Scenario-based risk evaluation

• Published in: Finance and stochastics Vol. 25; no. 4; pp. 725 - 756
• Main Authors: Wang, Ruodu, Ziegel, Johanna F.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021; Springer Nature B.V
• Subjects: Actuarial science; Economic crisis; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Insurance; Management; Mathematics; Mathematics and Statistics; Probability Theory and Stochastic Processes; Quantitative Finance; Regulation of financial institutions; Risk assessment; Risk factors; Risk management; Robustness; Statistics for Business; Stress adjustment; 91G70; Basel Accords; 91B05; C69; Scenarios; G28; Risk measures; Dependence adjustment
• ISSN: 0949-2984; 1432-1122
• DOI: 10.1007/s00780-021-00460-9

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 establish axiomatic characterisations of scenario-based risk measures that are comonotonic-additive or coherent, and we obtain a novel ES-based representation result. We propose several novel scenario-based risk measures, including various versions of Max-ES and Max-VaR, and study their properties. The theory is illustrated with financial data examples.