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On the Basel Liquidity Formula for Elliptical Distributions


  • 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)


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, Open Access Journal, 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

    1. repec:wsi:ijtafx:v:08:y:2005:i:05:n:s0219024905003104 is not listed on IDEAS
    2. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(1), pages 1-14, February.
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    More about this item


    Basel Accords; liquidity risk; risk measures; expected shortfall; elliptical distributions; generalized hyperbolic distributions;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law


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