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Value-at-Risk and Expected Shortfall for Quadratic Portfolio of Securities with Mixture of Elliptic Distribution Risk Factors

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  • Jules SADEFO KAMDEM

Abstract

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 contained derivatives instruments. In this paper, we postpone to estimate both the expected shortfall and 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. To illustrate our method, we give special attention to mixture of normal distributions, and mixture of Student t-distributions. Key Words: Classical analysis, Computational Finance, Elliptic distributions, Risk Management

Suggested Citation

  • Jules SADEFO KAMDEM, 2004. "Value-at-Risk and Expected Shortfall for Quadratic Portfolio of Securities with Mixture of Elliptic Distribution Risk Factors," Computing in Economics and Finance 2004 12, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:12
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    Citations

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    Cited by:

    1. SADEFO KAMDEM Jules, 2004. "VaR and ES for linear Portfolios with mixture of elliptically distributed Risk Factors," GE, Growth, Math methods 0403004, University Library of Munich, Germany.
    2. Jules Sadefo Kamdem, 2005. "Value-At-Risk And Expected Shortfall For Linear Portfolios With Elliptically Distributed Risk Factors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(05), pages 537-551.
    3. Jules Sadefo Kamdem, 2012. "VaR and ES for linear portfolios with mixture of generalized Laplace distributions risk factors," Annals of Finance, Springer, vol. 8(1), pages 123-150, February.
    4. Raymond BRUMMELHUIS & Jules Sadefo-Kamdem, 2009. "Var For Quadratic Portfolio'S With Generalized Laplace Distributed Returns," Working Papers 09-06, LAMETA, Universtiy of Montpellier, revised Jun 2009.
    5. SADEFO KAMDEM Jules, 2004. "VaR and ES for Linear Portfolios with mixture of Generalized Laplace Distributed Risk Factors," Risk and Insurance 0406001, University Library of Munich, Germany.
    6. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.

    More about this item

    Keywords

    Value-at-Risk; Expected Shortfall; Quadratic Portfolios of Equities; Applied Numerical Analysis.;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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