Actuarial pricing, capital modelling and reserving

Pricing Squad

Issue 3 -- May 2016

Welcome back to Pricing Squad!

Pricing Squad is a newsletter for fellow pricing practitioners and actuaries in general insurance. Enjoy, and let me know your comments and ideas for future issues.

Today's issue is about the rationales we use to justify modelled risk curves in pricing segmentation. Our brains like to hear convincing stories. But what happens when two convincing stories support opposing conclusions to each other?

Rationales and rationalising

How can you tell whether the shape of a risk curve coming out of a GLM or a non-linear pricing model is sensible?

You can often rationalise both ways

For example, is there a good rationale for risk decreasing for higher deductibles? Is there a good rationale for risk increasing with higher deductibles?

Yes and yes.

Yes, the risk can decrease when deductibles are high because in this case more of the risk is retained by the policyholder.

But the risk can also increase when deductibles are high because people who choose high deductibles often do this recklessly and for affordability reasons. These policy holders tend to be high-risk.

When creating an internal database of GLM models, typical rating curve shapes and rationales used by companies to justify these shapes, I have come across more examples of opposing rationales used by various clients. Below are a few more examples.

Example -- Vehicle value

It is perfectly possible to argue that high-value vehicles should be less likely to have claims. The justification is that these vehicles are owned by more affluent and responsible policy holders, who make generally better drivers. These policyholders are also less financially stressed, which could help them drive safely. They might also drive more carefully to reduce the risk of damage to a high-value car. Additionally, expensive cars have better safety equipment, reducing the likelihood of a claim.

On the other hand, high-value cars often drive more miles, which will naturally increase risk. They are also more likely to be driven for fun and enjoyment, leading to a higher risk of speeding and reckless driving. Finally, it might be that other rating factors, such as age and address, play a larger role in determining positive behavioural characteristics for owners of more expensive cars. This might leave the vehicle value curve not just flat, but possibly increasing to compensate for discounts resulting from age, address and similar factors.

So which one is it? Or do both effects come into force and manifest themselves in different parts of the vehicle value rating curve?

Example -- Number of drivers

Typically on a motor policy, the risk of most types of claims increases with the number of declared drivers. Usual rationales include that adding drivers means that a bad driver is more likely to be amongst them, that each driver may be less experienced with this particular vehicle or that the vehicle might simply be driven more.

But it is also possible to get the opposite result from a model and this can be justified too. For example, if the worst driver is being used as the rated risk then the presence of other drivers dilutes the effect of the bad driver. It is also possible that other factors or interactions already sufficiently capture the effect of the number of drivers on the policy, causing the risk factor itself to compensate and subvert expectations.

Again, which set of rationales is more true?

What you can do

Analysts are routinely guilty of confirmation bias - they look only for the rationales which confirm their modelled findings. This is likely to lead to bad models which will attract poor business with high loss ratios.

To reduce the chances of being misled by spurious rationalising, keep track of as many market and historical rating curves and their rationales as you can (our internal database, for example, lists over 500 patters and rationales). This will allow you to think about the following questions in an informed way:

  • Is there an opposite rationale to the one I am using for this factor or interaction?
  • Is my rationale more likely to be correct than alternative rationales for my specific line of business?
  • Has this rationale been utilised in a similar model in the last one, two or five years?
  • If an opposing rationale was used in the past, what has changed since then?
  • Is the rationale used for a different peril relevant to this particular peril model?

Can we help you?

If you are interested in new pricing ideas to radically simplify your current analytical procedures and deliver reduced loss ratio quickly, or if you are simply looking for an actuarial contractor, please get in touch.

Thank you for reading, and have a great day, Jan Iwanik, FIA PhD

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