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Insurance Regulation and Life Catastrophe Risk: Treatment of Life Catastrophe Risk Under the SCR Standard Formula of Solvency II and the Necessity of Partial Internal Models

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Abstract

The regulatory regime in Europe is undergoing a fundamental change that will serve as a benchmark for the regulators in other countries. This paper analyses the influence of regulation imposed by Solvency II on life catastrophe risk management activities. The interplay of extreme mortality risks and risk management activities is demonstrated, and the special characteristics of different causes of life catastrophe risk are identified. The advice of the Committee of European Insurance and Occupational Pensions Supervisors, now the European Insurance and Occupational Pensions Authority, regarding the life catastrophe risk sub-module of the solvency capital requirement standard formula is to apply a unified single mortality catastrophe shock scenario. We show that this approach does not properly reflect life catastrophe risk and that it potentially prevents the recognition of more sophisticated risk management instruments for the solvency capital requirement calculation. As a result of this analysis, proposals are made for how these shortcomings can be resolved by using a simple generic partial internal model. This model facilitates the recognition of non-proportional risk transfer techniques and thus provides incentives for their use. We show that these proposals are in line with and relevant to the current trend towards the potential development of a more liquid market for extreme mortality risks.

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Notes

  1. Artemis (2014).

  2. cf. Blake et al. (2011); Routhenstein and Schreiber (2011).

  3. For example, Bagus (2007); Risk Management Solutions, Inc. (2007).

  4. The product is paid for before it is produced. The interval between the purchase of the product (payment of the premium) and the production of the service (payment of the claim) ranges up to several decades.

  5. Lorent (2008).

  6. Monkiewicz (2007).

  7. See, for example, Trainar (2006).

  8. cf. Weiss (1993, p. 462 f.).

  9. For example, Eling and Holzmüller (2008); Elderfield (2009).

  10. For example, Gatzert and Wesker (2012); Wagner and Zemp (2012).

  11. Cummins et al. (1993), in particular p. 438.

  12. Doff (2008).

  13. Holzmüller (2009).

  14. Siegel (2013).

  15. See, for example, Dong et al. (1996).

  16. cf. Harrington and Niehaus (1999).

  17. Butt (2007).

  18. Also cf. Cummins and Weiss (2009).

  19. Kleindorfer and Klein (2003).

  20. Born and Klimaszewski-Blettner (2009, 2013).

  21. Klein and Wang (2007).

  22. Klein (1998), in particular p. 23.

  23. Schreiber and Silverman (2006); De Mey (2007); Swiss Re (2009); Munich Re (2010); Artemis (2014).

  24. Cummins et al. (1995a, 1995b).

  25. CEIOPS (2009a, 2010a, section 3.3.7).

  26. EIOPA (2011a), in particular pp. 14, 115, 78, 77, 63ff, 77ff respectively.

  27. See Ernst & Young (2012, p. 19).

  28. Munich Re (2012, p. 1).

  29. Verheugen et al. (2009), in particular pp. 1, 2, 4, 2 respectively.

  30. For referencing purposes, we refer to the name of the original document when it was published. For readability, we always refer to EIOPA in the text.

  31. CEIOPS (2009a).

  32. An analogous formula is used to determine the insurer’s overall SCR from the SCRs for the various modules (life underwriting risk, market risk, etc.). Owing to the absolute relevance of the correlation formulas and the correlation matrices, there has been an intensive discussion about them. We refer to CEIOPS (2009e) for an extensive overview.

  33. CEIOPS (2010b, p. 5).

  34. As discussed, the reasons for this choice are manifold; however, this choice does not imply that a similar analysis might not be worthwhile for the other sub-modules.

  35. CEIOPS (2008); EIOPA (2011a, p. 78); EIOPA (2011b, p. 18).

  36. CEIOPS (2009a, § 3.203).

  37. CEIOPS (2009a, § 3.202).

  38. For example, the treatment of multiple insurance policies regarding the same insured person or the treatment of groups of policies.

  39. cf. CEIOPS (2009b, 2009c).

  40. In the sense of consultation paper no. 52, see CEIOPS (2009b).

  41. In the sense of consultation paper no. 31, see CEIOPS (2009c).

  42. An alignment with the International Financial Reporting Standards (IFRS) is also not generally granted: a purely parametric reinsurance contract, for instance, would need to be accounted as derivative due to the missing reference to a concrete insurance portfolio.

  43. cf., for example, Takeda (2002); Kraut (2013).

  44. CEIOPS (2010a, § 3.356).

  45. An exemplary and illustrative market where such a situation could arise will be discussed in the following section together with the recognition of risk management instruments.

  46. See comments during the consultation process regarding Consultation Paper No. 49, CEIOPS (2009a).

  47. For example, CRO Forum (2007).

  48. In some European countries, there are government insurance programmes that, for example, work as a reinsurer of last resort for terrorism risk. However, such programmes are more common for non-life than life insurance. Cf. CRO Forum (2007).

  49. For example, Swiss Re (2007).

  50. With the term group life portfolio, we refer to portfolios where, typically, a company insures all its employees. In some markets, the term group life is also used for cases where, basically, individual life policies are offered to all employees of a company under specific terms. Here, the classification depends on the policy penetration among the company’s employees.

  51. In the World Trade Center, there were 2,606 deaths of around 15,000 people in the building when attacked (Wikipedia, 2014a); in the Pentagon, there were 125 deaths (Wikipedia, 2014a) of around 31,000 people working there (Wikipedia, 2014b). For an elaborate list of industrial accidents, we refer to EM-DAT (EM-DAT, 2014).

  52. See below for details on common risk models.

  53. CEIOPS (2009a, section 3.8.1).

  54. Risk Management Solutions, Inc. (2007, p. 2), for example, counts pandemics to occur every 24 years on average over the last three centuries.

  55. The following analysis will, however, show that the differentiation between low-diversification and high-diversification events is more crucial than the additional differentiation by portfolio type within the high-diversification events.

  56. The approach with a correlation matrix would be consistent with the design of the standard formula and would not constitute a crucial change to the generic model. However, as the considered scenarios are tail events, each originating from a specific cause, we do not take it for granted that the implicitly used normal distribution assumption in this approach is realistic. Even more important, however, is that we do not see an additional facilitation for the recognition of risk management instruments. Nevertheless, such a “square root formula” could be an alternative way to reflect the diversification between the different shock scenarios.

  57. Note that this will, in our view, hardly be achieved with a mere adaption of the size of the unified shock scenario, which is only a theoretical option. As discussed, Solvency II also does not permit the use of undertaking-specific parameters for the life underwriting risk module.

  58. For specific portfolios, the result may deviate because risk models consider portfolio characteristics such as age distribution or geographical location.

  59. CEIOPS (2009a, § 3.190); overview of several relevant studies: Huynh et al. (2013, p. 5); Swiss Re’s model: Swiss Re (2007, p. 63 ff.) or, recently, Kramer (2012, pp. 26–29); risk modelling firms Milliman and RMS: Bagus (2007, 2008) or Risk Management Solutions, Inc. (2007, 2010, 2012); information on the calibration of risk models of the modelling firms Milliman and RMS is also provided in the offering circulars of various mortality cat bonds.

  60. Also cf. Huynh et al. (2013, p. 11), on the calibration of catastrophic mortality bonds.

  61. According to QIS5.

  62. CEIOPS (2009d, p. 14).

  63. Catastrophe excess of loss reinsurance, for instance, might exclude pandemic risk. Cat bonds, which are based on a population index, are not expected to be triggered by (conventional) terrorist attacks, industrial accidents or natural catastrophes.

  64. See, for example, Doherty (1997) or Niehaus (2002).

  65. For the example of risk swaps, cf. Takeda (2002); for multi-party risk pools, cf. Kraut (2013).

  66. We recall that Solvency II is calibrated to the VaR99.5%.

  67. CEIOPS (2009b).

  68. cf. Wagner and Zemp (2012).

  69. cf. Kraut (2013).

  70. We recall from the previous section that Swiss Re quantifies a conservative all-inclusive stress with 1.6 per mille to 1.8 per mille. Taking the average of 1.7 per mille and subtracting the low-diversification events shock leads to the result.

  71. Depending on company type, the SCR for life catastrophe risk contributes 8–16 per cent (≈10 per cent) to the SCR for life underwriting risk. The share of SCR for life underwriting risk after diversification is around 24 per cent of the overall SCR.

  72. This earthquake ultimately also caused the Fukushima Daiichi nuclear disaster.

  73. First loss estimates saw potential life insurance claims for a large Chinese insurance company in the billion dollar range (Reuters, 2008).

  74. For example, Schreiber and Simpson (2008); Swiss Re (2009); Munich Re (2010); Artemis (2014).

  75. cf. Huynh et al. (2013).

  76. cf. De Mey (2007).

  77. cf. Cummins et al. (1995a, p. 6).

  78. cf. Jeanmart and Jones (2012).

  79. As examples of recent studies, we refer to: Blake et al. (2011); Lane (2011); Routhenstein and Schreiber (2011); Schreiber (2011).

  80. A.M. Best Company (1991).

  81. Of course, this shall not neglect the fact that other parts of the Solvency II standard formula, inter alia the correlation matrices, have a big absolute impact on the SCR and are relevant for the overall discussion about Solvency II. This is, however, not the focus of this paper.

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Acknowledgements

A travel grant by Versicherungsforen Leipzig is gratefully acknowledged by Gunther Kraut. The authors are indebted to Günter Schwarz for valuable input and are thankful for the helpful comments from two anonymous reviewers as well as from the participants at the 2nd World Risk and Insurance Economics Congress (WRIEC). All remaining errors are the authors’.

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Kraut, G., Richter, A. Insurance Regulation and Life Catastrophe Risk: Treatment of Life Catastrophe Risk Under the SCR Standard Formula of Solvency II and the Necessity of Partial Internal Models. Geneva Pap Risk Insur Issues Pract 40, 256–278 (2015). https://doi.org/10.1057/gpp.2014.10

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