GLM pricing

[clueless]

Hi I am a bit unclear about the use of GLM in pricing. I have sat the previous general insurance paper ST3 before, and understand fairly well about the burning cost/freq & severity pricing. I work in Life and have never seen GLM in practice.

For the traditional methods, you choose data -> divide data into homogenious groups-> adjust data for the usual->project data to ultimate position->then add loadings to give the theoretical office premium.

But the outputs of the GLM are the relativities between different rating groups. It doesn't give us the absolute premium rates to charge for the prospective period. Do we then need to use the traditional methods to work out the risk premium for the base(or benchmark) rating group, and then the RPs for the other rating groups will follow from the relativities from the GLM?

Or is it the case that GLM is only used to check on the appropriateness of the rating structure as derived from the traditional methods?

A slightly different question, I read somewhere in the course note that GLM is mainly used in the commercial line of business. So in the exam, if the question is relating to a personal line of business, should I assume that GLM would not be used and I don't need to make any comments on this?

For example, in assignment question X2.6. This question is asking to suggest appropriate checks on the correctness of the risk premium for household contents. The solution does not mention GLM, but I think if GLM can be used in this situation, there are a range of suitable answers can be generated, e.g. the choice of variables, statistical tests of factor significance, model residual checks, etc.

Thank you in advance for anyone's comments

 

[Duncan Brydon]

Thanks for your question.

The GLM software will calculate the figure that relates to the base risk (i.e. the risk with a relativity of 1 for all factors). (There might not actually be an individual policy with a relativity of 1 for all factors.)

In calculating the risk premium, we will need to adjust to allow for inflation, trends etc to the expected average payment date for claims under the new rating series. This is sometimes done within the GLM software and sometimes after the software has been run.

The risk premiums for other risks can then be found from the relativities from the GLM.

Generalised Linear Modelling is widely used for personal lines pricing so you should not assume that it would not be relevant.

We will review the solution to X2.6 in light of your comments.

I hope this helps
Duncan

 

[clueless]

Thanks Duncan. Your answer confirms my understanding, i.e. you do need RP for a base group before you apply the relativities to derive the rest of the rating series. I don't think this is very clear in the note.

It is interesting that you say that there might not actually be an individual policy with a relativity of 1 for all factors. How then can the risk premium for this base group be derived without any data?

I would thought you need to define one of the rating groups you have in your data as the base group. For example, for a motor policy, one may pick a female driver age 40-45 driving a vehicle belonging to group 1 with over 20 years' driving experience as the base group. You can then derive RP based on the data relating to policyholders falling into this group using, say, burning cost approach.

 

[Duncan Brydon]

My comment regarding the possibility that there might be no individual policy with a relativity of one for all factors was just an aside. It is not important for the exam. This would happen if the intersection of all the base levels was empty (which is unlikely for a big motor book but might occur for say a small book of pet insurance).

The GLM will allow you to get a risk premium for all rating cells, including the empty ones. In simple terms, we are fitting a “line” to some “points”. The fact that there are no points in a particular region doesn’t prevent us from estimating the response there.

Suppose we use just one rating factor ‘age’ and we have no policyholders aged 50. Suppose we choose 50 as the base level age. We can still estimate the claim frequency for those aged 50 from the line we have fitted based on the data for all the other ages.

I hope this helps
Duncan