Risk aggregation in Solvency II through recursive log-normals

It is argued that the accuracy of risk aggregation in Solvency II can be improved by updating skewness recursively. A simple scheme based on the log-normal distribution is developed and shown to be superior to the standard formula and to adjustments of the Cornish–Fisher type. The method handles tail-dependence if a simple Monte Carlo step is included. A hierarchical Clayton copula is constructed and used to confirm the accuracy of the log-normal approximation and to demonstrate the importance of including tail-dependence. Arguably a log-normal scheme makes the logic in Solvency II consistent, but many other distributions might be used as vehicle, a topic that may deserve further study.