Backtesting Parametric Value-at-Risk With Estimation Risk

One of the implications of the creation of Basel Committee on Banking Supervision wasthe 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 basedon VaR estimates. Therefore, appropriately constructed tests for assessing the out-of-sampleforecast accuracy of the VaR model (backtesting procedures) have become of crucial practicalimportance. In this paper we show that the use of the standard unconditional and independencebacktesting procedures to assess VaR models in out-of-sample composite environmentscan be misleading. These tests do not consider the impact of estimation risk and thereforemay use wrong critical values to assess market risk. The purpose of this paper is to quantifysuch estimation risk in a very general class of dynamic parametric VaR models and tocorrect 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 ourcorrected unconditional test can provide more accurately sized and more powerful tests thanthe uncorrected one. Finally, an application to Samp;P500 Index shows the importance of thiscorrection and its impact on capital requirements as imposed by Basel Accord