Estimation Risk Effects on Backtesting for Parametric Value-at-Risk Models

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. Thereby the correct specification of parametric VaR models became of crucial importance in order to provide accurate and reliable risk measures. If the underlying risk model is not correctly specified, VaR estimates understate/overstate risk exposure. This can have dramatic consequences on stability and reputation of financial institutions or lead to sub-optimal capital allocation. We show that the use of the standard unconditional backtesting procedures to assess VaR models is completely misleading. These tests do not consider the impact of estimation risk and therefore 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 specification analyses. A Monte Carlo study illustrates our theoretical findings in finite-samples. Finally, an application to S&P500 Index shows the importance of this correction and its impact on capital requirements as imposed by Basel Accord, and on the choice of dynamic parametric models for risk management.