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The Actuary The magazine of the Institute & Faculty of Actuaries
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GI: The price is right

Price optimisation is a relatively new approach to personal lines pricing. It combines traditional cost-based methods with market and consumer behaviour analysis. The result of this comprehensive approach is a more sophisticated pricing segmentation that takes advantage of market inefficiencies. The general idea of optimised pricing was presented in The Actuary’s September 2008 issue; here, some of the practical aspects are discussed.

Traditional pricing based on loss models is a cost-based approach. Price optimisation introduces a new element — the elasticity of demand based on the customer’s willingness to pay. A comprehensive price optimisation programme is based on three types of models:

1. Claim propensity models express how customer attributes are predictive of their losses. Developing these models has traditionally been the task of actuaries, and countless tools have been developed for this purpose including overall rate level indication, one- and two-way segmentation, credibility-weighted segmentation, minimum bias procedures, generalised linear models and generalised additive models.

2. Market situation models express how the company’s competitive position and the market’s competitive intensity vary by segment or niche within the market. Since every distribution channel targets a different market, more than one model may be needed for a multi-channel business.

3. Customer behaviour models express how a customer’s attributes and the market’s situation are predictive of the customer’s behaviour. Separate models are needed for new and renewal business, and models can vary by distribution channel. These three types of models need to be combined to simulate the relationship between price changes and the targeted function of volume and profitability for given financial objectives and relevant constraints.

The efficiency frontier
Unfortunately, not every combination of volume and profit is achievable. Of the combinations which are achievable, most are not optimal. The optimal combinations form the efficiency frontier. The pricing actuary’s objective is to locate the company on the efficient frontier. Figure one shows a sample efficiency frontier. The horizontal axis represents the company’s profit. The current renewal rate is 85% and the current business position is shown by the red dot. Other positions can deliver more profit at the same renewal rate or more renewals at the same profit. The current situation is clearly sub-optimal.

The light blue dot [strategy 2” represents a new rate structure and a different business mix. The new business mix delivers the same level of profit and an increase of retention to 85.7%. There is no other business mix which could produce better retention with the same profit. Therefore, this is an optimal point.

The easiest part of price optimisation is developing and updating the claim propensity models because pricing actuaries are normally comfortable with these models and most companies have well thought-out and documented loss models in place. The mathematics of the market situation and customer behaviour models are usually familiar to pricing actuaries. These models are mathematically similar to those used in loss modelling. Standard choices are generalised linear, non-linear and additive models. New statistical aspects of these models include the use of retrospective sampling instead of a straightforward prospective approach and careful selections of the model link functions due to low conversion ratios observed in the data. Another practical difference between the claims propensity and consumer behaviour models is that the latter include new variables, unusual interactions and are more strongly related to lifestyle characteristics. Since these are merely technical difficulties, actuaries can learn these new techniques fairly quickly.

A big challenge for many insurers is that price optimisation creates a new process within the organisation. Rates are no longer set by actuaries and then agreed with the underwriters based on market analysis reports. Market research is now fully integrated into the pricing process. The volatility of the UK personal lines market is another practical difficulty. Figure two shows the average monthly market price for a target basket of 1000 private motor risks in the broker channel. As market prices change so rapidly, the market situation models need to be updated weekly or monthly. This must be done in an organised and documented way, leaving a good audit trail.

Real-time pricing
Another challenge is that, because of the volatility of the market, the insurer’s competitive position is likely to change before the updated rates take effect. Access to a real-time pricing facility can increase the insurer’s control over its competitive position. If real-time pricing is not available, the future state of the market can be anticipated from trends in specific market segments, based on the actual market price movements and intensity of competition. The following steps will increase the chances of a successful price optimisation implementation:

>> Updating the documentation of your claim propensity models. The optimisation implementation project will be an excellent opportunity for others to discuss these models with you again.
>> Making sure that your renewal database is complete and available for analysis. We typically recommend starting with the renewal process because more historical information is usually available for renewals than for new business.
>> Collecting market data. Brokers and aggregators are usually willing to share their quotation data, but it can take some time before you are able to accumulate a large data library. This channel-specific data is often much more useful than market-wide consumer intelligence.
>> Learning as much as possible from your market data. Companies that had already conducted periodic competitive market analyses and understood their relative competitiveness by micro-market segment were better able to facilitate the implementation of price optimisation.

Revolutionary appeal
Price optimisation is a technological revolution which will create new winners and losers both among insurance businesses and the individuals working in pricing. Intermediaries and direct writers who have good access to market data and maintain control over the final price can benefit hugely from price optimisation. The broker channel insurers can win as well, especially if they adopt pricing optimisation early. In our recent case study, a big broker-channel motor insurer simultaneously increased average premiums and improved the number of policies retained by one percentage point without compromising the ultimate predicted loss ratio.

Price optimisation creates challenges for actuaries as well. We need to learn new techniques and be prepared to alter the way we look at personal lines pricing. If actuaries manage to become acknowledged experts in price optimisation, we will be able to contribute more to our companies and assume more responsibility for their success.

Francisco GÓmez- Alvado is a senior consultant with Towers Perrin in Madrid
Jan Iwanik is a consultant with Towers Perrin in London