Exam B-01, #26c - Exponential Interpolation

snpod5

Everyone's favorite topic!

First question ... can you help me understand why the answer key uses the 12-24 parameters for restating the CPL for AY 2022 @ 24mo? With the restated CPC = 800, I'm guessing this might be a typo, and that we should use the 24-36 parameters (since it's in the original range of 500 observed @ 24mo, 1000 observed @ 36mo).

Second question, with two sub-parts ... let's talk endpoints.

• If restated CPC is the same value as a range breakpoint, should we default to the parameters of the lower range? A good example of this is AY 2022 @ 36mo - observed counts = 1000, restated counts = 1000. The restated CPL is slightly different if you use 24-36 parameters (361,337) vs 36-48 parameters (358,886). Is it better to think of the ranges as [x,y) ; i.e. inclusive of the left endpoint, but excluding the right endpoint?
• This endpoint scenario arises when observed CPC = restated CPC. Since Berq-Sherm is not actually changing the claim counts, can you help me understand the intuition on why we would still interpolate for those specific data points (rather than using observed CPL)?

Thanks again!

Graham

Oh yes, I took a survey! Everyone LOVES the interpolation step of the BS-Paid method! 🤣

Question 1:

Those ranges are calculated using formulas and the formulas somehow got copied incorrectly when I created that exam question. I believe I've fixed it now.

Question 2:

• It's actually very unlikely that the restated CPC would exactly equal the range breakpoint so in practice this would probably not come up. But in the situation where this does occur, I don't think there is any specific guidance so you can use the regression parameters from either range. The whole Berquist-Sherman method is full of assumptions and approximations anyway so I would say that common sense judgment regarding your final unpaid loss estimates is much more important than which interval you use for the interpolation.
• Next question: Theoretically, if observed CPC = restated CPC, then even when interpolating you should get the same CPL values. Any difference is due to the rounding of the exponential regression parameters. In the practice exam problem, the value of 180,000 (for AY 24 @ 12) gets interpolated to 180,299, so not exactly the same but if I had kept all the decimals for the regression parameters instead of rounding (like I did in the statement of the problem) you should get exactly 180,000.
• As a final comment, if you see that restated CPC didn't change, you can save a calculation and just use the original observed CPL without bothering to interpolate.