 1999), hence not coherent — Basel FRTB replaced VaR with 97.5% Expected Shortfall in 2019. Says nothing about the tail beyond the threshold, which is precisely where losses are most consequential.

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