Abstract
Choosing a proper external risk measure is of great regulatory importance, as exemplified in the Basel II and Basel III Accord which use Value-at-Risk (VaR) with scenario analysis as the risk measures for setting capital requirements. We argue 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 are 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.
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