Value at risk
Estimate a loss threshold at a stated probability
Value at risk is a specified quantile of the loss distribution over a stated horizon. Historical simulation uses observed scenarios, parametric approaches impose a distributional model, and Monte Carlo approaches simulate model-based outcomes. VaR describes a threshold, not the average or maximum loss beyond it. Confidence level, horizon, valuation method and loss convention must be explicit.
Choose VaR for studying loss quantiles or comparing risk-model calibration when exposures and a defensible loss distribution can be constructed. Pair the threshold with tail-severity measures and scenario analysis.
Strengths
- Provides a clearly defined quantile with observable exceedances
- Supports comparison of forecast coverage across models
Limitations
- Says little about losses beyond the threshold
- Tail estimates are sensitive to sparse observations and distributional assumptions
Know the boundary
A 99% VaR is neither a worst-case loss nor a statement that losses cannot exceed the threshold.