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Solvency II's Market Risk Standard Formula: How Credible Is the Proclaimed Ruin Probability

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  • Alexander Braun
  • Hato Schmeiser
  • Florian Schreiber

Abstract

We assess the credibility of the ruin probability allegedly associated with themarket risk standard formula of Solvency II, the new regulatory framework for theEuropean insurance industry. For this purpose, we draw on the empirical risk-returnprofiles of six major asset classes and derive mean-variance efficient portfolio compo-sitions, taking into account both short-sale constraints and the prevailing legal invest-ment limits in Germany. In a next step, the capital requirements under the standardformula are calculated for each asset allocation. Employing the respective results, wethen invert an internal model for market risk based on full statistical distributionsinstead of mere stress factors to estimate the actual ruin probabilities correspondingto the efficient portfolios. In most cases, the latter deviate substantially from theproclaimed target of the regulator. Since a large fraction of small to medium-sizedcompanies is likely to resort to the standard formula, the introduction of Solvency IIcould lead to a lot more ambiguity about insolvency risk in the European insurancesector than currently expected.

Suggested Citation

  • Alexander Braun & Hato Schmeiser & Florian Schreiber, 2015. "Solvency II's Market Risk Standard Formula: How Credible Is the Proclaimed Ruin Probability," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 38(1), pages 1-30.
    • Handle: RePEc:wri:journl:v:38:y:2015:i:1:p:1-30
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    Citations

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    Cited by:

    1. Beer, Simone & Braun, Alexander & Marugg, Andrin, 2019. "Pricing industry loss warranties in a Lévy–Frailty framework," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 171-181.
    2. Alexander Braun & Hato Schmeiser & Florian Schreiber, 2018. "Return on Risk-Adjusted Capital Under Solvency II: Implications for the Asset Management of Insurance Companies," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 43(3), pages 456-472, July.
    3. Bølviken, Erik & Guillen, Montserrat, 2017. "Risk aggregation in Solvency II through recursive log-normals," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 20-26.
    4. Kyriakos Georgiou & Athanasios N. Yannacopoulos, 2023. "Probability of Default modelling with L\'evy-driven Ornstein-Uhlenbeck processes and applications in credit risk under the IFRS 9," Papers 2309.12384, arXiv.org.
    5. Shim Jeungbo & Lee Seung-Hwan, 2017. "Dependency between Risks and the Insurer’s Economic Capital: A Copula-based GARCH Model," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 11(1), pages 1-29, January.
    6. Roy Kouwenberg, 2018. "Strategic asset allocation for insurers under Solvency II," Journal of Asset Management, Palgrave Macmillan, vol. 19(7), pages 447-459, December.
    7. Aur'elien Alfonsi & Adel Cherchali & Jose Arturo Infante Acevedo, 2019. "A full and synthetic model for Asset-Liability Management in life insurance, and analysis of the SCR with the standard formula," Papers 1908.00811, arXiv.org.

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