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Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors |
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| Authors: | Stefan Jaschke Claudia Klüppelberg Alexander Lindner |
| Institution: | a Federal Financial Supervisory Authority (BaFin), Graurheindorfer Str. 108, 53117, Bonn, Germany;b Center of Mathematical Sciences, Munich University of Technology, D-85747, Garching, Germany |
| 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. |
| Keywords: | Quadratic forms of Gaussian vectors Tail behavior Delta– gamma method Value-at-Risk Quantile estimation |
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