Value at Risk (VaR) in Trading: Historical, Parametric & Monte Carlo Models [2026]
Date Published
1. What Value at Risk Really Measures
The Three Methodologies Compared
For a portfolio of $100,000 with a daily return volatility of 1.2%, a 99% 1-day parametric VaR is calculated as: VaR_0.99 = 2.326 * sigma * Portfolio Value = $2,791. This means on 99 out of 100 days, daily losses should not exceed $2,791.
2. Tail-Risk Methodology Matrix
Parametric vs Historical vs Monte Carlo vs Expected Shortfall
Below is the empirical comparison of tail-risk models evaluated during severe historical market dislocations.
Methodology | Distributional Assumption | 99% 1-Day Est ($100k) | Crisis Reliability (2008 / 2020) Parametric (Normal) | Gaussian Bell Curve | $2,791 | Severe Failure (Underestimates tail by 4x) Historical Simulation | Past Empirical Sample | $3,850 | Moderate (Captures past crashes) Monte Carlo (Fat-Tail) | Student-t / GARCH Vol | $4,420 | Robust (Simulates volatility clustering) Conditional VaR (CVaR) | Expected Tail Loss Beyond VaR | $5,240 | Superior (Models true catastrophic loss)
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