Capital modellers say that our roundtables are a great opportunity to discuss what is going on across the market. At the most recent roundtable last month, we discussed one of the most challenging areas of capital modelling: modelling dependencies. 

Firms recognised limitations in the longstanding approaches for dependencies. For example, more than two-thirds of firms either had recently made, or were planning to make, changes in each the following areas:

• Eliciting expert judgements around dependencies
• Modelling explicit drivers between different risk types, and
• Modelling tail risk scenarios.

Nevertheless, the discussions highlighted some clear common areas of good practice, particularly around model parameterisation and calibration, with many firms applying the 4-step process described below.

Identifying the drivers of risk

The first step is to identify common risk drivers across the business. Firms agreed that a good starting point is getting underwriters’ views on which factors drive the risk in each of their lines. From these discussions, they compile a longlist of drivers for each line of business across the book.

Select key drivers

Once the longlist in stage 1 has been collated, a comparison across lines of business will quickly identify areas of commonality. When performing this comparison, firms noted that it was critical not only to identify common drivers across classes, but also those that are linked to non-insurance exposures (eg a link between claims shocks and market movements, or catastrophes and management stretch which may drive increased operational risk).

In addition, it’s helpful to group the drivers into a smaller number of higher-level drivers, to ensure the parameterisation process is manageable. There was less consensus on the target number of high-level drivers, with the majority of firms focused on around 8 to 12 key drivers, but some with more, eg up to 40 different drivers being modelled. 

Mapping the impact

The third stage is to assess the impact of the high-level drivers across the business. We discussed a variety of approaches seen across the market, ranging from simpler qualitative to more complex quantitative approaches.

Converting to a dependency structure

There were a variety of approaches discussed for how best to convert the information collected above into a capital model dependency structure. The two most common approaches are:

• Using a scoring system based on the number of common drivers, and their relative strengths to parameterise a predetermined dependency structure (eg nested T copulas)
• Direct modelling of the drivers by implementing a driver-based custom dependency structure. 

Remaining issues

The discussions also highlighted some of the key challenges which were prompting potential changes in approach, these included:

• What is the best way to measure and capture differences in the relationship between classes in the body, and the relationship in the tail of the distribution?
• What is the best way to manage non-modelled drivers?
• Does a driver that is likely to produce a shock change typically have more of an impact on capital than a driver that changes in a more gradual way, or vice versa?
• What is the best way to maximise the data available to understand the strength of the link between the risk drivers and each line of business?

I always enjoy hearing other people’s thoughts and discussing the latest developments, which is one of the reasons why I find the roundtables so interesting. Feel free to get in touch if you would like to discuss these ideas further over a virtual coffee.