Aggregation-robustness and model uncertainty of regulatory risk measures

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.

A Review on Ambiguity in Stochastic Portfolio Optimization

“…If β < 1/γ , then P → h dP is, for fixed marginals, Lipschitz in the Wasserstein distance of the copula. Concerning the choice of the risk functional R, we want to point out that the AV@R is aggregation-robust, see Embrechts et al [14], which implies that the AV@R is less sensitive to model uncertainty at the level of the dependence structure than, for instance, the Valueat-Risk. Hence, the AV@R will be of special interest in our subsequent analysis.…”

Robust Estimation of Value-at-Risk through Distribution-Free and Parametric Approaches Using the Joint Severity and Frequency Model: Applications in Financial, Actuarial, and Natural Calamities Domains

“…Detailed descriptions and the backgrounds of different risk measures can be found in Embrechts et al (2015). In addition to operational risk, this measure has applications in the market risk and credit risk domains (Embrechts and Hofert 2014;Dias 2013;Andersson et al 2001).…”

“…The majority of the research publications which use real-world data in modern QRM rely on proprietary data (Aue and Kalkbrener 2006;OpRisk Advisory and Towers Perrin 2010;Gomes-Gonçalves and Gzyl 2014;Rachev et al 2006;Embrechts et al 2015;Li et al 2014). In some rare cases, the data cited is available only in loss data exchanges where users must pay a fee or donate their own specialized loss data in order to access and analyze the data (Aue and Kalkbrener 2006;Gomes-Gonçalves and Gzyl 2014;Rachev et al 2006;Li et al 2014).…”

“…(c) We investigate the performance of the classical and DPFS and CPFS methodologies using both simulation experiments and publicly available real-world datasets from a diverse range of application domains; namely, financial market losses (Data available from Yahoo Finance 2017), chemical spills handled by the US Coast Guard (Data available at National Response Center 1990), automobile accidents (Charpentier 2014), and US hurricane losses (Charpentier 2014). The use of publicly available data sets this work distinctly apart from the majority of the empirical research into modern QRM which uses proprietary data (Aue and Kalkbrener 2006;OpRisk Advisory and Towers Perrin 2010;Gomes-Gonçalves and Gzyl 2014;Rachev et al 2006;Embrechts et al 2015;Li et al 2014). Tests using simulations and real-world data demonstrate the merit of the two statistical approaches.…”

“…www.mdpi.com/journal/risks Risks 2017, 5, 41 2 of 30 Embrechts et al 2015;Li et al 2014), denoted as VaR, is a quantitative risk metric used to answer this key question. Developing methods for the robust estimation of VaR for a generalized setting is a problem which is currently of interest in QRM.…”