Correlation Under Stress in Normal Variance Mixture Models

28 Pages Posted: 26 Jan 2010 Last revised: 12 Oct 2012

See all articles by Michael Kalkbrener

Michael Kalkbrener

Deutsche Bank AG - Risk Management

Natalie Packham

Berlin School of Economics and Law; Humboldt University Berlin

Date Written: August 27, 2012


We investigate correlations of asset returns in stress scenarios where a common risk factor is truncated. Our analysis is performed in the class of normal variance mixture (NVM) models, which encompasses many distributions commonly used in financial modelling. For the special cases of jointly normally and t-distributed asset returns we derive closed formulas for the correlation under stress. For the NVM distribution, we calculate the asymptotic limit of the correlation under stress, which depends on whether the variables are in the maximum domain of attraction of the Frechet or Gumbel distribution. It turns out that correlations in heavy-tailed NVM models are less sensitive to stress than in medium- or light-tailed models. Our analysis sheds light on the suitability of this model class to serve as a quantitative framework for stress testing, and as such provides valuable information for risk and capital management in financial institutions, where NVM models are frequently used for assessing capital adequacy.

Keywords: Stress testing, risk management, correlation, normal variance mixture distribution, multivariate normal distribution, multivariate t-distribution

JEL Classification: C00, G21, C52

Suggested Citation

Kalkbrener, Michael and Packham, Natalie, Correlation Under Stress in Normal Variance Mixture Models (August 27, 2012). Available at SSRN: or

Michael Kalkbrener

Deutsche Bank AG - Risk Management ( email )

31 West 52nd Street, 12th Floor
New York, NY 10019

Natalie Packham (Contact Author)

Berlin School of Economics and Law ( email )

Badensche Strasse 50-51
Berlin, D-10825


Humboldt University Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099

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