RT Journal Article
T1 On multivariate extensions of the conditional Value-at-Risk measure
A1 Di Bernandino, E.
A1 Fernández-Ponce, J.M.
A1 Palacios-Rodríguez, F.
A1 Rodríguez-Griñolo, Rosario
K1 Copulas and dependence
K1 Level sets of distribution functions
K1 Multivariate risk measures
K1 Stochastic orders
K1 Value-at-Risk
AB CoVaR is a systemic risk measure proposed by Adrian and Brunnermeier (2011) able to measure a financial institution’s contribution to systemic risk and its contribution to the risk of other financial institutions. CoVaR stands for conditional Value-at-Risk, i.e. it indicates the Value at Risk for a financial institution that is conditional on a certain scenario. In this paper, two alternative extensions of the classic univariate Conditional Value-at-Risk are introduced in a multivariate setting. The two proposed multivariate CoVaRs are constructed from level sets of multivariate distribution functions (resp. of multivariate survival distribution functions). These vector-valued measures have the same dimension as the underlying risk portfolio. Several characterizations of these new risk measures are provided in terms of the copula structure and stochastic orderings of the marginal distributions. Interestingly, these results are consistent with existing properties on univariate risk measures. Furthermore, comparisons between existent risk measures and the proposed multivariate CoVaR are developed. Illustrations are given in the class of Archimedean copulas. Estimation procedure for the multivariate proposed CoVaRs is illustrated in simulated studies and insurance real data.
PB ELSEVIER SCI LTD
YR 2015
FD 2015-03-01
LK https://hdl.handle.net/10433/21273
UL https://hdl.handle.net/10433/21273
LA en
NO Insurance: Mathematics and Economics, Vol. 61, p. 1 - 16
NO Departamento de Economía, Métodos Cuantitativos e Hª Económica, Área de Estadística e I.O., Universidad Pablo de Olavide
NO Departamento de Estadísitca e I.O. Universidad de Sevilla
DS RIO
RD May 9, 2026