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Scenario Sets, Risk Measures and Stress Testing Part 1: Theory

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Systemic Risk: Mathematical Modelling and Interdisciplinary Approaches

We examine the relationship between multivariate scenarios sets and risk measures. Our interest is motivated by the use of scenario sets in the stress testing of banks and insurance companies whose portfolio values and solvency are dependent on changes in underlying financial risk factors. Although regulators suggest that financial institutions should consider extreme but plausible scenarios, there is no clear guidance on exactly how this should be done. We explain the connection between sets based on the notion of half-space depth (HD) and the Value-at-Risk risk measure. We then introduce general depth concepts related to coherent risk measures and show how these lead to scenario sets based on, for example, the expectile or the expected shortfall risk measure. The boundaries of these sets also have interesting interpretations in terms of capital allocation. Finally we explain how the sets might be used in ordinary (forward) stress testing and so-called reverse stress testing.

This talk is part of the Isaac Newton Institute Seminar Series series.

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