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Undertaking specific parameters under solvency II: reduction of capital requirement or not?

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Abstract

Solvency II regulation provides different approaches for the calculation of the solvency capital requirement (SCR): standard formula with simplification, standard formula, standard formula with undertaking specific parameters (USP), partial internal model and full internal model. In particular this regulation describes a subset of the Standard Formula market parameters (standard deviations) that may be replaced by USP, in order to calculate the SCR deriving from Premium and Reserving Risks of a Non-Life insurance company. This paper aims to explain the data requirements, methodologies and results according the so-called standardized methods proposed in the Solvency II regulation for the USP. Applying the standardized methods to three companies respectively of small, medium and large sizes and developing some sensitivity analysis, regarding the change in data from year to year, peaks and other issues which standardized methods look sensitive, the paper shows when the USP could reduce the SCR in comparison with the Standard Formula approach.

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Notes

  1. In R this test is very simple to implement: we could apply the lm function and then we calculate the F-statistics of the significance test with the summary function. If the p value is much less than 0.05, we reject the null hypothesis that β1 = 0 and concluding that there is a significant relationship between the variables in the linear regression model of the data set used. The R function lm is used to fit linear models. It can be used to carry out regression, single stratum analysis of variance and analysis of covariance.

  2. If we use L-BFGS-B method with box constraints rather than BFGS method, we would get almost the same results.

  3. For many others companies analyzed in Cerchiara and Santoni [6] (not shown in this paper) mixing parameter assumes values very close to 1, the superior extreme of the domain.

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Authors and Affiliations

  1. Department of Economics, Statistics and Finance, University of Calabria, Via P. Bucci, 3C, 87036, Arcavacata di Rende, CS, Italy

    Rocco Roberto Cerchiara & Valentina Demarco

Authors
  1. Rocco Roberto Cerchiara
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  2. Valentina Demarco
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Correspondence to Rocco Roberto Cerchiara.

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Cerchiara, R.R., Demarco, V. Undertaking specific parameters under solvency II: reduction of capital requirement or not?. Eur. Actuar. J. 6, 351–376 (2016). https://doi.org/10.1007/s13385-016-0139-6

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  • DOI: https://doi.org/10.1007/s13385-016-0139-6

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