Solvency II requires that firms with Internal Models derive the Solvency Capital Requirement directly from the probability distribution forecast generated by the Internal Model. A number of UK insurance undertakings do this via an aggregation model consisting of proxy models and a copula. Since 2016 there have been a number of industry surveys on the application of these models, with the 2019 Prudential Regulation Authority (“PRA”) led industry wide thematic review identifying a number of areas of enhancement. This concluded that there was currently no uniform best practice. While there have been many competing priorities for insurers since 2019, the Working Party expects that firms will have either already made changes to their proxy modelling approach in light of the PRA survey, or will have plans to do so in the coming years. This paper takes the PRA feedback into account and explores potential approaches to calibration and validation, taking into consideration the different heavy models used within the industry and relative materiality of business lines.

The development of an economic capital model requires a decision to be made regarding how to aggregate capital requirements for the individual risk factors while taking into account the effects of diversification. Under the Individual Capital Adequacy Standards framework, UK life insurers have commonly adopted a correlation matrix approach due to its simplicity and ease in communication to the stakeholders involved, adjusting the result, where appropriate, to allow for non-linear interactions. The regulatory requirements of Solvency II have been one of the principal drivers leading to an increased use of more sophisticated aggregation techniques in economic capital models. This paper focusses on a simulation-based approach to the aggregation of capital requirements using copulas and proxy models. It describes the practical challenges in parameterising a copula including how allowance may be made for tail dependence. It also covers the challenges associated with fitting and validating a proxy model. In particular, the paper outlines how insurers could test, communicate and justify the choices made through the use of some examples.