Economics at your fingertips  

Aggregation-robustness and model uncertainty of regulatory risk measures

Paul Embrechts (), Bin Wang and Ruodu Wang ()

Finance and Stochastics, 2015, vol. 19, issue 4, 763-790

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 modelled 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 they 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. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Value-at-risk; Expected shortfall; Dependence uncertainty; Risk aggregation; Aggregation-robustness; Inhomogeneous portfolio; Basel III; 62G35; 60E15; 62P05; C10 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18) Track citations by RSS feed

Downloads: (external link) (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla ().

Page updated 2019-04-12
Handle: RePEc:spr:finsto:v:19:y:2015:i:4:p:763-790