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Systemic Fragility Measures

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Part of the Studies in Systems, Decision and Control book series (SSDC,volume 409)


The risk of default of sovereigns and banking institutions has proved to be of major concern for regulators during the Global financial and the recent euro area sovereign debt crises. In such turbulent times for markets and regulators, the consistent and assessment of the individual and systemic risks of banks and sovereigns is of utmost importance.

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  1. 1.

    Sturzenegger and Zettelmeyer (2008) find that the historical sovereign recovery rates are usually between 30 and 70%. Lucas et al. (2014) use those results as motivation to choose 25% recovery rate for their default estimations. We decide to be more conservative with regard to the loss given default assumption, as the recent negotiations for the Private Sector Involvement (PSI) in the Greek bailout packages suggest haircuts between 50 and 70%. As non-institutional investors are the main participants in the CDS markets, we argue that their expectations of default risk are what the CDS spreads reflect, thus we remain with the usual recovery rate convention in financial literature. For a discussion on how different recovery rates affect the PoD estimates, please refer to our robustness checks Sect. 4.5 and to Gorea and Radev (2014).

  2. 2.

    The extension to the multivariate case is trivial.

  3. 3.

    In the text, we abbreviate the measure related to banks as PNBD and the one related to sovereigns as PNSD.

  4. 4.

    PAO is also sometimes referred to as a probability of spillover effects (PSE).

  5. 5.

    The extension to higher dimensions, although more involving, is straightforward, as long as one keeps account of the default contingencies to be added or subtracted.

  6. 6.

    The banks used in our analysis are listed in Table 4.1.

  7. 7.

    Note that the levels of SFM between Figs. 4.13 and 4.14 are not directly comparable, because of the different number of dimensions of the underlying distributions.

  8. 8.

    For the sake of brevity, we report the results only for several of the couples. The remaining results are available upon request.

  9. 9.

    For details, see Sect. 3.2.2.

  10. 10.

    The relative insensitivity of the cross-entropy distribution to changes of the prior distribution assumption is also analytically shown in Segoviano (2006).


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Correspondence to Deyan Radev .

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Radev, D. (2022). Systemic Fragility Measures. In: Measuring Systemic Risk. Studies in Systems, Decision and Control, vol 409. Springer, Cham.

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