Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

Authors:
Stefan Jaschke;Claudia Klüppelberg;Alexander Lindner
Affiliations:
Federal Financial Supervisory Authority (BaFin), Graurheindorfer Str. 108, 53117 Bonn, Germany;Center of Mathematical Sciences, Munich University of Technology, D-85747 Garching, Germany;Center of Mathematical Sciences, Munich University of Technology, D-85747 Garching, Germany
Venue:
Journal of Multivariate Analysis
Year:
2004

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Abstract

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta-gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.