Credit risk and solvency capital requirements


Credit risk permeates the assets of most insurance companies. This article develops a framework for computing credit capital requirements under the constant position paradigm and taking into account recovery rates. Although this framework was originally derived under the Solvency 2 regulation, it also provides concepts that can be useful under other international regulations. After a brief survey of the existing technology on rating transitions and default probabilities, the paper provides new results on risk premium adjustment factors. Then, three different procedures for reconstructing constant position market-consistent histories of credit portfolios from quoted Merrill Lynch indices are given. The reconstructed historical credit values are modeled via mixed empirical-Generalized Pareto Distribution (GPD) dynamics and a detailed parameter estimation is performed. Several validations of the estimation are also provided. Finally, credit Solvency Capital Requirements are computed and an analysis of the results per rating class is given.

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    In structural approaches, it is possible to use the Girsanov theorem or the Wang [30] transform to construct the risk-neutral universe. Note that in the latter approach, a distorsion of decumulative historical probabilities, rather than of probabilities, is applied.

  2. 2.

    For AAA bonds, the models predict a null SCR because the recovery rate is \(100\%\) for all these bonds in our database.


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The authors would like to thank Philippe Desurmont, Anthony Floryszczak, Donatien Hainaut, François-Xavier de Lauzon, Jacques Lévy-Véhel, Hubert Rodarie, Li Shen, Xia Xu, and Christian Walter for their useful comments.

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Corresponding author

Correspondence to Olivier Le Courtois.


Appendix 1

See Table 6.

Table 6 Bond dataset as of 31 / 12 / 2014

Appendix 2

See Table 7.

Table 7 Average 1-year corporate transition rates (%). Source: Standard and Poor’s

Appendix 3

See Tables 8, 9 and 10.

Table 8 Parameter a of the standard formula
Table 9 Parameter b of the standard formula
Table 10 Parameter c of the standard formula

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Allali, J., Le Courtois, O. & Majri, M. Credit risk and solvency capital requirements. Eur. Actuar. J. 8, 487–515 (2018).

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  • Credit spread
  • Risk premium adjustment factor
  • Solvency capital requirement
  • General pareto distribution
  • Market consistency
  • Rating transition
  • Credit benchmarking
  • Constant position