A Directional Multivariate Value at Risk
Ra\'ul Torres,
Rosa E. Lillo and
Henry Laniado
Papers from arXiv.org
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 $\alpha$, the $100\alpha\%$ 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 $\alpha$. 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 $\mathbb{R}^{n}$, or to a property of the univariate quantile that is desirable to be extended to $\mathbb{R}^{n}$. 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 \textit{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.
Date: 2015-02
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)
Published in Insurance: Mathematics and Economics, Volume 65, November 2015, Pages 111-123
Downloads: (external link)
http://arxiv.org/pdf/1502.00908 Latest version (application/pdf)
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1502.00908
Access Statistics for this paper
More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().