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Model behaviour: Unlocking the potential of price elasticity in general insurance




Damiano Massimi and Thibault Imbert discuss the potential benefits of behavioral modeling in P&C insurance, in particular by combining it with price elasticity

Price elasticity is a well-known concept in economics and its adoption is increasingly pervasive in the pricing of airline, hotel and car rental reservations. However, its inclusion in the general insurance pricing process has not yet been fully implemented.

What is Behavioral Modeling?

Behavioral modeling attempts to explain a customer’s buying behavior and identify the main factors influencing the decision.

In an insurance context, behavioral modeling is addressed at different stages of a policy’s life cycle, from the first quote issued to renewal and beyond. Its four main applications are:

  • Conversion: plan to buy a new policy
  • Mid-term cancellation: provide for the termination of the contract during its lifetime (subject to regulations)
  • Retention: provide for the renewal of the contract at its expiry
  • Cross-sell/up-sell:
    • Cross-selling – what products the customer can buy from the company (e.g. buying home insurance when they already have car insurance)
    • Upsell – what additional coverage will be added (eg adding fire and theft to existing automotive product).

Behavioral modeling can be used regardless of distribution channel, but generally brings the most value to direct business, especially on aggregators, where price sensitivity is highest and most information is available. We will assume this context later in the article.

Price elasticity and price test

Price elasticity is defined as where D is demand and P is price. Elasticity measures the sensitivity of demand response to a price change.

The random price testing process refers to a randomly assigned price adjustment (regardless of risk) on each quote or policy – e.g. -a%,0%,a+%, assuming this is permitted from a regulatory point of view. This process is used to capture price sensitivity when converting or renewing. The resulting charge or discount is a variable called price test (PT ), which contains the value of the price adjustment applied to each quote or policy.

Modeling approach

Behavioral models are developed in the same way as risk models. Generalized Linear Models (GLM), Generalized Additive Models (GAM), and Machine Learning (ML) models account for the vast majority. Using a GLM or GAM approach, the following demand formula is obtained:

Where: is the vector of customer details.

is pricing information (proposed price, competitors’ prices, pricing positioning, etc.).

are functions resulting from modeling GLM or GAM.

Taking price elasticity into account requires the addition of additional terms to equation (1):

This additional term , to test elasticity, can be seen as introducing interactions between PT and other variables (X), PT being independent of P.

As , and are functions obtained during modeling, with .

Demand can then be simply estimated by applying formula (2), with PT=0 , which leads to (1)=(2).

How to measure and predict price elasticity

Since the information on demand and the price test variable are available, it is possible to evaluate the price elasticity by variable (e.g. driver age, vehicle brand), thus obtaining the observed price elasticity.

However, this can lead to high volatility and significant noise in the results due to a potential lack of exposure for certain modalities. It may therefore not be possible to correctly assess the price elasticity for all possible profiles. Going from the observed price elasticity to the predicted price elasticity is the solution to solve this problem.

This can be done using equation (2):

  1. Simulate the demand for each row in the database and each price test level, obtaining the expected demand for each profile and different premium levels.
  2. Evaluate the price elasticity using the expected demand and get the expected price elasticity at the policy level.
  3. View or use the resulting predicted elasticity.

Figure 1 shows an example of price elasticity as a function of the proximity between the price offered and the “best price on the market”, defined as the cheapest price offered on the market for the same product. It can be provided (eg external data) or predicted (eg reverse engineering).

“Estimating price elasticity shows that more than price, ranking drives demand”


The primary benefit of behavioral modeling for insurance is to improve pricing strategy and optimize portfolio performance. Figure 1 shows that the price elasticity is much higher for policies priced close to the cheapest (“best price ratio” close to 1) than for policies priced lower or higher, more and more as you go to the extremes.

Three immediate conclusions can be drawn from this example (for aggregator activities):

  1. Being significantly cheaper than the market does not increase demand.
  2. Being unreasonably more expensive does not reduce demand.
  3. Being the cheapest or not has a strong impact on demand: more than price, ranking drives demand.

look beyond

Price elasticity will support the assessment of how demand changes in response to price changes. The insurance company can then quantify the expected change in demand following a change in pricing strategy, and design improved strategies.

Two main approaches are generally followed for the following steps:

  • Scenario testing – simulating multiple scenarios, evaluating the impact on performance and volumes, and making a decision on the best scenario to implement, based on the desired outcome.
  • Pricing optimization – finding the optimal premium level for each client so that the company’s ambition is achieved at the portfolio level.

The advantages and disadvantages of both approaches are summarized in Table 1.

Behavioral modeling, including in particular price elasticity, is still a relatively new subject in the field of insurance and its potential is not yet fully perceived. However, implementing a modeling framework that incorporates this aspect can bring various benefits, ranging from better understanding of customers to higher sales, and from better profitability to better rating structure relevance. commercial.

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Image credit | Peter-Csuth