Robust Backtesting Tests for Value-at-Risk Models

Backtesting methods are statistical tests designed to uncover excessive risk-taking from financial institutions. We show in this paper that these methods are subject to the presence of model risk produced by a wrong specification of the conditional VaR model, and derive its effect on the asymptotic distribution of the relevant out-of-sample tests. We also show that in the absence of estimation risk, the unconditional backtest is affected by model misspecification but the independence test is not. Our solution for the general case consists on proposing robust subsampling techniques to approximate the true sampling distribution of these tests. We carry out a Monte Carlo study to see the importance of these effects in finite samples for location-scale models that are wrongly specified but correct on average. An application to Dow-Jones Index shows the impact of correcting for model risk on backtesting procedures for different dynamic VaR models measuring risk exposure