External Risk Measures and Basel Accords

Choosing a proper external risk measure is of great regulatory importance, as exemplified in the Basel II and Basel III Accords, which use value‐at‐risk with scenario analysis as the risk measures for setting capital requirements. We argue that a good external risk measure should be robust with respect to model misspecification and small changes in the data. A new class of data‐based risk measures called natural risk statistics is proposed to incorporate robustness. Natural risk statistics are characterized by a new set of axioms. They include the Basel II and III risk measures and a subclass of robust risk measures as special cases; therefore, they provide a theoretical framework for understanding and, if necessary, extending the Basel Accords.