An Extensive Comparison of Some Well-Established Value at Risk Methods

In the last two decades, several methods for estimating Value at Risk have been proposed in the literature. Four of the most successful approaches are conditional autoregressive Value at Risk, extreme value theory, filtered historical simulation and time-varying higher order conditional moments. In this paper, we compare their performances under both an empirical investigation using 80 assets and a large Monte Carlo simulation. From our analysis, we conclude that most of the methods seem not to imply huge numerical difficulties and, according to usual backtests and performance measurements, extreme value theory presents the best results most of the times, followed by filtered historical simulation.