Using Dynamic Financial Models to Assess Outwards Reinsurance

At this time of year strategic discussions about reinsurance purchasing begin to hot up and my colleagues and I gear up to provide our opinion on the effectiveness of different outwards reinsurance programmes.

In this article I will illustrate why a dynamic financial model (DFM) is an excellent tool for assessing the value of a reinsurance programme to an insurer.

I use “dynamic financial model” but I really just mean the type of stochastic model that is typically used by insurance/reinsurance companies to model the future financial position of the company. So you may be more familiar with just “Internal Model”, “Capital Model”, or something else.

A holistic view

Two of the main goals of reinsurance are to reduce the volatility of future profits and to reduce the probability of net assets falling to an intolerable level (e.g. a level that would result in a credit rating downgrade or would result in insolvency).

To assess how effective a reinsurance programme is at doing these things it is important to consider the impact of the programme on the insurer as a whole. This is because diversification between different product lines partially mitigates the impact on the company of under-performers. Therefore, it would be a waste of money for the company to pay a reinsurer to take on the risk that would otherwise be mitigated for free.

To illustrate this, let’s consider a company that underwrites a number of different products and also that is considering whether to buy a reinsurance programme. In particular, the reinsurance programme covers a single product line should incurred claims on that line exceed $5m.

As the company has been underwriting the same products at the same level for a long period of time, we have decided to see what the annual historical claims experience of the company would have looked like if it had bought this reinsurance over the period 1990 to 2015.

The first chart below shows the claims experience for the motor product line over this period, gross and net of the proposed reinsurance.

Gross_And_Net_Claims

We can see that the net claims experience is clearly less volatile than the gross claims experience. In particular, in 1991, net claims are about 72% of what they were without the reinsurance.

The next chart shows the experience for the remaining classes, which are not covered by the reinsurance.

Gross_Claims_Classes

You can see that each of the classes generate a similar volume of claims.

Finally, the chart below shows the gross and net claims over the same period but for the whole company.

Total_Gross_And_Net_Claims

We can see that the claims experience is less volatile in aggregate than for the motor product line, due to diversification. Furthermore, the net claims volatility is almost indistinguishable from that of the gross claims volatility. In particular, in 2011, when the motor product line would have had net claims that were 72% of gross claims, the company’s net claims would have been 96% of gross claims.

This holistic view enables us to see that with the proposed reinsurance the volatility of the company’s net claims would not have been lower than its historical gross claims, even though it would have been for the individual business segment. Hence, the insurer should not buy the reinsurance.

The benefit of a dynamic financial model

We can see that a holistic view of the impact of reinsurance is very useful when considering its value to the company. However, the analysis that was performed above is usually not possible for an insurer, as its data is either insufficient or is not representative of future experience. This is when a DFM can be used.

For the benefit of those not familiar with simulation, a DFM essentially attempts to generate the sort of financial data contained in the graphs above but as if the insurer was always in the financial position it is now. In fact, this under-sells what a DFM does, as it generates thousands or millions of “years” worth of data and does so at a much more granular level than is considered in the analysis above.

In more technical language, a DFM is a stochastic model of an insurance company, which simulates the possible future financial position of the company, given the current state of the company, market conditions and the company’s beliefs about the future.

This enables an insurer to perform similar analyses to the one in the previous section but without needing an impossibly large database of homogeneous historical data.

An output of an analysis involving a DFM which is analogous to the charts above is a plot of the simulated gross and net claims (below).

Simulated_Total_Gross_And_Net_Claims

As with the previous charts this one shows claims gross and net of the proposed reinsurance for the same company. However, instead of a handful of years, this time I show ten thousand simulations.

With this data the company can perform the sort of analysis touched on above even though it doesn’t have a large dataset of homogeneous historical experience. Furthermore, even if it did have relevant historical data, by simulating thousands or millions of outcomes the insurer can get a much more informed view of the impact of the proposed reinsurance programme.

Final word

As we’ve seen from the examples above, to achieve the main goals of reinsurance it is important to consider risk holistically. In essence, this is because some risk is mitigated by diversification for free and so it is wasteful to pay a reinsurer to mitigate it.

Having illustrated the importance of a holistic assessment, I gave a glimpse as to why DFMs are particularly useful for reinsurance assessment.

If you have any insights on evaluating reinsurance or using DFMs please share them by leaving a comment.