Scenario-Based Risk Evaluation

37 Pages Posted: 29 Aug 2018 Last revised: 25 Sep 2019

See all articles by Ruodu Wang

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Johanna Ziegel

University of Bern

Date Written: August 20, 2018


Risk measures such as Expected Shortfall (ES) and Value-at-Risk (VaR) have been prominent in banking regulation and financial risk management. Motivated by practical considerations in the assessment and management of risks, including tractability, scenario relevance and robustness, we consider theoretical properties of scenario-based risk evaluation. We propose several novel scenario-based risk measures, including various versions of Max-ES and Max-VaR, and study their properties. We establish axiomatic characterizations of scenario-based risk measures that are comonotonic-additive or coherent and an ES-based representation result is obtained. These results provide a theoretical foundation for the recent Basel III & IV market risk calculation formulas. We illustrate the theory with financial data examples.

Keywords: Scenarios, Risk Measures, Expected Shortfall, Model Uncertainty, Basel Accords, Stress Adjustment, Dependence Adjustment

Suggested Citation

Wang, Ruodu and Ziegel, Johanna, Scenario-Based Risk Evaluation (August 20, 2018). Available at SSRN: or

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1

Johanna Ziegel

University of Bern

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