Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different dependence scenarios on the factors of the portfolio. Besides summarizing the most relevant analytical bounds, including a discussion of their sharpness, we introduce a numerical algorithm which allows for the computation of reliable (sharp) bounds for the VaR of high-dimensional portfolios with dimensions d possibly in the several hundreds. We show that additional positive dependence information will typically not improve the upper bound substantially. In contrast higher order marginal information on the model, when available, may lead to strongly improved bounds. Several examples of practical relevance show how explicit VaR bounds can be obtained. These bounds can be interpreted as a measure of model uncertainty induced by possible dependence scenarios.
Model uncertainty and VaR aggregation / Paul Embrechts;Giovanni Puccetti;Ludger Rüschendorf. - In: JOURNAL OF BANKING & FINANCE. - ISSN 0378-4266. - STAMPA. - 37:(2013), pp. 2750-2764. [10.1016/j.jbankfin.2013.03.014]
Model uncertainty and VaR aggregation
PUCCETTI, GIOVANNI;
2013
Abstract
Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different dependence scenarios on the factors of the portfolio. Besides summarizing the most relevant analytical bounds, including a discussion of their sharpness, we introduce a numerical algorithm which allows for the computation of reliable (sharp) bounds for the VaR of high-dimensional portfolios with dimensions d possibly in the several hundreds. We show that additional positive dependence information will typically not improve the upper bound substantially. In contrast higher order marginal information on the model, when available, may lead to strongly improved bounds. Several examples of practical relevance show how explicit VaR bounds can be obtained. These bounds can be interpreted as a measure of model uncertainty induced by possible dependence scenarios.File | Dimensione | Formato | |
---|---|---|---|
13JBF.pdf
Accesso chiuso
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
703.35 kB
Formato
Adobe PDF
|
703.35 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.