Diversification benefits, and the associated correlation parameters, are critical in determining risk-based capital requirements for many companies. Under Solvency II, firms will be required to justify the use of the standard formula parameters, or else derive their own if those prescribed are deemed to be inappropriate. However, setting and validating correlation parameters can be challenging, with reliance often placed upon high-level discussions and expert judgment.

Historically, the degree of dependency between risks has always been difficult to quantify. Where data is reliable and plentiful, regression analysis can be carried out between risks, and results can be derived and validated. But for risks with insufficient or flawed data (operational risks, for example), it is very difficult to derive meaningful correlations. Consequently, models are often built with the end result already in mind, influenced by the expert's view of the correlations, with little justification as to how the estimate was derived. This can lead to an incomplete view of how the risks behave, and can be difficult to justify and validate.

One possible solution is to use knowledge from business experts to build up a complete picture of each risk, and then build a causal model to derive correlations between them. This approach allows information already within the business to be extracted and provides a multitude of options for sensitivity analysis and stress testing. Furthermore, by documenting the initial discussions and model build, the process provides a clear audit trail for validation.

The article "Correlation from cause" in the latest edition of Milliman's Issues in brief looks at how this approach works and how it can help firms satisfy the use test, a particularly challenging requirement for those intending to use an internal model. The information contained within the model can help to identify the drivers and signals that would lead to a change in the correlation between risks. These can be monitored and used in the day-to-day decision-making process of the firm. This will lead to enhanced communication among the risk owners, board members, and staff working in the business, and is a big step toward satisfying some of the modeling requirements of Solvency II.

This article was first published on LinkedIn.