Value at Risk (VaR)
Quantitative Finance glossary · Quantitative Finance
Definition
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.
Value at Risk (VaR) in plain English
Value at Risk answers a nervous question a bank asks every day: 'On a normal-ish bad day, how much could I lose?' A 99% one-day VaR of $1 million means that on 99 out of 100 days you won't lose more than a million — but it says nothing about how ugly that leftover 1% of days gets. People compute it three ways: assume losses follow a tidy bell curve (parametric), just look at how bad things actually got in past data (historical simulation), or run thousands of simulated futures (Monte Carlo). Its big flaw is that it draws a line at the cliff's edge but refuses to look over it, so regulators (Basel FRTB, 2019) shifted toward Expected Shortfall, which averages the losses in that scary tail instead of ignoring them.
Also called: VaR
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