A Directional Multivariate Value at Risk

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dc.contributor.author Torres Díaz, Raúl Andrés
dc.contributor.author Lillo Rodríguez, Rosa Elvira
dc.contributor.author Laniado Rodas, Henry
dc.contributor.editor Universidad Carlos III de Madrid. Departamento de Estadística
dc.date.accessioned 2015-02-24T13:31:04Z
dc.date.available 2015-02-24T13:31:04Z
dc.date.issued 2015-01-01
dc.identifier.issn 2387-0303
dc.identifier.uri http://hdl.handle.net/10016/20088
dc.description.abstract In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability alfa, the 100alfa% VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is alfa. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretation as a risk measure. However, its extension to the multivariate framework is not unique because a unique definition of multivariate quantile does not exist. In the current literature, the multivariate quantiles are related to a specific partial order considered in Rn, or to a property of the univariate quantile that is desirable to be extended to Rn. In this work, we introduce a multivariate value at risk as a vector-valued directional risk measure, based on a directional multivariate quantile, which has recently been introduced in the literature. The directional approach allows the manager to consider external information or risk preferences in her/his analysis. We have derived some properties of the risk measure and we have compared the univariate VaR over the marginals with the components of the directional multivariate VaR. We have also analyzed the relationship between some families of copulas, for which it is possible to obtain closed forms of the multivariate VaR that we propose. Finally, comparisons with other alternative multivariate VaR given in the literature, are provided in terms of robustness.
dc.description.sponsorship The authors acknowledge financial support from the Spanish Ministry of Economy and Competition, research project ECO2012-38442.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.relation.ispartofseries UC3M Working papers. Statistics and Econometrics
dc.relation.ispartofseries 15-01
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Multivariate risks
dc.subject.other Value at risk
dc.subject.other Directional approach
dc.title A Directional Multivariate Value at Risk
dc.type workingPaper
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. ECO2012-38442
dc.type.version submitedVersion
dc.identifier.uxxi DT/0000001333
dc.identifier.repec ws1501
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