The Effect of Non-Proportional Reinsurance: A Revision of Solvency II Standard Formula

Abstract

Solvency II Standard Formula provides a methodology to recognise the risk-mitigating impact of excess of loss reinsurance treaties in premium risk modelling. We analyse the proposals of both Quantitative Impact Study 5 and Commission Delegated Regulation highlighting some inconsistencies. This paper tries to bridge main pitfalls of both versions. To this aim, we propose a revision of non-proportional adjustment factor in order to measure the effect of excess of loss treaties on premium risk volatility. In this way, capital requirement can be easily assessed. As numerical results show, this proposal appears to be a feasible and much more consistent approach to describe the effect of non-proportional reinsurance on premium risk.

An optimal reinsurance simulation model for non-life insurance in the Solvency II framework

“…) . Although the analysis of the effects of a treaty on the volatility is crucial and it could be also interesting for a direct comparison with the risk mitigation factors defined by the Solvency II standard formula (see, e.g., the non-proportional factor defined in [29] and analysed in [18,19]), the coefficient of variation gives only a partial view of the risk profile of an insurer. For instance, it does not consider the effect on the skewness of the distribution as well as the presence of possible sliding commissions in proportional treaties.…”

Premium Risk Net of Reinsurance: From Short-Term to Medium-Term Assessment

“…Focusing on reinsurance recognition in the new regulation, the solution provided by Solvency II SF is based on a lognormal distribution assumption. This approach can lead to an overestimation of the risk mitigating effect of this kind of reinsurance (see (Clemente 2018)), because it neglects the systematic component that usually affects the number of claims (see (Daykin et al 1994); (Gisler 2009); and (Savelli and Clemente 2009)), while proportional reinsurance does not affect net aggregate claims' cost distribution, but insurers' risk profile can change because of reinsurance pricing (see (Clemente et al 2015)).…”