The Risk Map: A new tool for validating risk models

• Propose a new way of thinking about the validity of risk models.
• Account for both frequency and magnitude of extreme losses.
• No assumptions about the distribution of the returns.
• Can accommodate any tail-risk measure: VaR, stressed VaR, ES, CoVaR.
• Can be used to validate trading risk models, margin models, and systemic risk models.

This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is defined as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR defined at an extremely low probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.