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

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).

Number of Pages in PDF File: 29

working papers series