A key issue in implementing VaR and related risk measures is to obtain accurate estimates for the tails of the conditional profit and loss distribution at the relevant horizons. In the financial literature two main directions have been followed to estimate profit and loss distribution  conditional distributions for market risk management: fully nonparametric historical simulation methods and semi-parametric/nonparametric bootstrap methods based on dynamic models for asset returns.

VaR forecasts can be heavily affected by a few influential points, especially when long forecast horizons are considered. Robustness can be enhanced by fitting a generalized Pareto distribution to the tails of the residual distribution and sampling tail residuals from this density. However to ensure a sufficiently large breakdown point for the estimator of the generalized Pareto tails, a robust estimation is needed (see Dell’Aquila, Ronnchetti, 2006).The aim of the paper is to compare selected approaches to computing Value at Risk. We will consider classical and robust conditional (GARCH) and unconditional (EVT) semi-nonparametric models where tail events are modeled using generalized Pareto distribution. In the result we want to answer the question if the robust semi-nonparametric procedure generate more accurate VaRs than classical approach does. Generally, we show that robust VaR predictions are accurate and stable over time.
Section 2 introduces semi-nonparametric bootstrap and extreme value estimation methods for VaR predictions, along with their robust version. Section 3 presents the real data application to VaR prediction and backtesting for European and Canadian indices, comparing the performance of classical and robust semi-nonparametric VaR prediction methods. Section 4 concludes.