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A Liquidation Risk Adjustment For Value At Risk And Expected Shortfall

Author

Listed:
  • Lakshithe Wagalath

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • Jorge Zubelli

    (IMPA - Instituto Nacional de Matemática Pura e Aplicada)

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 Zubelli, 2018. "A Liquidation Risk Adjustment For Value At Risk And Expected Shortfall," Post-Print hal-02572794, HAL.
    • Handle: RePEc:hal:journl:hal-02572794
    DOI: 10.1142/S0219024918500103
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    Cited by:

    1. David Evangelista & Yuri Thamsten, 2020. "On finite population games of optimal trading," Papers 2004.00790, arXiv.org, revised Feb 2021.
    2. 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.
    3. Theo Berger & Christina Uffmann, 2021. "Assessing liquidity‐adjusted risk forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(7), pages 1179-1189, November.
    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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