Comparing VaR Approximation Methods that Use the First Four Moments as Inputs

This article compares four methods used to approximate value at risk (VaR) from the first four moments of a probability distribution: Cornish–Fisher, Edgeworth, Gram–Charlier, and Johnson distributions. Increasing rearrangements are applied to the first three methods. Simulation results suggest that for large sample situations, Johnson distributions yield the most accurate VaR approximation. For small sample situations with small tail probabilities, Johnson distributions yield the worst approximation. A particularly relevant case would be in banking applications for calculating the size of operational risk to cover certain loss types. For this case, the rearranged Gram–Charlier method is recommended.