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On the Basel Liquidity Formula for Elliptical Distributions

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  • Janine Balter
  • Alexander J. McNeil

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 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," Papers 1803.07590, arXiv.org.
    • Handle: RePEc:arx:papers:1803.07590
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    References listed on IDEAS

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    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.
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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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