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A Liquidation Risk Adjustment For Value At Risk And Expected Shortfall

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  • LAKSHITHE WAGALATH

    (IESEG School of Management — LEM, (CNRS), 1 Parvis de la Défense, 92044, Paris La Défense Cedex, France†Instituto de Matematica Pura e Aplicada, Estr. Dona Castorina, 110, Jardim Botanico, Rio de Janeiro, RJ 22460-320, Brasil)

  • JORGE P. ZUBELLI

    (#x2020;Instituto de Matematica Pura e Aplicada, Estr. Dona Castorina, 110, Jardim Botanico, Rio de Janeiro, RJ 22460-320, Brasil)

Abstract

This paper proposes an intuitive and flexible framework to quantify liquidation risk for financial institutions. We develop a model where the “fundamental” dynamics of assets is modified by price impacts from fund liquidations. We characterize mathematically the liquidation schedule of financial institutions and study in detail the fire sales resulting endogenously from margin constraints when a financial institution trades through an exchange. Our study enables to obtain tractable formulas for the value at risk and expected shortfall of a financial institution in the presence of fund liquidation. In particular, we find an additive decomposition for liquidation-adjusted risk measures. We show that such a measure can be expressed as a “fundamental” risk measure plus a liquidation risk adjustment that is proportional to the size of fund positions as a fraction of asset market depths. Our results can be used by risk managers in financial institutions to tackle liquidity events arising from fund liquidations better and adjust their portfolio allocations to liquidation risk more accurately.

Suggested Citation

  • Lakshithe Wagalath & Jorge P. Zubelli, 2018. "A Liquidation Risk Adjustment For Value At Risk And Expected Shortfall," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-21, May.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:03:n:s0219024918500103
    DOI: 10.1142/S0219024918500103
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    References listed on IDEAS

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    1. Yann Braouezec & Lakshithe Wagalath, 2016. "Risk-based capital requirements and optimal liquidation in a stress scenario," Working Papers 2016-ACF-01, IESEG School of Management.
    2. Rama Cont & Arseniy Kukanov & Sasha Stoikov, 2014. "The Price Impact of Order Book Events," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 47-88.
    3. Lakshithe Wagalath, 2017. "Lost In Contagion? Building A Liquidation Index From Covariance Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-26, 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.
    5. Andrei Shleifer & Robert Vishny, 2011. "Fire Sales in Finance and Macroeconomics," Journal of Economic Perspectives, American Economic Association, vol. 25(1), pages 29-48, Winter.
    6. Kempf, Alexander & Korn, Olaf, 1999. "Market depth and order size1," Journal of Financial Markets, Elsevier, vol. 2(1), pages 29-48, February.
    7. Lakshithe Wagalath, 2017. "Lost In Contagion? Building A Liquidation Index From Covariance Dynamics," Post-Print hal-01745354, HAL.
    8. Rama Cont & Lakshithe Wagalath, 2012. "Fire Sales Forensics: Measuring Endogenous Risk," Working Papers hal-00697224, HAL.
    9. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
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    Cited by:

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    3. Enrique Molina‐Muñoz & Andrés Mora‐Valencia & Javier Perote, 2021. "Backtesting expected shortfall for world stock index ETFs with extreme value theory and Gram–Charlier mixtures," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4163-4189, July.
    4. M. Andrea Arias-Serna & Jean-Michel Loubes & Francisco J. Caro-Lopera, 2020. "Risk Measures Estimation Under Wasserstein Barycenter," Papers 2008.05824, arXiv.org.

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