IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v6y2018i3p92-d168425.html
   My bibliography  Save this article

On the Basel Liquidity Formula for Elliptical Distributions

Author

Listed:
  • Janine Balter

    (Deutsche Bundesbank, 40212 Düsseldorf, Germany
    The opinions expressed in this paper are those of the author and do not necessarily reflect views shared by the Deutsche Bundesbank or its staff.)

  • Alexander J. McNeil

    (The York Management School, University of York, Freboys Lane, York YO10 5GD, UK)

Abstract

A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L (profit-and-loss) are linear in the risk-factor changes. A generalization of the formula is derived under the more general assumption that risk-factor changes are multivariate elliptical. It is shown that the Basel formula tends to be conservative when the elliptical distributions are from the heavier-tailed generalized hyperbolic family. As a by-product of the analysis, a Fourier approach to calculating expected shortfall for general symmetric loss distributions is developed.

Suggested Citation

  • Janine Balter & Alexander J. McNeil, 2018. "On the Basel Liquidity Formula for Elliptical Distributions," Risks, MDPI, vol. 6(3), pages 1-13, September.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:3:p:92-:d:168425
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/6/3/92/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/6/3/92/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Krzysztof Podgórski & Jonas Wallin, 2016. "Convolution-invariant subclasses of generalized hyperbolic distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(1), pages 98-103, January.
    3. 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.
    4. 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.
    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. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.
    2. Orla McCullagh & Mark Cummins & Sheila Killian, 2023. "Decoupling VaR and regulatory capital: an examination of practitioners’ experience of market risk regulation," Journal of Banking Regulation, Palgrave Macmillan, vol. 24(3), pages 321-336, September.

    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. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    2. Maria Grazia Zoia & Gianmarco Vacca & Laura Barbieri, 2020. "Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions," Risks, MDPI, vol. 8(4), pages 1-21, November.
    3. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    4. Masahiko Egami & Rusudan Kevkhishvili, 2020. "Time reversal and last passage time of diffusions with applications to credit risk management," Finance and Stochastics, Springer, vol. 24(3), pages 795-825, July.
    5. Pfeifer Dietmar & Mändle Andreas & Ragulina Olena, 2017. "New copulas based on general partitions-of-unity and their applications to risk management (part II)," Dependence Modeling, De Gruyter, vol. 5(1), pages 246-255, October.
    6. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    7. 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.
    8. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2024. "On comprehensive families of copulas involving the three basic copulas and transformations thereof," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-36.
    9. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    10. Dimitris Bertsimas & Agni Orfanoudaki, 2021. "Algorithmic Insurance," Papers 2106.00839, arXiv.org, revised Dec 2022.
    11. Tim J. Boonen & Wing Fung Chong & Mario Ghossoub, 2024. "Pareto‐efficient risk sharing in centralized insurance markets with application to flood risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 91(2), pages 449-488, June.
    12. Claudia Ceci & Katia Colaneri & Rdiger Frey & Verena Kock, 2019. "Value adjustments and dynamic hedging of reinsurance counterparty risk," Papers 1909.04354, arXiv.org.
    13. Karlsson, Sune & Mazur, Stepan & Nguyen, Hoang, 2023. "Vector autoregression models with skewness and heavy tails," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    14. Sundusit Saekow & Phisanu Chiawkhun & Woraphon Yamaka & Nawapon Nakharutai & Parkpoom Phetpradap, 2024. "Estimation of Contagion: Bayesian Model Averaging on Tail Dependence of Mixture Copula," Mathematics, MDPI, vol. 12(21), pages 1-23, October.
    15. Yuanying Guan & Zhanyi Jiao & Ruodu Wang, 2022. "A reverse ES (CVaR) optimization formula," Papers 2203.02599, arXiv.org, revised May 2023.
    16. Shahzad, Muhammad Faisal & Abdulai, Awudu, 2020. "Adaptation to extreme weather conditions and farm performance in rural Pakistan," Agricultural Systems, Elsevier, vol. 180(C).
    17. Xuehai Zhang, 2019. "Value at Risk and Expected Shortfall under General Semi-parametric GARCH models," Working Papers CIE 126, Paderborn University, CIE Center for International Economics.
    18. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.
    19. Rudiger Frey & Kevin Kurt & Camilla Damian, 2020. "How Safe are European Safe Bonds? An Analysis from the Perspective of Modern Portfolio Credit Risk Models," Papers 2001.11249, arXiv.org, revised Jul 2020.
    20. Santos, Douglas G. & Candido, Osvaldo & Tófoli, Paula V., 2022. "Forecasting risk measures using intraday and overnight information," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).

    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:gam:jrisks:v:6:y:2018:i:3:p:92-:d:168425. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.