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Multivariate Elliptical Truncated Moments

Author

Listed:
  • Juan Arismendi

    (ICMA Centre, Henley Business School, University of Reading)

  • Simon Broda

    (Department of Quantitative Economics, University of Amsterdam Tinbergen Institute Amsterdam)

Abstract
In this study, we derived analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth-, first-, and second-order moments of quadratic forms of the multivariate normal, Student's t, and generalised hyperbolic distributions. The resulting formulae were tested in a numerical application to calculate an analytic expression of the expected shortfall of quadratic portfolios with the benefit that moment based sensitivity measures can be derived from the analytic expression. The convergence rate of the analytic expression is fast { one iteration { for small closed integration domains, and slower for open integration domains when compared to the Monte Carlo integration method. The analytic formulae provide a theoretical framework for calculations in robust estimation, robust regression, outlier detection, design of experiments, and stochastic extensions of deterministic elliptical curves results.

Suggested Citation

  • Juan Arismendi & Simon Broda, 2016. "Multivariate Elliptical Truncated Moments," ICMA Centre Discussion Papers in Finance icma-dp2016-06, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2016-06
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    References listed on IDEAS

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    Cited by:

    1. Galarza, Christian E. & Matos, Larissa A. & Castro, Luis M. & Lachos, Victor H., 2022. "Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Ogasawara, Haruhiko, 2021. "A non-recursive formula for various moments of the multivariate normal distribution with sectional truncation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Baishuai Zuo & Chuancun Yin, 2022. "Multivariate doubly truncated moments for generalized skew-elliptical distributions with application to multivariate tail conditional risk measures," Papers 2203.00839, arXiv.org.
    4. Ouzan, Samuel, 2020. "Loss aversion and market crashes," Economic Modelling, Elsevier, vol. 92(C), pages 70-86.
    5. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.
    6. Roozegar, Roohollah & Balakrishnan, Narayanaswamy & Jamalizadeh, Ahad, 2020. "On moments of doubly truncated multivariate normal mean–variance mixture distributions with application to multivariate tail conditional expectation," Journal of Multivariate Analysis, Elsevier, vol. 177(C).

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    More about this item

    Keywords

    Multivariate truncated moments; Quadratic forms; Elliptical Truncation; Tail moments; Parametric distributions; Elliptical functions;
    All these keywords.

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