Using ICRFS-Plus to calculate optimal outgoing reinsurance programs
Designing a new reinsurance program or evaluating an existing outgoing reinsurance program is a breeze with ICRFS-Plus™. Probability distributions for the liability streams will allow you to understand the risks you are taking. The result of changing retention limits on Value-at-Risk is available almost instantly.
Obtaining layered data
Using the COM interface, it is effortless to extract layered loss development arrays from unit record transactional databases. An example of creating such an ICRFS-Plus database from unit record transactional data is available here.
Assessing a current outgoing reinsurance program
In order to assess an outgoing reinsurance program, both the net of reinsurance and gross triangles are modelled in MPTF. The two triangles typically exhibit high process correlation. If the net data has lower inflation than the gross data, then we know that the losses that are growing are being ceded to the reinsurers. Otherwise the converse will be true.
Moreover, if the net of reinsurance reserves does not have a coefficient of variation less than the coefficient of variation of the gross reserves, then the outgoing reinsurance program is deemed non-optimal. In that case, the percentage capital the cedant requires above the mean to attain a specified percentile for the net reserves is not less than it is for the gross reserves. If the two coefficients of variation are equal, then the outgoing reinsurance program is tantamount to coinsurance or proportional reinsurance.
Click here for a real live example.
Adverse development cover
To price adverse development cover, either retrospectively or prospectively, forecast distributions are obtained for each cell and their correlations using a PTF based model. The PALD module is then used to simulate the distributions of aggregates from the correlated lognormals.
The Reinsurance module allows one to select various attachment points and view resulting distributions for the insurer and reinsurer by calendar period. Value-at-Risk and other statistics can also be compared.
An example involving adverse development cover is illustrated in demonstration video 2.2. It involves a layered triangle, $1Mxs$1M, although this can be applied to any triangle. This particular video is also rich in other statistical ideas.
An example involving adverse development cover for the aggregate of a number of lines of business using the MPTF module is included in demonstration video 3.1.
Pricing Layers
For the three layers limited $1M, $1Mxs$1M, limited $2M a composite model is designed in MPTF. It is found that outward reinsurance where each individual loss is limited to $1M ($1,000,000) is not more capital efficient than outward reinsurance where each individual loss is limited $2M ($2,000,000). The coefficient of variation of net reserves limited to $1M is the same as the coefficient of variation of reserves limited to $2M. Forecasts for the triangle $1Mxs$1M are used to price that layer.
For a layered composite data set 0-25K, 25K-50K,..., 150K-200K, it is also found that the coefficient of variation of the net reserves limited to $xK does not depend on x!
Highest process correlations are between neighbouring layers. The development period peak shifts to the right as you move to higher layers. Calendar year trends are statistically the same for neighbouring layers and any change in trends occur in the same periods for all layers.
Click here to view the example of the analysis of these layers.
Pricing low frequency/high severity
Using real life data it is shown how to price higher layers even though the triangles for the higher layers are replete with zeros. A composite model is designed for the layered composite data set Lim 0.5M, Lim 1M,..., Lim 4M and Groundup. Both process correlations and parameter correlations between the layers are very high. These induce high correlations in predicted lognormals between the cells in any two layers.
Click here to view this demonstration.