Modelling dependencies between internal and external models using vine copulas

Dependencies are a major theme in capital modelling, and these are often some of the most material and subjective judgements in an internal model. Most internal models rely to some extent on external models, and dependencies between internal and external models are increasingly important, given the growing tendency for risks in one area of the risk profile to impact outcomes in other risk areas; the impact of economic conditions on underwriting performance, and the importance of non-physical climate-change risks are just some examples. This paper provides a novel method, which goes part way to addressing a limitation in apparent standard practice, by enabling the specification of more than one dependence relationship between sets of pre-simulated data. It therefore sets actuaries up to be able to deal with the ever-more correlated world around us.