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Bank insolvency risk, Z-score measures and unimodal returns: A refinement

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  • Mercadier, Mathieu
  • Strobel, Frank

Abstract

We develop refined probability bounds for bank insolvency risk measures based on the Z-score, analogous to those given by Cantelli’s inequality under the additional assumption of unimodality of returns, drawing on the one-sided Vysochanskii-Petunin inequality. Illustrating empirically for US banks, we argue that (i) unimodality of returns is not an overly restrictive assumption in this context, and (ii) the refined measures provide a less conservative alternative to insolvency probability bounds drawing on the (two-sided) Vysochanskii-Petunin inequality, particularly for banks with higher levels of insolvency risk.

Suggested Citation

  • Mercadier, Mathieu & Strobel, Frank, 2024. "Bank insolvency risk, Z-score measures and unimodal returns: A refinement," The Quarterly Review of Economics and Finance, Elsevier, vol. 98(C).
    • Handle: RePEc:eee:quaeco:v:98:y:2024:i:c:s106297692400125x
    DOI: 10.1016/j.qref.2024.101919
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    More about this item

    Keywords

    Bank; Insolvency risk; Z-score; Unimodality; One-sided Vysochanskii-Petunin inequality;
    All these keywords.

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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