Actuarial pricing, capital modelling and reserving

Pricing Squad

Issue 2 -- December 2015

Welcome 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 predicting demand price elasticity using converted quotes only. I have been asked about it by two different people; one working for an insurer and one for a broker. The insurance person is interested in this subject because he struggles with data quality provided by his brokers, while the broker struggles with the volumes of data provided by aggregators.

Predict demand price elasticity using converted quotes only

Have you ever needed to predict insurance demand without having access to unconverted quotes? I have. It happened when I was modelling new business elasticity on aggregators and my colleagues in IT refused to maintain a database with more than 10 million unconverted quotes.

Scrap the conversion model

Can it be done? Yes. You can get more out of the information embedded in your price test if you step outside the paradigm of modelling conversion first and then elasticity as its derivative. Just model elasticity.

What do you need the conversion model for anyway? Does it matter whether there are one million or one billion quotes behind your 50k conversions? No. All that matters is the quality of your 50k and how you can turn 50k into 100k.

How to get elasticity from converted quotes only?

For sake of simplicity let's say that a random half of all quotes gets a price test at +10% and the other half is priced at -10%. You would expect that among your converted quotes there will be more with a -10% price test than a +10% price test, right? This is simply because, everything else being equal, cheaper quotes convert more effectively.

You can quantify and predict elasticity from this difference. For instance if, say, only 33% of your converted quotes have +10% price test then demand price elasticity is (66% ÷ 33%) ÷ (10% + 10%) = 10.

Done. No unconverted quotes, no conversion models.

As long as there are enough converted quotes in each price test bucket this logic is very powerful. It can be applied by segment, smoothed with a multivariate elasticity model or used inside a GLM-free algorithm.


A batch of 33k renewal quotes with 25k accepts was subjected to a heavily segmented rate change. Below, volume impact calculated using converted quotes only is compared to a converted + unconverted prediction, with both predictions obtained from the online Impact Express tool.

Converted quotes only Converted and unconverted quotes
Volume change-5.7%-5.4%
Premium change-1.5%-1.8%

The two results are quite close and this demonstrates how precisely we can model elasticity using converted quotes only.

In the next issue...

The next Pricing Squad will be about one of the following (or you can let me know your personal favourite topic):
  • Opposing rationales in GLMs.
  • What is new on the aggregators.
  • Why by-peril modelling is bad for you.

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

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