Selection of efficient market risk models: Backtesting results evaluation with DEA approach

•The paper is focused on the evaluation of different VaR models.•Standard approaches evaluate the quantities of VaR violations for one particular confidence level.•We propose the application of DEA methodology in order to judge the results assuming different confidence levels.

Performance evaluation of financial models for pricing and risk estimation and subsequent selection of models that should be regarded as efficient is one of the most important tasks of financial engineering. The decision-making units in financial institutions consider various criteria, the most important being the correctness of the obtained results. Notwithstanding, some complex decision-making tasks require model evaluation under various circumstances or with different input data. In most cases it happens that a model, which seems to be perfect under given settings, is outperformed by another model, when the conditions change, and that there is no model that dominates under all circumstances. In this paper we suggest to apply a Data envelopment analysis (DEA) as a tool for overall evaluation of market risk estimation models. Instead of suggesting new DEA models, we try to utilize its standard formulation in order to analyze its suitability within a new topic of financial decision-making. Specifically, we evaluate several market risk models combining selected copula functions and marginal distributions over a large set of probability levels.