Marginal expected shortfall: Systemic risk measurement under dependence uncertainty

2025-04-28

AI Summary

Marginal Expected Shortfall (MES) suffers from uncertainty in measuring systemic risk contributions of financial institutions due to unknown dependence structures among risks. Method: We propose a distributionally robust quantification framework that, under known marginal distributions and completely unknown dependence structure, rigorously derives the tightest possible analytical bounds on MES. Leveraging three background risk models and CAPM/WIPM-consistent linear regression assumptions, we incorporate partial dependence information—such as covariance constraints and tail dependence bounds—to tighten these bounds. The approach integrates extreme value theory, distributionally robust optimization, and factor models (additive, minimum, multiplicative) to ensure analytical tractability. Contribution/Results: Our framework yields computationally efficient, theoretically grounded bounds that significantly enhance the robustness and regulatory applicability of MES. It provides both theoretical foundations and practical tools for macroprudential assessment and stress testing.

Technology Category

Multiagent Systems: Multiagent Systems under UncertaintyMachine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Stochastic Optimization

Application Category

Security and Privacy: Large-scale security measurementsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Measuring the contribution of a bank or an insurance company to the overall systemic risk of the market is an important issue, especially in the aftermath of the 2007-2009 financial crisis and the financial downturn of 2020. In this paper, we derive the worst-case and best-case bounds for marginal expected shortfall (MES) -- a key measure of systemic risk contribution -- under the assumption of known marginal distributions for individual companies' risks but an unknown dependence structure. We further derive improved bounds for the MES risk measure when partial information on companies' risk exposures -- and hence their dependence -- is available. To capture this partial information, we utilize three commonly used background risk models: the additive, minimum-based, and multiplicative factor models. Finally, we present an alternative set of improved MES bounds based on a linear regression relationship between individual companies' risks and overall market risk, consistent with the assumptions of the Capital Asset Pricing Model in finance and the Weighted Insurance Pricing Model in insurance.

Problem

• Measure systemic risk contribution under dependence uncertainty
• Derive worst-case and best-case bounds for MES
• Improve MES bounds using partial dependence information

Innovation

• Bounds for MES under unknown dependence structure
• Improved MES bounds using partial dependence information
• Linear regression-based MES bounds consistent with CAPM