Chapter 37: Section 2 -Carrying out an analysis of surplus

[Bill SD]

Hi,
I found two parts of this section on page 8 difficult to follow, given my lack of pricing experience.

1) "It is important in building such a model to ensure that the elements of the revenue account are self-consistent in their own right.
It is not sufficient to project premiums, investment income, death claims, lapses etc independently.
In other words, any such projection must be based upon a set of mutually consistent variables.
Both the resulting relationships between the elements of the accounts and the absolute values of those elements should be realistic."

Presume the latter part of the final sentence ("the absolute values of those elements should be realistic") means, for example that all elements (premium size, claim amount, investment return) should incorporate same inflation/other economic assumptions.
But what would be an example of the former part ("the resulting relationships between the elements of the accounts...should be realistic")?

2) "‘Profit test results’ in the above context means the cashflows for a single policy. This ‘scaling up’ will need to take into consideration the expected numbers of contracts of each type, including by rating factor."

Therefore the analysis of surplus is carried out separately for each rating factor? (For example a motor insurer would conduct separate analysis for each postcode, driver age, etc in its portfolio) I guess, in practice, the extent to which an insurer groups similar characteristics/rating factors together (for example, consider all 50-60 year old drivers in one analysis) , depends on the size of the insurers portfolio.

 

[Lindsay Smitherman]

Hi

1) 'The resulting relationships between the elements of the accounts should be realistic' means that there should be internal consistency between cashflows that are being projected. In particular, asset and liability cashflows should be consistent. For example, the amount of investment income being generated should be consistent with the amount of premiums being assumed to be received and therefore the amount of assets held by the company.

2) This paragraph is referring to the use of 'model points', which are described in Chapter 17 (Modelling). The point that you quote relates to the inclusion of future new business in the projection model, for which the company of course would not have any existing data to use. So it would determine some appropriate 'model points': data that represent the policies the insurer expects to sell. It makes sense to use one model point for each (material) combination of rating factors, eg (using your example) a 55 year old male driver living in area X (to represent all male drivers in that area who are aged 50-60). However, it wouldn't make sense for the company to include the cashflows from only one of those policies in its projection, and similarly just one policy for each of the other rating factor combinations that it chooses. It needs to 'scale up' the cashflows projected for each model point by multiplying them by the number of policies that it expects to sell with those characteristics.

Hope that helps to clear that up.