Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2018 035

Correlation Under Stress In Normal Variance Mixture Models

Michael Kalkbrener
Natalie Packham

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 nancial
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 nancial institutions, where NVM models are frequently used for assessing capital
adequacy. We also demonstrate how our results can be applied for more prudent stress

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