IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v23y2019i4d10.1007_s00780-019-00401-7.html
   My bibliography  Save this article

Financial risk measures for a network of individual agents holding portfolios of light-tailed objects

Author

Listed:
  • Claudia Klüppelberg

    (Technical University of Munich)

  • Miriam Isabel Seifert

    (Ruhr University Bochum)

Abstract

We investigate a financial network of agents holding portfolios of independent light-tailed risky objects whose losses are asymptotically exponentially distributed with distinct tail parameters. We show that the asymptotic distributions of portfolio losses belong to the class of functional exponential mixtures which we introduce in this paper. We also provide results for value-at-risk and expected shortfall risk measures, as well as for their conditional counterparts. Compared to heavy-tail settings, we establish important qualitative differences in the asymptotic behaviour of portfolio risks under a light-tail assumption which have to be accounted for in practical risk management.

Suggested Citation

  • Claudia Klüppelberg & Miriam Isabel Seifert, 2019. "Financial risk measures for a network of individual agents holding portfolios of light-tailed objects," Finance and Stochastics, Springer, vol. 23(4), pages 795-826, October.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:4:d:10.1007_s00780-019-00401-7
    DOI: 10.1007/s00780-019-00401-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-019-00401-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-019-00401-7?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jiang, Jun & Tang, Qihe, 2008. "Reinsurance under the LCR and ECOMOR treaties with emphasis on light-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 431-436, December.
    2. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    3. Rustam Ibragimov, 2009. "Portfolio diversification and value at risk under thick-tailedness," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 565-580.
    4. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, December.
    5. Das, Bikramjit & Fasen-Hartmann, Vicky, 2018. "Risk contagion under regular variation and asymptotic tail independence," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 194-215.
    6. Jianming Xia, 2004. "Multi-agent investment in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 241-259, May.
    7. Girardi, Giulio & Tolga Ergün, A., 2013. "Systemic risk measurement: Multivariate GARCH estimation of CoVaR," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3169-3180.
    8. Hernández, Camilo & Junca, Mauricio, 2015. "Optimal dividend payments under a time of ruin constraint: Exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 136-142.
    9. Oliver Kley & Claudia Klüppelberg & Gesine Reinert, 2016. "Risk in a Large Claims Insurance Market with Bipartite Graph Structure," Operations Research, INFORMS, vol. 64(5), pages 1159-1176, October.
    10. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    11. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    12. Paul Embrechts & Bin Wang & Ruodu Wang, 2015. "Aggregation-robustness and model uncertainty of regulatory risk measures," Finance and Stochastics, Springer, vol. 19(4), pages 763-790, October.
    13. Brechmann, Eike C. & Hendrich, Katharina & Czado, Claudia, 2013. "Conditional copula simulation for systemic risk stress testing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 722-732.
    14. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    15. Edward M. H. Lin & Edward W. Sun & Min-Teh Yu, 2018. "Systemic risk, financial markets, and performance of financial institutions," Annals of Operations Research, Springer, vol. 262(2), pages 579-603, March.
    16. Camilo Hernandez & Mauricio Junca, 2014. "Optimal dividend payment under time of ruin contraint: Exponential case," Papers 1410.3793, arXiv.org, revised May 2015.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dette, Holger & Golosnoy, Vasyl & Kellermann, Janosch, 2022. "Correcting Intraday Periodicity Bias in Realized Volatility Measures," Econometrics and Statistics, Elsevier, vol. 23(C), pages 36-52.
    2. Miriam Isabel Seifert, 2023. "Characterization of valid auxiliary functions for representations of extreme value distributions and their max-domains of attraction," Papers 2311.15355, arXiv.org.
    3. Golosnoy, Vasyl & Gribisch, Bastian, 2022. "Modeling and forecasting realized portfolio weights," Journal of Banking & Finance, Elsevier, vol. 138(C).

    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. Claudia Kluppelberg & Miriam Isabel Seifert, 2016. "Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits," Papers 1612.07132, arXiv.org.
    2. Xia Han & Liyuan Lin & Ruodu Wang, 2022. "Diversification quotients: Quantifying diversification via risk measures," Papers 2206.13679, arXiv.org, revised Mar 2024.
    3. Li, Hengxin & Wang, Ruodu, 2023. "PELVE: Probability Equivalent Level of VaR and ES," Journal of Econometrics, Elsevier, vol. 234(1), pages 353-370.
    4. Xia Han & Liyuan Lin & Ruodu Wang, 2023. "Diversification quotients based on VaR and ES," Papers 2301.03517, arXiv.org, revised May 2023.
    5. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
    6. Rustam Ibragimov & Paul Kattuman & Anton Skrobotov, 2021. "Robust Inference on Income Inequality: $t$-Statistic Based Approaches," Papers 2105.05335, arXiv.org, revised Nov 2021.
    7. Khamis Hamed Al‐Yahyaee & Syed Jawad Hussain Shahzad & Walid Mensi & Seong‐Min Yoon, 2021. "Is there a systemic risk between Sharia, Sukuk, and GCC stock markets? A ΔCoVaR risk metric‐based copula approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2904-2926, April.
    8. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Risk quantification for commodity ETFs: Backtesting value-at-risk and expected shortfall," International Review of Financial Analysis, Elsevier, vol. 70(C).
    9. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    10. Yuanying Guan & Zhanyi Jiao & Ruodu Wang, 2022. "A reverse ES (CVaR) optimization formula," Papers 2203.02599, arXiv.org, revised May 2023.
    11. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    12. Ortega-Jiménez, P. & Sordo, M.A. & Suárez-Llorens, A., 2021. "Stochastic orders and multivariate measures of risk contagion," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 199-207.
    13. Fiala, Tomas & Havranek, Tomas, 2017. "The sources of contagion risk in a banking sector with foreign ownership," Economic Modelling, Elsevier, vol. 60(C), pages 108-121.
    14. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2014. "Risk in a large claims insurance market with bipartite graph structure," Papers 1410.8671, arXiv.org, revised Nov 2015.
    15. Daniel Velásquez-Gaviria & Andrés Mora-Valencia & Javier Perote, 2020. "A Comparison of the Risk Quantification in Traditional and Renewable Energy Markets," Energies, MDPI, vol. 13(11), pages 1-42, June.
    16. Kley, Oliver & Klüppelberg, Claudia & Paterlini, Sandra, 2020. "Modelling extremal dependence for operational risk by a bipartite graph," Journal of Banking & Finance, Elsevier, vol. 117(C).
    17. Alexander J. McNeil, 2020. "Modelling volatile time series with v-transforms and copulas," Papers 2002.10135, arXiv.org, revised Jan 2021.
    18. Di Lascio, F. Marta L. & Giammusso, Davide & Puccetti, Giovanni, 2018. "A clustering approach and a rule of thumb for risk aggregation," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 236-248.
    19. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Sanctions and the Russian stock market," Research in International Business and Finance, Elsevier, vol. 40(C), pages 150-162.
    20. Furman, Edward & Wang, Ruodu & Zitikis, Ričardas, 2017. "Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 70-84.

    More about this item

    Keywords

    Asymptotic exponential distribution; Expected shortfall; Financial network; Risk management; Value-at-risk;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    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:spr:finsto:v:23:y:2019:i:4:d:10.1007_s00780-019-00401-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.