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

Author

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  • J. Sadefo Kamdem

    (Equations aux Dérivées Partielles et Physique Mathématique - - URCA - Université de Reims Champagne-Ardenne)

  • A. Genz

    (WSU - Washington State University)

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • J. Sadefo Kamdem & A. Genz, 2008. "Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options," Post-Print hal-02938642, HAL.
    • Handle: RePEc:hal:journl:hal-02938642
    DOI: 10.1016/j.csda.2007.12.006
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    References listed on IDEAS

    as
    1. Carvalho, Carlos M. & Lopes, Hedibert F., 2007. "Simulation-based sequential analysis of Markov switching stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4526-4542, May.
    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.
    3. Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
    4. 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.
    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. Jules Sadefo Kamdem, 2007. "VaR and ES for linear portfolios with mixture of elliptic distributions risk factors," Post-Print hal-02938574, HAL.
    7. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269, July.
    8. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    9. R. Brummelhuis & A. Córdoba & M. Quintanilla & L. Seco, 2002. "Principal Component Value at Risk," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 23-43, January.
    10. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    11. Lu, Zeng-Hua, 2006. "The numerical evaluation of the probability density function of a quadratic form in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1986-1996, December.
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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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