IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v3y2015i1p18n3.html
   My bibliography  Save this article

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

Author

Listed:
  • Bernhart German

    (Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany)

  • Mai Jan-Frederik

    (XAIA Investment GmbH, Sonnenstraße 19, 80331 München, Germany)

  • Scherer Matthias

    (Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany)

Abstract

Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.

Suggested Citation

  • Bernhart German & Mai Jan-Frederik & Scherer Matthias, 2015. "On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-18, May.
    • Handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:18:n:3
    DOI: 10.1515/demo-2015-0003
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2015-0003
    Download Restriction: no
    File URL: https://libkey.io/10.1515/demo-2015-0003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. F. Ballani & M. Schlather, 2011. "A construction principle for multivariate extreme value distributions," Biometrika, Biometrika Trust, vol. 98(3), pages 633-645.
    2. Jiménez, Javier Rojo & Villa-Diharce, Enrique & Flores, Miguel, 2001. "Nonparametric Estimation of the Dependence Function in Bivariate Extreme Value Distributions," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 159-191, February.
    3. Anne‐Laure Fougères & John P. Nolan & Holger Rootzén, 2009. "Models for Dependent Extremes Using Stable Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 42-59, March.
    4. Segers, Johan, 2012. "Max-stable models for multivariate extremes," LIDAM Reprints ISBA 2012012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Damiano Brigo & Kyriakos Chourdakis, 2012. "Consistent single- and multi-step sampling of multivariate arrival times: A characterization of self-chaining copulas," Papers 1204.2090, arXiv.org, revised Apr 2012.
    6. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," The Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
    7. Joe, Harry, 1990. "Families of min-stable multivariate exponential and multivariate extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 75-81, January.
    8. Segers, Johan, 2012. "Max-Stable Models For Multivariate Extremes," LIDAM Discussion Papers ISBA 2012011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    10. Ressel, Paul, 2013. "Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 246-256.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mai, Jan-Frederik, 2018. "Extreme-value copulas associated with the expected scaled maximum of independent random variables," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 50-61.
    2. Carsten Bormann & Julia Schaumburg & Melanie Schienle, 2016. "Beyond Dimension two: A Test for Higher-Order Tail Risk," Journal of Financial Econometrics, Oxford University Press, vol. 14(3), pages 552-580.
    3. Kiriliouk, Anna, 2020. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space," Econometrics and Statistics, Elsevier, vol. 16(C), pages 121-135.
    4. Kiriliouk, Anna, 2017. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space with application to generalized max-linear models," LIDAM Discussion Papers ISBA 2017027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Mai Jan-Frederik, 2020. "The de Finetti structure behind some norm-symmetric multivariate densities with exponential decay," Dependence Modeling, De Gruyter, vol. 8(1), pages 210-220, January.
    6. Rootzen, Holger & Segers, Johan & Wadsworth, Jennifer, 2017. "Multivariate generalized Pareto distributions: parametrizations, representations, and properties," LIDAM Discussion Papers ISBA 2017016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Charpentier, A. & Fougères, A.-L. & Genest, C. & Nešlehová, J.G., 2014. "Multivariate Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 118-136.
    8. Belzile, Léo R. & Nešlehová, Johanna G., 2017. "Extremal attractors of Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 68-92.
    9. Mai Jan-Frederik, 2020. "The de Finetti structure behind some norm-symmetric multivariate densities with exponential decay," Dependence Modeling, De Gruyter, vol. 8(1), pages 210-220, January.
    10. Mai Jan-Frederik, 2024. "Sharp bounds on the survival function of exchangeable min-stable multivariate exponential sequences," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-12.
    11. Bücher, Axel & Jäschke, Stefan & Wied, Dominik, 2015. "Nonparametric tests for constant tail dependence with an application to energy and finance," Journal of Econometrics, Elsevier, vol. 187(1), pages 154-168.
    12. Rootzén, Holger & Segers, Johan & Wadsworth, Jennifer L., 2018. "Multivariate generalized Pareto distributions: Parametrizations, representations, and properties," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 117-131.
    13. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    14. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    15. Ye, Wuyi & Luo, Kebing & Liu, Xiaoquan, 2017. "Time-varying quantile association regression model with applications to financial contagion and VaR," European Journal of Operational Research, Elsevier, vol. 256(3), pages 1015-1028.
    16. Maarten R C van Oordt & Chen Zhou, 2019. "Estimating Systematic Risk under Extremely Adverse Market Conditions," Journal of Financial Econometrics, Oxford University Press, vol. 17(3), pages 432-461.
    17. Cumperayot, Phornchanok & Kouwenberg, Roy, 2013. "Early warning systems for currency crises: A multivariate extreme value approach," Journal of International Money and Finance, Elsevier, vol. 36(C), pages 151-171.
    18. José Afonso Faias & Juan Arismendi Zambrano, 2022. "Equity Risk Premium Predictability from Cross-Sectoral Downturns [International asset allocation with regime shifts]," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 12(3), pages 808-842.
    19. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    20. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:18:n:3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.