Contrast three ways to estimate VaR: Monte Carlo simulation, historical simulation, and the parametric (variance–covariance) method

The parametric method assumes normally distributed returns and uses expected returns, volatilities and correlations; it is quick but misstates risk for fat-tailed returns and for options, whose payoffs are non-linear. Historical simulation revalues today's portfolio under the actual returns of a past window and reads VaR from the chosen percentile; it needs no distribution assumption and handles options, but depends entirely on whether the window contains stressful periods. Monte Carlo simulation draws many scenarios from an assumed model, fully revalues the portfolio in each, and reads off the percentile; it suits complex instruments and can include fat tails, but depends on the model and is computationally heavy. The trap is assuming historical simulation captures risks absent from its look-back period.