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Group product pricing

T

Trevor

Member
Hi, I am trying to understand the details of the group pricing formula in
Chapter 18, section 3.2 of the CMP:
RP = Z*A +(1-Z)*E

I know E is the standard book rate, Z is the credibility factor.
However I want to know exactly what is represented by “A”

My understanding is when we are pricing for a specific group, we use the past experience for that group, and then adjust the standard book rate to get a book rate for them specifically.

Now I have 2 interpretations of “A”:
  1. If E is a standard book rate. (ie: a mortality table rates for all ages), and then A should be the group rate (adjusted from standard rate).
    This way the formula would work mathematically (imagine this as a vector calculation) : Z*table+(1-Z)*table.
    “A” will incorporate adjustment for past and future experience.
    Z will be how much do we want to rely our final premium on this past experience
    In this case, “RP” will be resultant premium based on expected past and future experience.
    Therefore, the overall group rate in this case is A, and RP represents the actual premium being charged

  2. “A” is some experience adjustment, not actually a rate
    Putting in a weight Z helps to derive the group rate, RP.
    Therefore the overall group rate is RP. “A” is just some number for adjustment.
    In this case, I think the formula is rather unusual: Z*scalar number +(1-Z)*table
    However, this approach sounds more intuitive: we incorporate past experience to the standard rate in order to derive an overall book rate.

The reason I am asking this is because I want to demonstrate in my solution, that I know what am I talking about; rather than just hitting points on the examiner report by luck/memory work.

Can anyone explain this to me?
 
In the first case, my solution will read:
The group’s past experience will be considered to derive a group rate
This group rate is then weighted against the standard rate via a credibility factor, Z
The final premium rate will be a weighted average of the group rate and the standard book rate:
RP = Z*A +(1-Z)*E

the second case however reads:
The group’s past experience will be considered to derive a group rate.
The standard rate will be adjusted using the past experience via a credibility factor Z.
The final group rate will be a weighted average of the past experience and the standard book rate:
RP = Z*A +(1-Z)*E

the two answers shows similar idea, but different understanding of the process and formula.
I am worried that explaining the technical details wrongly shows that I dont actually understand the material, therefore not awarded credits.
 
Hi Trevor,

I'm struggling a bit to see what you're saying in each case.

"A" must be a rate, or it doesn't make sense to do a weighted average, so I'm leaning towards your first definition. However I'm not keen on the first sentence in your item 1 above ("If E is a standard book rate. (ie: a mortality table rates for all ages), and then A should be the group rate (adjusted from standard rate)") because we calculate A from the past experience of the group in question - we don't adjust it from a standard rate. What we'd do is take last year's claims experience for the group and turn that into a rate. The only adjustments we'd need would be to reflect any changes in the composition of the group between last year and the coming year (so for things like restructures in the company or changes in location).

I would say:
A is the burning cost of the scheme in question, expressed as a rate - this is independent of standard book rates
E is the standard book rate
RP is the risk premium that will be charged to the group and will be a weighted average of the two (of course loadings for expenses, profit etc will also be needed).

I hope this helps,

Anna
 
Hi Anna,

Thanks for your explanation, it is very clear now.
What led me into asking this is question 5(i) of Mock Exam 3, I struggled to explain the calculation process in detail although knowing the concept at a high level.

Referring to the last bullet point in Mock Exam 3 solutions page 8:
"The final risk premium for the scheme would be a weighted average of the book rate, and the expected cost of claims derived from past experience of the scheme."

The "book rate" refers to the standard book rate, and the "expected cost of claims" is referring to the burning cost.

This is very clear now, thanks :)
 
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