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Solvency II in the Insurance Industry pp 23–84Cite as

Application of the Data Model: Pillar One

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Part of the book series: Contributions to Management Science ((MANAGEMENT SC.))

Abstract

Pillar One covers the available capital and the capital requirements which may be calculated by the pre-defined standard formula approach, by a partial internal model, or by a full internal model.

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Notes

  1. 1.

    For example, in the German GAAP requirements for IVW Private Lines presented in Sect. 1.3.2.

  2. 2.

    Mostly used in internal non-life models.

  3. 3.

    Because both fixed income assets expire at the end of the year, there is more or less a free choice of classification.

  4. 4.

    After application of this run-off factor, the chain ladder estimates on the base of the paid triangles equal those on the base of the incurred triangles.

  5. 5.

    In the formula, CPt, k denotes the cumulated payments of the accident year t at the end of the development period k and CDFk denotes the cumulated development factors for all periods after period k obtained as product of the one-period development factors as explained in Appendix A.

  6. 6.

    In this formula, TR denotes the tax rate, AV the asset value, and BSE the local GAAP (LG) balance sheet equity. With respect to IFRS, the asset value also covers the ceded provisions.

  7. 7.

    In this formula, DBE denotes the discounted best estimate provisions where the BE provisions equal the technical provisions under IFRS.

  8. 8.

    This parameter covers reserve risks as well as operational risks.

  9. 9.

    In this formula, BP resp. DBP denote the nominal resp. discounted balance year payments (in contrast to the cumulated accident year payments CP), and DCoC denotes the discounted cost of capital.

  10. 10.

    Compare Sect. 2.2.4.

  11. 11.

    According to the difference between the initial risk free rate of 4.0% and the actual risk free rate of 2.5%.

  12. 12.

    See Appendix B with an alternative representation of the MCEV to clarify the tax effects.

  13. 13.

    As will be explained in a later section, this loss ratio covers regular losses and catastrophe losses.

  14. 14.

    The percentage for the premium and catastrophe risk will be calculated in Sect. 2.2.6.

  15. 15.

    The parameter will be derived in a later section.

  16. 16.

    In this formula, PR denotes the premiums and AC the administration costs.

  17. 17.

    While developing the standard formula, its’ impacts have been tested by five quantitative impact studies (QIS), increasing the complexity at each iteration. As a result, it has been argued whether the standard formula provides a comprehensive and easily applicable model approach for small and middle sized entities.

  18. 18.

    With respect to life insurance business, there are further adjustments according to loss absorbing capacity by technical provisions effected by surplus participation systems.

  19. 19.

    As a consequence of this, the accident business of the IVW Private Lines has to be classified as health business although it is non-life business according to the local classification.

  20. 20.

    The printed figure only shows the first five years. The whole figure contains the factors for 90 years. For maturities longer than 90 years, the increase shall be 20%.

  21. 21.

    This aggregation approach implies a normal distribution assumption that is not realistic in every case.

  22. 22.

    Also included are securitisations, derivatives (excluding credit derivatives which are already treated under the spread risk module), deposits with ceding and credit institutions, see EIOPA-14-322, p. 71.

  23. 23.

    Less respectively greater or equal than three month (3M).

  24. 24.

    According to the model assumptions, an increase of 5.0% has been applied to the actual net earned premium as introduced in Sect. 1.3.1.

  25. 25.

    See Sect. 2.1.2.

  26. 26.

    Catastrophe risk will be treated in more detail in Sect. 2.4.1.

  27. 27.

    See Appendix C with respect to the full correlation matrix.

  28. 28.

    In the following formula, VaR denotes the value at risk, EXP the exponential function and LN the natural logarithm.

  29. 29.

    See Sect. 2.1.2.

  30. 30.

    See Sect. 2.1.2.

  31. 31.

    The risk map approach will be explained in Sect. 3.1.2 in more detail.

  32. 32.

    A random impact can be interpreted as the set of all causes that determine a certain outcome.

  33. 33.

    There are additional criteria to define a random variable being out of scope of this chapter.

  34. 34.

    With regard to the severities, distribution characteristics are normally obtained by applying the companies’ exposure to the externally provided models.

  35. 35.

    With respect to the first event, the determination of the net expected value has been slightly simplified, because the likelihood to exceed the limit has not been taken into account. Thus, simulated expected values may be higher.

  36. 36.

    For further information see Cantle et al. (2012).

  37. 37.

    In this formula, LRNet, RG denotes the net liquid result with respect to regular claims.

  38. 38.

    According to the quantiles of the empirical distribution, the ruin probability can be estimated as 0.12%.

  39. 39.

    This happens, for example, if the extra-ordinary tax depreciations are considered as a separate component of a profit and loss calculation.

  40. 40.

    It should be noticed that a fix number of MC simulations corresponds to a fix number of TVaR values. Thus, there is only an approximate mapping between VaR and TVaR principle.

  41. 41.

    A real internal model with realistic parameterizations would have been beyond any scope of a relatively simple data model.

  42. 42.

    Additivity can be generated by modelling those risks as a linear function of the diversified BSCR. This is, by no means, a realistic assumption.

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Authors and Affiliations

  1. Institute for Insurance Studies (ivwKöln), TH Köln – University of Applied Sciences, Cologne, Germany

    Maria Heep-Altiner, Torsten Rohlfs, Fabian Clasen, Gabriel Gallinger, Martin Gerlach, Valeria Keller, Andre Loeken, Harry Moor, Teresa Olbrich & Jakob Schwering

  2. Department of Accounting and Finance, Kemmy Business School, University of Limerick, Limerick, Ireland

    Martin Mullins & Barry Sheehan

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  1. Maria Heep-Altiner
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  2. Martin Mullins
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  3. Torsten Rohlfs
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  6. Martin Gerlach
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  7. Valeria Keller
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Correspondence to Maria Heep-Altiner .

Editor information

Editors and Affiliations

  1. Institute for Insurance Studies (ivwKöln), TH Köln – University of Applied Sciences, Cologne, Germany

    Maria Heep-Altiner

  2. Department of Accounting and Finance, Kemmy Business School, University of Limerick, Limerick, Ireland

    Martin Mullins

  3. Institute for Insurance Studies (ivwKöln), TH Köln – University of Applied Sciences, Cologne, Germany

    Torsten Rohlfs

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Heep-Altiner, M. et al. (2018). Application of the Data Model: Pillar One. In: Heep-Altiner, M., Mullins, M., Rohlfs, T. (eds) Solvency II in the Insurance Industry. Contributions to Management Science. Springer, Cham. https://doi.org/10.1007/978-3-319-77060-4_2

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