Value-at-Risk and Expected Shortfall for Quadratic portfolio of securities with mixture of elliptic Distributed Risk Factors
<|reference_start|>Value-at-Risk and Expected Shortfall for Quadratic portfolio of securities with mixture of elliptic Distributed Risk Factors: Generally, in the financial literature, the notion of quadratic VaR is implicitly confused with the Delta-Gamma VaR, because more authors dealt with portfolios that contains derivatives instruments.   In this paper, we postpone to estimate the Value-at-Risk of a quadratic portfolio of securities (i.e equities) without the Delta and Gamma greeks, when the joint log-returns changes with multivariate elliptic distribution. We have reduced the estimation of the quadratic VaR of such portfolio to a resolution of one dimensional integral equation. To illustrate our method, we give special attention to the mixture of normal and mixture of t-student distribution. For given VaR, when joint Risk Factors changes with elliptic distribution, we show how to estimate an Expected Shortfall .<|reference_end|>
@article{kamdem2003value-at-risk,
    title={Value-at-Risk and Expected Shortfall for Quadratic portfolio of
  securities with mixture of elliptic Distributed Risk Factors},
    author={Jules Sadefo Kamdem},
    journal={arXiv preprint arXiv:cs/0310043},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0310043},
    primaryClass={cs.CE math.CA}
}