Model uncertainty and VaR aggregation

Embrechts, Paul; Puccetti, Giovanni; Rüschendorf, Ludger

doi:10.1016/j.jbankfin.2013.03.014

Cited by 295 publications

(283 citation statements)

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“…The diversification ratio measures a kind of diversification benefit, and is for instance widely used in operational risk (see examples in Embrechts et al (2013)). In the latter context, X i corresponds to next year's operational risk loss in business line i, i = 1, .…”

Section: Aggregation and Diversification Under Dependence Uncertaintymentioning

confidence: 99%

“…When Embrechts et al (2013) introduced the Rearrangement Algorithm to numerically calculate VaR p (S n ) based on a discretized approximation.…”

Section: Aggregation and Diversification Under Dependence Uncertaintymentioning

confidence: 99%

“…There have been extensive discussions on the problematic diversification and aggregation issues of VaR due to its lack of subadditivitity; see for example Embrechts et al (2013). Daníelsson et al (2005) argue that the violation of subadditivity for VaR is rare in practice.…”

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confidence: 99%

“…As often is the case in practice, the dependence structure among individual risks in a portfolio is difficult to obtain from a statistical point of view, while the marginal distributions of the individual risks (assets) may typically be easier to model; see for instance Embrechts et al (2013) and Bernard et al (2014). Modeling a high-dimensional dependence structure is well-known to be data-costly, and dimension reduction techniques such as vine copulas, hierarchical structures, and very specific parametric models often have to be implemented.…”

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confidence: 99%

“…Partial solutions for the worst-case and best-case values of VaR are to be found in Wang et al (2013), Puccetti and Rüschendorf (2013) and Bernard et al (2014), based on the notion of complete mixability introduced in Wang and Wang (2011). A fast algorithm to numerically calculate the worst-case and best-case values of VaR under general conditions was introduced in Embrechts et al (2013). For the best-case ES, some partial analytical results can be found in Bernard et al (2014) and Cheung and Lo (2013), and a numerical procedure was proposed by Puccetti (2013).…”

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confidence: 99%

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Aggregation-robustness and model uncertainty of regulatory risk measures

2015

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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.

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Section: Aggregation and Diversification Under Dependence Uncertaintymentioning

confidence: 99%

“…When Embrechts et al (2013) introduced the Rearrangement Algorithm to numerically calculate VaR p (S n ) based on a discretized approximation.…”

Section: Aggregation and Diversification Under Dependence Uncertaintymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Aggregation-robustness and model uncertainty of regulatory risk measures

2015

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Ordering of Insurance Risk

Rüschendorf

2015

Wiley StatsRef: Statistics Reference Online

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Ordering of risks is a basic tool for analyzing risks and their premiums. It is an extension of the classical mean‐variance approach of Markovitz. We introduce some of the basic orderings as stochastic order and stop loss order and present some applications for the comparison of individual and collective risk models to the diversification of risks and to reinsurance contracts. In particular, we demonstrate the dramatic influence of positive dependence in a risk portfolio on the total risk. Obtaining sharp bounds on the influence of positive dependence in a portfolio on the total risk is an actual active research area.

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