Aggregation-Robustness and Model Uncertainty of Regulatory Risk Measures

26 Pages Posted: 2 Feb 2015

See all articles by Paul Embrechts

Paul Embrechts

Swiss Federal Institute of Technology Zurich; Swiss Finance Institute

Bin Wang

Beijing University of Technology

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: January 31, 2015

Abstract

Research related to aggregation, robustness, and model uncertainty of regulatory risk measures, for instance, Value-at-Risk (VaR) and Expected Shortfall (ES), is of fundamental importance within quantitative risk management. In risk aggregation, marginal risks and their dependence structure are often modeled separately, leading to uncertainty arising at the level of a joint model.

In this paper, we introduce a notion of qualitative robustness for risk measures, concerning the sensitivity of a risk measure to the uncertainty of dependence in risk aggregation. It turns out that coherent risk measures, such as ES, are more robust than VaR according to the new notion of robustness. We also give approximations and inequalities for aggregation and diversification of VaR under dependence uncertainty, and derive an asymptotic equivalence for worst-case VaR and ES under general conditions. We obtain that for a portfolio of a large number of risks VaR generally has a larger uncertainty spread compared to ES. The results warn that unjustified diversification arguments for VaR used in risk management need to be taken with much care, and potentially support the use of ES in risk aggregation. This in particular reflects on the discussions in the recent consultative documents by the Basel Committee on Banking Supervision.

Keywords: Value-at-Risk; Expected Shortfall; dependence uncertainty; risk aggregation; aggregation-robustness; inhomogeneous portfolio; Basel III

JEL Classification: C10

Suggested Citation

Embrechts, Paul and Wang, Bin and Wang, Ruodu, Aggregation-Robustness and Model Uncertainty of Regulatory Risk Measures (January 31, 2015). Finance Stochastics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2558525

Paul Embrechts

Swiss Federal Institute of Technology Zurich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Bin Wang

Beijing University of Technology ( email )

100 Ping Le Yuan
Chaoyang District
Beijing, Beijing 100020
China

Ruodu Wang (Contact Author)

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

Waterloo, Ontario N2L 3G1
Canada

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