The Risk Map: A New Tool for Backtesting Value-at-Risk Models

29 Pages Posted: 12 May 2011

See all articles by Gilbert Colletaz

Gilbert Colletaz

University of Orleans

Christophe Hurlin

University of Orleans

Christophe Perignon

HEC Paris - Finance Department

Multiple version iconThere are 2 versions of this paper

Date Written: May 1, 2011

Abstract

This paper presents a new tool for validating Value-at-Risk (VaR) models. This tool, called the Risk Map, jointly accounts for the number and the magnitude of the VaR exceptions and graphically summarizes all information about the performance of a risk model. It relies on the concept of VaR super exception, which is de…fined as a situation in which the trading loss exceeds both the standard VaR and a VaR defined at an extremely low coverage probability. We then formally test whether the sequence of exceptions and super exceptions passes standard model validation tests. We show that the Risk Map can be used to backtest VaR for market risk, credit risk, or operational risk, to assess the performance of a margining system on a derivatives exchange, and to validate systemic risk measures (e.g. CoVaR).

Suggested Citation

Colletaz, Gilbert and Hurlin, Christophe and Perignon, Christophe, The Risk Map: A New Tool for Backtesting Value-at-Risk Models (May 1, 2011). International Conference of the French Finance Association (AFFI), May 11-13, 2011. Available at SSRN: https://ssrn.com/abstract=1836885 or http://dx.doi.org/10.2139/ssrn.1836885

Gilbert Colletaz (Contact Author)

University of Orleans ( email )

Rue de Blois
B.P. 6739
45067 Orleans Cedex 2, Orleans cedex 2 45067
France

Christophe Hurlin

University of Orleans ( email )

Université d'Orléans
Rue de Blois B.P. 6739 45
France

Christophe Perignon

HEC Paris - Finance Department ( email )

1 rue de la Liberation
Jouy-en-Josas Cedex, 78351
France

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