The Effects of Contingent Convertible (CoCo) Bonds on Insurers’ Capital Requirements Under Solvency II


The Liikanen Group proposes contingent convertible (CoCo) bonds as a potential mechanism to enhance financial stability in the banking industry. Especially life insurance companies could serve as CoCo bond holders, as they are already the largest purchasers of bank bonds in Europe. We develop a stylised model with a direct financial connection between banking and insurance and study the effects of various types of bonds such as non-convertible bonds, write-down bonds and CoCos on banks’ and insurers’ risk situations. In addition, we compare insurers’ capital requirements under the proposed Solvency II standard model as well as under an internal model that ex ante anticipates additional risks due to possible conversion of the CoCo bond into bank shares. In order to check the robustness of our findings, we consider different CoCo designs (write-down factor, trigger value, holding time of bank shares) and compare the resulting capital requirements with those for holding non-convertible bonds. We identify situations in which insurers benefit from buying CoCo bonds due to lower capital requirements and higher coupon rates. Furthermore, our results highlight how the Solvency II standard model can mislead insurers in their CoCo investment decision due to economically irrational incentives.

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  1. 1.

    See Liikanen Group (2012).

  2. 2.

    The trigger is typically a fixed core capital ratio set by the regulator. See, for example, FINMA (2011).

  3. 3.

    See Avdjiev et al. (2013, pp. 48–49). Banks that have issued CoCo bonds include Lloyds Bank (2009), UBS (2012), Barclays (2013) and Deutsche Bank (2012).

  4. 4.

    See Bank for International Settlements (2011).

  5. 5.

    See Krahnen (2013, p. 15).

  6. 6.

    See Insurance Europe and Oliver Wyman (2013).

  7. 7.

    See Glasserman and Nouri (2012).

  8. 8.

    Bank for International Settlements (2011).

  9. 9.

    Eling et al. (2007).

  10. 10.

    Gatzert and Wesker (2012).

  11. 11.

    Flannery (2002).

  12. 12.

    Shang (2013).

  13. 13.

    Pennacchi (2011).

  14. 14.

    Glasserman and Nouri (2012).

  15. 15.

    A bank’s risk-weighted assets are usually determined at the end of each quarter. See Zähres (2011, p. 7).

  16. 16.

    Note that for simplicity reasons, we assume that the bank’s assets exhibit a risk weight of 100 per cent. Thus, total assets V t equal the amount of risk-weighted assets at time t.

  17. 17.

    We find c* by valuing the bonds discounted expected cash flows for a given bank risk and then iterating over c until we find the coupon value c* such that the face value equals the present value. See Pennacchi (2011).

  18. 18.

    See Glasserman and Nouri (2012, p. 1819).

  19. 19.

    See Brigo et al. (2013, p. 12) for a similar approach.

  20. 20.

    See GDV (2014, p. 28).

  21. 21.

    See EIOPA (2013b, p. 116).

  22. 22.

    Among European life insurers, market risk accounts for up to 70 per cent of the overall SCR. See Fitch Ratings (2011).

  23. 23.

    Laas and Siegel (2013).

  24. 24.

    See EIOPA (2013b, p. 133).

  25. 25.

    EIOPA (2013b, pp. 136–137).

  26. 26.

    See EIOPA (2013b, p. 139).

  27. 27.

    ST0CC amounts to the second part of Eq. (11) evaluated at time t=1.

  28. 28.

    The second case also applies to a write-down bond.

  29. 29.

    See EIOPA (2013b, pp. 147–154).

  30. 30.

    See EIOPA (2013b, p. 148).

  31. 31.

    See EIOPA (2013c, p. 45).

  32. 32.

    Reichling et al. (2007, p. 104).

  33. 33.

    EIOPA (2013b, pp. 148–149).

  34. 34.

    We use the insurer’s average asset return between time t=0 and t=1.

  35. 35.

    Specifically, we use the following time series: WZ9810, WZ9812, WZ9814, WZ9816, WZ9818, WZ9820, WZ9822, WZ9824, WZ9826, WZ3431 and WZ3433. See

  36. 36.

    Source: Datastream.

  37. 37.

    Pennacchi (2011, p. 19).

  38. 38.

    Based on the 2012 average stock and real estate investment weight of the largest life insurance enterprises in Europe. See EIOPA (2013a).

  39. 39.

    See BaFin (2012).

  40. 40.

    See Deutsche Bank Annual Report (2012).

  41. 41.

    See Avdjiev et al. (2013).

  42. 42.

    Chen et al. (2013).

  43. 43.

    See Chen et al. (2013, p. 22).

  44. 44.

    The low conversion ratio (φ=0.25) in calibration IV corresponds to the issued CoCo bond by Rabobank in 2011 with a write-down factor of 75 per cent. See Corcuera et al. (2013, p. 134).

  45. 45.

    The accompanying letter ratings represent the Standard & Poor’s rating scale.


  1. Avdjiev, S., Kartasheva, A.V. and Bogdanova, B. (2013) ‘CoCos: A primer’, BIS Quarterly Review, September: 43–56.

    Google Scholar 

  2. Bank for International Settlements (2011) Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems (rev.), Basel: Bank for International Settlements, from

  3. Brigo, D., Garcia, J. and Pede, N. (2013) CoCo bonds valuation with equity and credit-calibrated first passage structural models, Imperial College of London, London, UK, working paper.

  4. Chen, N., Glasserman, P., Nouri, B. and Pelger, M. (2013) Contingent capital, tail risk, and debt-induced collapse, Columbia Business School Research Paper, No. 13–90.

  5. Corcuera, J.M., Spiegeleer, J., Ferreiro-Castilla, A., Kyprianou, A., Madan, D. and Schoutens, W. (2013) ‘Pricing of contingent convertibles under smile conform models’, Journal of Credit Risk 9 (3): 121–140.

    Article  Google Scholar 

  6. Deutsche Bank (2012) Annual Review 2012, Frankfurt am Main: Deutsche Bank Aktiengesellschaft, from

  7. Eling, M., Schmeiser, H. and Schmit, J.T. (2007) ‘The solvency II process: Overview and critical analysis’, Risk Management and Insurance Review 10 (1): 69–85.

    Article  Google Scholar 

  8. European Insurance and Occupational Pensions Authority (EIOPA) (2013a) EU/EEA (re)insurance statistics’ (formerly ‘Statistical annex to EIOPA financial stability report’), from

  9. European Insurance and Occupational Pensions Authority (EIOPA) (2013b) ‘Technical specification on the long term guarantee assessment (part I)’, from

  10. European Insurance and Occupational Pensions Authority (EIOPA) (2013c) ‘Technical specification on the long term guarantee assessment (part II)’, from

  11. Federal Financial Supervisory Authority (BaFin) (2012) ‘Mitteilungen der Bundesanstalt für Finandienstleistungsaufsicht’, BaFin Journal.

  12. Fitch Ratings (2011) Solvency II Set to Reshape Asset allocation and Capital Markets, Insurance Rating Group special report.

  13. Flannery, M. (2002) No pain, no gain? Effecting market discipline via reverse convertible debentures, working paper, University of Florida.

  14. Gatzert, N. and Wesker, H. (2012) ‘A comparative assessment of Basel II/III and Solvency II’, The Geneva Papers on Risk and Insurance—Issues and Practice 37 (3): 539–570.

    Article  Google Scholar 

  15. Gesamtverband der Deutschen Versicherungswirtschaft e. V. (GDV) (2014) Statistical Yearbook of German Insurance 2014, Berlin: GDV.

  16. Glasserman, P. and Nouri, B. (2012) ‘Contingent capital with a capital-ratio trigger’, Management Science 58 (10): 1816–1833.

    Article  Google Scholar 

  17. Insurance Europe and Oliver Wyman (2013) Funding the Future: Insurers’ Role as Institutional Investors, Brussels: Insurance Europe and Oliver Wyman.

  18. Krahnen, J.P. (2013) Rescue by regulation? Key points of the Liikanen Report. SAFE Policy Center White Paper No. 9.

  19. Laas, D. and Siegel, C.F. (2013) Basel accords versus Solvency II: Regulatory adequacy and consistency under the postcrisis capital standards. Risk Management and Insurance Working Paper No. 132, University of St. Gallen.

  20. Liikanen et al. (2012) High-Level Expert Group on Reforming the Structure of the EU Banking Sector (‘Liikanen Report’).

  21. Pennacchi, G. (2011) A structural model of contingent bank capital, FRB of Cleveland Working Paper No. 10-04 (rev.), Federal Reserve Bank of Cleveland.

  22. Reichling, P., Bietke, D. and Henne, A. (2007) Praxishandbuch Risikomanagement und Rating: Ein Leitfaden. 2nd edn, Wiesbaden: Gabler Verlag.

    Google Scholar 

  23. Shang, K. (2013) Understanding Contingent Capital. Technical Report, Casualty Actuarial Society.

  24. Swiss Financial Market Supervisory Authority (FINMA) (2011) Addressing Too Big To Fail—The Swiss SIFI Policy, Bern: Swiss Financial Market Supervisory Authority.

  25. Zähres, M. (2011) Contingent Convertibles—Bank Bonds Take on a New Look. EU Monitor–Financial Market Special, Frankfurt am Main: Deutsche Bank Research.

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  • We proof formula (9) with induction in δ T :

    Let δ T =2. Note that by convention, empty products are equal to 1, that is ∏i=jnf(i)=1 for all n<j and all functions f. With formula (8) it follows

    Let δ T δ T +1. By using the case δ T =2 and formula (8), it follows that the fraction of equity held after the (δ T +1)th conversion is

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Niedrig, T., Gründl, H. The Effects of Contingent Convertible (CoCo) Bonds on Insurers’ Capital Requirements Under Solvency II. Geneva Pap Risk Insur Issues Pract 40, 416–443 (2015).

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  • contingent convertible (CoCo) bond
  • Basel III
  • Solvency II
  • life insurance
  • interconnectedness