November 20th, 2008

## Reinsurer Diversification: The Guy Carpenter Model

Posted at 1:01 AM ET

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Instrat®, Guy Carpenter’s quantitative services unit, has developed a reinsurer credit model. It allows an analyst to input a mixture of reinsurers and measure the impact of the diversification effect. The model allows for the specification of correlation levels for reinsurer defaults. It also allows for the chance of partial recoveries.

In the following, we consider the case of a ceding company with USD30 million in reinsurance recoverables, with an average date of recovery 5 years in the future. We consider three different reinsurance panels:

1. A single AA rated reinsurer
2. Three AA rated reinsurers, each responsible for USD10 million of the recoverable
3. Three differently rated reinsurers, AA, A and BBB, each responsible for USD10 million of the recoverable

The five-year probabilities of some level of default are 0.26 percent for the AA reinsurer, 0.63 percent for the A rated reinsurer, and 2.14 percent for the BBB reinsurer. We then simulate the model under the assumption of no correlation of default between the reinsurers.

Results for Simulation Assuming Zero Correlation between Reinsurers

Reviewing the results, we find that with a 0.1 percent probability (return period of 1:1,000) the default amount will be USD17.7 million or higher for the single AA reinsurer. This is much higher than the results for the two diversified cases, indicating the benefits of diversification. Note that in the case of the diversified portfolio with two lower rated players, the result is better than the single AA rated company.

The Guy Carpenter model allows for correlation between the reinsurers. For example, in developing the next table, we assume a 25 percent correlation rate. We also used a t-copula, which allows for a higher impact of correlation at the tail of the distribution.

Results for Simulation Assuming 25 percent Correlation between Reinsurers

The default level at the 0.1 percent probability remains at USD17.7 million for the single reinsurer, as a single counterparty is unaffected by correlation. The default level is driven up for the other two reinsurer panels, but still remains below the level for the single reinsurer.

The Guy Carpenter credit risk model is a powerful instrument for the analysis of counterparty risk. In addition to factors such as rating and correlation, parameters can be varied across additional criteria, such as time periods and recovery rates.

Earlier Installments

Reinsurer Diversification: Roots and Benefits >>

Reinsurer Diversification: Case Studies >>

Reinsurer Diversification: A Risk Metric Approach to Diversification >>