An Economic Evaluation of the Model Risk for Risk Models

Abstract

The recent experience from the global financial crisis has raised serious doubts about the accuracy of standard risk measures as a tool to quantify extreme downward risks. Standard risk measures are subject to a “model risk” due to the specification and estimation uncertainty. We propose a general adjustment of the Value-at-Risk to compute risk measures robust to the model risk. The proposed procedure aims empirically adjusting the imperfect quantile estimate assessing the good quality of VaR models such as frequency exceptions, independence of violations and magnitude of violations. Based on a long sample of U.S. data, we find an inverse U-shape relation between VaR model errors and the horizon: corrections (for model errors) are higher for short-term horizons but are also increasing for long-term horizons. We also provide a fair comparison between the main risk models using the same metric that corresponds to model risk required corrections.