On dependence consistency of CoVaR and some other systemic risk measures
AbstractThis paper is dedicated to the consistency of systemic risk measures with respect to stochastic dependence. It compares two alternative notions of Conditional Value-at-Risk (CoVaR) available in the current literature. These notions are both based on the conditional distribution of a random variable Y given a stress event for a random variable X, but they use different types of stress events. We derive representations of these alternative CoVaR notions in terms of copulas, study their general dependence consistency and compare their performance in several stochastic models. Our central finding is that conditioning on X>=VaR_\alpha(X) gives a much better response to dependence between X and Y than conditioning on X=VaR_\alpha(X). We prove general results that relate the dependence consistency of CoVaR using conditioning on X>=VaR_\alpha(X) to well established results on concordance ordering of multivariate distributions or their copulas. These results also apply to some other systemic risk measures, such as the Marginal Expected Shortfall (MES) and the Systemic Impact Index (SII). We provide counterexamples showing that CoVaR based on the stress event X=VaR_\alpha(X) is not dependence consistent. In particular, if (X,Y) is bivariate normal, then CoVaR based on X=VaR_\alpha(X) is not an increasing function of the correlation parameter. Similar issues arise in the bivariate t model and in the model with t margins and a Gumbel copula. In all these cases, CoVaR based on X>=VaR_\alpha(X) is an increasing function of the dependence parameter.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1207.3464.
Date of creation: Jul 2012
Date of revision: Aug 2012
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-23 (All new papers)
- NEP-BAN-2012-07-23 (Banking)
- NEP-RMG-2012-07-23 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Wei, Gang & Hu, Taizhong, 2002. "Supermodular dependence ordering on a class of multivariate copulas," Statistics & Probability Letters, Elsevier, Elsevier, vol. 57(4), pages 375-385, May.
- Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2010.
"Measuring systemic risk,"
1002, Federal Reserve Bank of Cleveland.
- Acharya, Viral V & Pedersen, Lasse H & Philippon, Thomas & Richardson, Matthew P, 2012. "Measuring Systemic Risk," CEPR Discussion Papers, C.E.P.R. Discussion Papers 8824, C.E.P.R. Discussion Papers.
- Chen Zhou, 2009. "Are banks too big to fail?," DNB Working Papers, Netherlands Central Bank, Research Department 232, Netherlands Central Bank, Research Department.
- Gauthier, Céline & Lehar, Alfred & Souissi, Moez, 2012. "Macroprudential capital requirements and systemic risk," Journal of Financial Intermediation, Elsevier, Elsevier, vol. 21(4), pages 594-618.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
- Girardi, Giulio & Tolga Ergün, A., 2013. "Systemic risk measurement: Multivariate GARCH estimation of CoVaR," Journal of Banking & Finance, Elsevier, Elsevier, vol. 37(8), pages 3169-3180.
- Danielsson, Jon & James, Kevin & Valenzuela, Marcela & Zer, Ilknur, 2014. "Model Risk of Risk Models," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2014-34, Board of Governors of the Federal Reserve System (U.S.).
- Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.