Backtesting Parametric Value-at-Risk With Estimation Risk

Abstract:     
One of the implications of the creation of 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 paper 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 paper 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 S&P500 Index shows the importance of this
correction and its impact on capital requirements as imposed by Basel Accord.

Number of Pages in PDF File: 39

Keywords: Backtesting; Basel Accord; Conditional Quantile; Estimation Risk; Forecast evaluation; Fixed, rolling and recursive forecasting scheme; Risk management; Value at Risk

JEL Classification: C52, C22, G21, G32

working papers series