Evaluation of backtesting techniques on risk models with different horizons

In this study different value-at-risk (VaR) models, which are used to measure market risk, are analyzed under different estimation approaches (filtered historical simulation, extreme value theory and Monte Carlo simulation) and backtested with different techniques. The autoregressive-moving-average and generalized-autoregressive-conditional-heteroscedasticity models are used to estimate VaR. In particular, selected VaR functions, marginal distributions and different horizons are combined over a set of extreme probability levels using the time series of the Financial Times Stock Exchange 100 Index. Several backtesting techniques are examined in this research, such as Kupiec’s proportion-of-failures test and Christoffersen’s independence test. This study shows that, for short horizons, some approaches underestimate VaR. However, various models present violation estimates that almost converge to the desired ones, according to the confidence levels used. Further, nonoverlapping returns tend to yield satisfactory results for most models. The main conclusion of this study is that the horizon selection can affect the estimation, and consequently the backtesting, of VaR models in some cases.