Aggregating risk capital, with an application to operational risk

Abstract

We describe a numerical procedure to obtain bounds on the distribution function of a sum of n dependent risks having fixed marginals. With respect to the existing literature, our method provides improved bounds and can be applied also to large non-homogeneous portfolios of risks. As an application, we compute the VaR-based minimum capital requirement for a portfolio of operational risk losses.

Operational Risk Quantification Using Extreme Value Theory and Copulas: From Theory to Practice

“…The biggest losses in BL3 therefore have a fundamental impact on the overall capital charges. This is in line with the concept of subexponentiality, 5 referred to in Embrechts and Puccetti (2006) as the "one loss causes ruin problem". This issue arises for heavytailed distributions including the GPD and lognormal distribution.…”

Properties of a Risk Measure Derived from Ruin Theory

“…We refer the reader, for example, to Volume 35, Issue 1 of the Geneva Papers on Risk and InsuranceIssues and Practice for articles dealing with regulation and solvency for insurance companies. Also, readers interested in studies using the VaR concept could see, for example, Luciano and Kast (2001) for a derivation of insurance contracts which are Mean-VaR efficient, Huang (2006) and the references therein for a study of optimal insurance under a VaR constraint or Embrechts and Puccetti (2006) for the computation of VaR-based minimum capital requirement for a portfolio of operational risk losses.…”

Construcción de la distribución de pérdidas y el problema de agregación de riesgo operativo bajo modelos LDA: una revisión

“…Al seguir la recomendación de Basilea, de obtener el VaR por líneas operativas, se encuentra que el VaR no es coherente a varios niveles de confiabilidad, al incluir la línea operativa con distribución de media infinita. Esta no subaditividad conduce a subestimaciones del VaR en el caso de perfecta dependencia (llamado también caso comonotónico), lo cual es consistente con un hallazgo previo de Embrechts y Puccetti [49]. Uno de los principales resultados de este artículo es que para modelos de media finita, el VaR es subaditivo, y agregar pér-didas mediante cópulas ayuda disminuir el cargo por capital, mientras que para modelos de media infinita, VaR no es coherente, y por ende, conduce a que las cópulas no reducen cargo de capital.…”