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Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options

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  • Sadefo Kamdem, J.
  • Genz, A.

Abstract

An application involving a financial quadratic portfolio, where the joint underlying log-returns follow a multivariate elliptic distribution, is considered. This motivates the need for methods for the approximation of multiple integrals over hyperboloids. Transformations are used to reduce the hyperboloid integrals to products of integrals which can be approximated with appropriate numerical methods. The application of these methods is demonstrated using some financial applications examples.

Suggested Citation

  • Sadefo Kamdem, J. & Genz, A., 2008. "Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3389-3407, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3389-3407
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    2. 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.
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    9. 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.
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    Cited by:

    1. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," JRFM, MDPI, vol. 10(1), pages 1-14, February.
    2. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    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. Sadefo Kamdem, J., 2010. "Sharp estimates for the CDF of quadratic forms of MPE random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1755-1771, September.
    5. 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.
    6. Sadefo Kamdem, J., 2009. "[Delta]-VaR and [Delta]-TVaR for portfolios with mixture of elliptic distributions risk factors and DCC," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 325-336, June.
    7. Abdoul Salam Diallo & Alfred Mbairadjim Moussa, 2014. "Addressing agent specific extreme price risk in the presence of heterogeneous data sources: A food safety perspective," Working Papers 14-15, LAMETA, Universtiy of Montpellier, revised Dec 2014.

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