Evaluation of backtesting on risk models based on data envelopment analysis

Grigorios Kontaxis and Ioannis E. Tsolas

Abstract

In this study, different value-at-risk (VaR) models, which are used to measure market risk, are analyzed under different estimation approaches and backtested with an alternative strategy. The methodologies examined include filtered historical simulation, extreme value theory, Monte Carlo simulation and historical simulation. Autoregressive-moving-average and generalized-autoregressive-conditional-heteroscedasticity models are used to estimate VaR. 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. Data envelopment analysis, which investigates the efficiency of VaR models using a number of different parameters, is carried out in lieu of standard backtesting techniques. This study shows that, for short horizons, some approaches underestimate VaR. However, a sufficient number of models present violation estimates that almost converge to the desired ones. Surprisingly, aside from historical simulation and some extreme value theory models, overlapping returns tend to yield conservative ten-day VaR estimations for most models; in cases of nonoverlapping returns, the results are satisfactory.