This week I will demonstrate how SAS can be used to calculate a Bornhuetter-Ferguson (BF) estimate of reserves. The BF method is a way of merging together the development to date with a priori estimate of the reserves. The priori estimate could come from a range of different sources. It might be from another reserving method, or from the claims handlers, or from the underwriters, or from industry benchmarks, or it could come from the pricing model or it may be from a different source entirely.
The BF method works by taking the current paid or incurred to date and adding to it the priori estimate multiplied by the estimated percentage of future development. So if 1000 has been paid to date and this is estimated to be 60% of the development and the priori estimate is 2000 then the BF estimate would be 1800. That is 1000 + (1 - 0.6) * 2000 = 1800.
As ever this post is a demonstration of what can be done in SAS. It is not intended as a guide to reserving or a recommendation of one particular reserving method over another.
I will start off with using my macro that creates an example triangle. I have added a few lines at the end which take the paid to date from the middle of the triangle into a separate dataset. This is sorted in reverse order to be used later.
Next I obtain the development factors. This is set to get the weighted 12 months development factors and put them into a dataset called Development_Factors_Volume_12.
Next I calculate the cumulative development factors using the below macro. I also take the percentage developed to be the inverse of the development factor and the percentage left to develop as one minus the percentage developed.
Finally I merge the development factors dataset to the paid table I created at the start. I also merge to this a separate dataset containing the priori estimates. This dataset is called Priori_Ultimate and has one field called PrioriUltimate. I then use the estimate of the percentage developed along with the priori ultimate and the paid to date to arrive at the estimate of reserves.
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