Standard backtesting tests for VaR models (such as Kupiec's test and Christoffersen's independence tests) rely on asymptotic (chi-squared) distributions to determine critical values and p-values. However, when sample sizes are small or when looking at high confidence levels (e.g., extreme events like 99% VaR), the number of expected exceptions is very low. In such cases, the asymptotic distribution is a poor approximation of the actual finite-sample distribution, leading to tests that are incorrectly sized (i.e., the actual rejection rates diverge from the nominal significance level).

To remedy this, risk managers should compute p-values using exact binomial calculations or Monte Carlo simulations (the Dufour approach). Monte Carlo simulated p-values provide an exact test for any sample size, effectively resolving the size distortion issues associated with relying on asymptotic distributions in small samples.