Financial Modelling

Modelling for insurers and reinsurers - case study (2)

Graph 2
Additionally, for each reinsurance contract that has been included explicitly in the stochastic model, a graph of the reinsurance premium versus the reinsurance recoveries can be examined. 

 

The graph above shows that for nearly 90% of the time there is no reinsurance recovery from the contract, however, when there is a claim it is likely that the recoveries will exceed the premium paid including reinstatements. Further, it can also been seen that the reinsurance limit of £50m is breached a small percentage of the time. Using graphical means such as these the insurer is able to quickly determine if a reinsurance contract is providing benefit.

In addition to the graphs, analysis by reinsurance contract can be produced from the model, an example of which is in the table below.

Reinsurance    Expected     Expected         Std Dev of     Expected        Reinsurance                   Cost
Contract         Premium     Recoveried       Recoveries     Reinsurer's    Probability of    Capital     of Capital
                                                                                 Proft               Loss
       1              5,289           2,926            5,834          2,363             21%             (8,481)         28%
       2              7,177           4,041            9,729          3,135             16%             (20,041)       16%
       3              8,238           5,189           15,393         3,048             11%             (45,456)         7%                                                                                        


Capital This is how much capital relief the insurer calculates that the contract provides
Cost of Capital = (RI Premium - RI Recoveries) / Capital

From the table above, it can be seen that given the insurers desire to increase return on capital it is reinsurance contract 1 that should be reviewed, for although it provides some £8.5m of capital relief this comes at a cost of 28%, some 10% greater than the insurers overall return.

Having performed all of the above analysis and examined a variety of graphical output for all of its reinsurance contracts individually and in aggregate, the insurer decides to re-run its model assuming all of its low levels of reinsurance do not exist i.e. it decides to have a higher net retention. Unfortunately, this increases the capital required with only a marginal increase in the overall return on capital. To counteract the increase in capital the insurer decides to purchase higher layers of reinsurance instead which has the impact of producing a return on capital of 22% with the total capital back to £200m.

This is not the end of the study because the insurer has analysed only one of many potential changes to the reinsurance programme. Therefore, the above process is repeated many times until the insurer has a number satisfactory reinsurance structures to consider. It is the outcome of this repeated analysis that is then taken to the next stage of the decision making process, which includes testing the various reinsurance proposals on the reinsurance market. 

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