Backtesting Parametric Value-at-Risk With Estimation Risk

One of the implications of the creation of the Basel Committee on Banking Supervision was the implementation of Value-at-Risk (VaR) as the standard tool for measuring market risk. Since then, the capital requirements of commercial banks with trading activities are based on VaR estimates. Therefore, appropriately constructed tests for assessing the out-of-sample forecast accuracy of the VaR model (backtesting procedures) have become of crucial practical importance. In this article we show that the use of the standard unconditional and independence backtesting procedures to assess VaR models in out-of-sample composite environments can be misleading. These tests do not consider the impact of estimation risk, and therefore, may use wrong critical values to assess market risk. The purpose of this article is to quantify such estimation risk in a very general class of dynamic parametric VaR models and to correct standard backtesting procedures to provide valid inference in out-of-sample analyses. A Monte Carlo study illustrates our theoretical findings in finite-samples and shows that our corrected unconditional test can provide more accurately sized and more powerful tests than the uncorrected one. Finally, an application to the S&P 500 Index shows the importance of this correction and its impact on capital requirements as imposed by the Basel Accord.

Keywords: 

• Backtesting,
• Basel Accord,
• Conditional quantile,
• Estimation risk,
• Fixed, rolling, and recursive forecasting scheme,
• Forecast evaluation,
• Risk management,
• Value-at-Risk