Backtesting Parametric Value-at-Risk With Estimation Risk

39 Pages Posted: 22 Mar 2007 Last revised: 5 Sep 2008

See all articles by Juan Carlos Escanciano

Juan Carlos Escanciano

Indiana University Bloomington - Department of Economics

Jose Olmo

Universidad de Zaragoza; University of Southampton

Date Written: September 4, 2008


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.

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

Suggested Citation

Escanciano, Juan Carlos and Olmo, Jose, Backtesting Parametric Value-at-Risk With Estimation Risk (September 4, 2008). CAEPR Working Paper No. 2007-005. Available at SSRN: or

Juan Carlos Escanciano (Contact Author)

Indiana University Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States
812-855-7925 (Phone)
812-855-3736 (Fax)

Jose Olmo

Universidad de Zaragoza ( email )

Gran Via, 2
50005 Zaragoza, Zaragoza 50005

University of Southampton ( email )

United Kingdom

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