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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
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    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.

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