Value-at-Risk Backtesting Procedures Based on Loss Functions: Simulation Analysis of the Power of Tests

Abstract

The definition of Value at Risk is quite general. There are many approaches that may lead to various VaR values. Backtesting is a necessary statistical procedure to test VaR models and select the best one. There are a lot of techniques for validating VaR models. Usually risk managers are not concerned about their statistical power. The goal of this paper is to compare statistical power of specific backtest procedures but also to examine the problem of limited data sets (observed in practice). A loss function approach is usually used to rank correct VaR models, but it is also possible to evaluate VaR models by using that approach. This paper presents the idea of loss functions and compares the statistical power of backtests based on a various loss functions with the Kupiec and Berkowitz approach. Simulated data representing asset returns are used here. This paper is a continuation of earlier pieces of research done by the author.