They help insurers understand how different risk characteristics affect expected claims and convert those relationships into practical rating factors. Although newer machine-learning methods are increasingly used across the insurance industry, GLMs remain popular because they combine statistical credibility with transparency, flexibility and relative ease of implementation.

For insurance professionals without a statistical background, however, GLM terminology can make the subject appear more complicated than it needs to be.

This guide explains how GLMs are used in insurance pricing, focusing on their practical application rather than detailed mathematical theory. It covers frequency and severity models, distributions, link functions, variable selection, model interpretation, validation and common implementation problems.

For a wider overview of the different techniques insurers use to calculate premiums, read: Actuarial Pricing Models and Methods: The Complete Guide.

What is a GLM in insurance pricing?

A Generalised Linear Model is a statistical method used to estimate the relationship between an outcome and one or more explanatory variables.

In insurance pricing, the outcome might be:

• The number of claims a policyholder is expected to make
• The average cost of those claims
• The total expected claims cost
• The probability that a claim will occur
• The likelihood that a customer will renew

The explanatory variables are the characteristics that may influence the outcome.

In motor insurance, for example, these could include:

• Driver age
• Vehicle type
• Location
• Annual mileage
• Driving history
• Policy excess

In commercial insurance, variables might include:

• Industry
• Turnover
• Payroll
• Number of employees
• Property values
• Previous claims
• Policy limits and deductibles

The GLM uses historical data to estimate how each characteristic is associated with expected risk.

Importantly, it estimates the effect of one variable while allowing for the other variables included in the model. This helps the actuary separate genuine risk effects from apparent relationships caused by the make-up of the portfolio.

For example, one region may appear to have high claims costs simply because it contains a larger proportion of high-value properties. Once property value is included in the model, the independent regional effect may be smaller than it first appeared.

How does a GLM differ from ordinary linear regression?

Standard linear regression works best when the outcome being modelled is continuous and reasonably symmetrical.

Insurance data rarely behaves in this way.

Claim counts:

• Cannot be negative
• Are usually whole numbers
• Often contain a large number of zeroes

Claim amounts are typically:

• Positive
• Highly variable
• Right-skewed
• Influenced by a relatively small number of large losses

GLMs extend ordinary linear regression by allowing the modeller to choose:

1. A statistical distribution suited to the outcome
2. A link function connecting the expected outcome to the explanatory variables

This makes GLMs more suitable for insurance pricing.

A GLM can be thought of as having three main parts:

• The response variable, such as claim frequency or severity
• The explanatory variables, such as age, location or turnover
• The link function, which determines how the variables combine to produce the prediction

A logarithmic link is commonly used in insurance pricing. This keeps predictions positive and creates multiplicative rating factors.

For example, a risk might have:

• A base factor of 1.00
• An age factor of 1.15
• A location factor of 1.10
• A vehicle factor of 0.95

These factors can be multiplied together to estimate how the risk differs from the selected base case.

Why do GLMs remain widely used?

GLMs are not the newest modelling technique available, but they continue to offer several practical advantages – such as:

They suit insurance data

Different GLM structures can be used for:

• Claim counts
• Claim severity
• Aggregate loss costs
• Binary outcomes
• Customer renewal and conversion

This flexibility makes them suitable for many insurance pricing problems.

They are transparent

The output from a GLM can usually be converted into clear coefficients or rating factors.

Actuaries can explain:

• Which variables affect the prediction
• Whether they increase or reduce expected risk
• The approximate size of each effect
• How much uncertainty surrounds the estimate

This is particularly valuable when models must be discussed with underwriters, senior management, model-validation teams or regulators.

They translate well into rating systems

GLM results can often be turned into:

• Rating tables
• Relativities
• Tariff structures
• Pricing tools
• Underwriting rules

This makes them easier to implement than some more complex modelling methods.

They support statistical testing

GLMs have an established framework for testing model fit, stability and uncertainty.

Actuaries can examine:

• Standard errors
• Confidence intervals
• Deviance
• Residuals
• Information criteria
• Statistical significance

These measures do not make modelling decisions automatically, but they provide a structured basis for challenge and review.

They provide a useful benchmark

Even when an insurer is exploring machine learning, a GLM is often retained as a benchmark.

This allows the insurer to ask whether a more complicated model:

• Produces a meaningful improvement
• Remains stable on new data
• Can be explained
• Can be implemented effectively
• Justifies its additional governance requirements

Frequency and severity modelling

One of the most common approaches in non-life insurance pricing is to model claim frequency and claim severity separately.

Claim frequency

Claim frequency measures how often claims occur.

It can be calculated as:

Number of claims ÷ exposure

Exposure might be measured in policy years, vehicle years, employee years or another relevant unit.

If an insurer records 500 claims across 10,000 policy years, the observed claim frequency is:

500 ÷ 10,000 = 0.05

This means five claims per 100 policy years.

A frequency GLM estimates how this expected frequency changes according to the characteristics of each risk.

Claim severity

Claim severity measures the average cost of a claim once a claim has happened.

It can be calculated as:

Total claims cost ÷ number of claims

If 500 claims cost £2.5 million in total, average severity is:

£2,500,000 ÷ 500 = £5,000

A severity GLM estimates how expected claim cost differs between risks.

Combining frequency and severity

Expected claims cost can then be estimated as:

Expected frequency × expected severity

For example:

• Expected frequency: 0.05
• Expected severity: £5,000

The expected claims cost is:

0.05 × £5,000 = £250

This is not normally the final customer premium. Further allowances may be needed for:

• Expenses
• Commission
• Reinsurance
• Cost of capital
• Profit
• Tax
• Large-loss or catastrophe loadings

Why separate the models?

Different characteristics may affect frequency and severity in different ways.

For example:

• Annual mileage may strongly affect how often motor claims happen
• Vehicle value may have a greater effect on claim size
• Driver age may influence both, but by different amounts

Modelling the two components separately helps the insurer understand where the expected risk is coming from.

Modelling total losses directly

An insurer can also model aggregate claims cost in a single model.

The Tweedie distribution is often used for policy-level data containing:

• Many policies with no claims
• Positive claim costs for policies that do claim
• A highly skewed distribution

This approach can be effective, although separate frequency and severity models may provide clearer insight into the drivers of risk.

Common distributions and link functions

The distribution selected for a GLM should reflect the type of outcome being modelled.

Poisson distribution

The Poisson distribution is frequently used for claim counts.

It is suitable for outcomes such as zero, one, two or more claims during a period of exposure.

A basic Poisson model assumes that the mean and variance are approximately equal. Insurance data often has more variation than this assumption allows, which is known as overdispersion.

Overdispersion may result from:

• Missing risk variables
• Differences between policyholders
• Claim clustering
• Changes in behaviour
• A small number of policies with several claims

The model should therefore be tested to determine whether the Poisson structure is adequate.

Negative binomial distribution

A negative binomial model is another option for claim frequency.

It allows the variance to be greater than the mean and may provide a better fit where claim counts are highly dispersed.

However, the model should not be selected purely because it fits the historical data more closely. Stability, interpretation and performance on unseen data also matter.

Gamma distribution

The Gamma distribution is commonly used for claim severity.

It is suitable for positive, right-skewed values where most claims are relatively modest and a smaller number are much larger.

A Gamma model with a log link produces positive predictions and multiplicative rating effects.

Inverse Gaussian distribution

The inverse Gaussian distribution may also be used for positive and highly skewed claim severities.

The choice between Gamma, inverse Gaussian and other methods should be based on:

• The shape of the data
• Model diagnostics
• Stability
• Predictive performance
• Treatment of large claims

Binomial distribution

A binomial GLM is used where the outcome has two possible states.

Examples include:

• Claim or no claim
• Renew or lapse
• Accept or decline
• Fraud or no fraud

A logit link is commonly used, producing what is usually known as logistic regression.

Tweedie distribution

The Tweedie distribution can model aggregate claims costs where many observations are zero and the positive values are continuous and skewed.

It is widely used as an alternative to separate frequency and severity models.

Common link functions

The link function connects the model’s explanatory variables to the expected outcome.

The most common links in insurance pricing include:

Log link: Often used for frequency and severity models. It keeps predictions positive and creates multiplicative rating factors.

Logit link: Commonly used for binary outcomes such as claim probability or renewal.

Identity link: Produces additive effects. It can be useful in some circumstances but may generate negative predictions when modelling positive outcomes.

Selecting pricing variables

​Selecting variables involves more than adding every available data field to the model.

Each variable should be considered from several perspectives.

Predictive relevance

The variable should have a plausible relationship with the outcome.

Evidence may come from:

• Historical analysis
• Actuarial judgement
• Underwriting experience
• External research
• Understanding how the risk arises

A relationship should not be accepted solely because it appears statistically significant.

Data quality

​A predictive variable may still be unsuitable if the data is unreliable.

Common issues include:

• Missing values
• Inconsistent definitions
• Changes in coding
• Manual-entry mistakes
• Poor historical coverage
• Different practices between teams

The way a field is recorded in live systems must match the way it was recorded in the modelling data.

Availability at the point of pricing

The variable must normally be available when the price is calculated.

Using information recorded after policy inception or after a claim creates data leakage. The model may then appear much more accurate during development than it will be in practice.

Stability

A variable may work historically but become unreliable if:

• Underwriting rules change
• Customer behaviour changes
• The product is redesigned
• Data collection changes
• The portfolio moves into new markets

The actuary should consider whether the relationship is likely to remain useful throughout the model’s intended lifespan.

Legal, regulatory and ethical considerations

A variable may be predictive but still inappropriate to use.

Insurers must consider:

• Applicable regulation
• Fair customer outcomes
• Proxy discrimination
• Explainability
• Reputational risk
• Internal policies

Operational usability

The insurer should also ask:

• Can the variable be captured accurately?
• Can it be verified?
• Can it be implemented in the rating system?
• Is it available across all channels?
• Could customers manipulate it?
• Will underwriters understand it?

A small improvement in model fit may not justify major operational complexity.

Categorical and continuous variables

Categorical variables place risks into groups.

Examples include:

• Vehicle type
• Region
• Industry
• Occupation
• Construction type

Each group is usually assigned a relativity compared with a reference category.

Where a category contains little exposure or few claims, the estimated effect may be unstable. Similar categories may therefore need to be combined, provided the grouping also makes practical sense.

Continuous variables include:

• Age
• Mileage
• Turnover
• Payroll
• Property value
• Years in business

The relationship between a continuous variable and risk is rarely a perfect straight line.

For example, motor claim frequency may fall sharply between ages 18 and 25, remain fairly stable through middle age and rise again later.

Possible ways to capture nonlinear relationships include:

• Banding
• Transformations
• Polynomial terms
• Splines
• Piecewise functions
• Actuarial smoothing

The aim is to represent the underlying relationship without creating an unnecessarily complex or unstable model.

Interactions between variables

An interaction occurs when the effect of one variable depends on another.

For example, the effect of annual mileage may differ between:

• Experienced and inexperienced drivers
• Private and commercial vehicle use
• Urban and rural areas

Other potential interactions include:

• Driver age and vehicle power
• Property age and construction type
• Industry and turnover
• Policy limit and business activity
• Location and flood exposure

Interactions can improve a model, but including too many can create:

• Overfitting
• Sparse data
• Unstable coefficients
• Complex rating structures
• Difficult implementation

Interactions should have a plausible explanation, sufficient supporting data and a measurable benefit when tested on new observations.

Interpreting GLM results

Categorical GLM results are usually expressed relative to a reference group.

Suppose a frequency model uses these driver-age categories:

• 18–24: 1.50
• 25–39: 1.10
• 40–59: 1.00
• 60 and over: 1.20

The 40–59 group is the reference category.

Holding the other variables constant, the model suggests that:

• The 18–24 group has an expected claim frequency 50% higher
• The 25–39 group has an expected frequency 10% higher
• The 60-and-over group has an expected frequency 20% higher

These factors should not be interpreted in isolation. The actuary should also consider:

• The amount of exposure
• The number of claims
• Confidence intervals
• Stability between periods
• Underwriting knowledge
• Whether the pattern is commercially credible

A highly estimated relativity based on very little data may need to be grouped, adjusted or supported by an external benchmark.

Statistical and practical significance

​A result can be statistically significant but too small to have meaningful commercial value.

Equally, an important segment may fail a conventional significance test because there is limited data.

Model decisions therefore require actuarial judgement alongside statistical evidence.

Model validation and diagnostics

​A GLM should not be accepted simply because it produces coefficients and appears to fit historical data.

Validation asks whether the model is:

• Predictively useful
• Stable
• Statistically appropriate
• Understandable
• Suitable for implementation

Training and test data

The available data is often divided into:

• Training data used to build the model
• Test data used to assess performance on unseen observations

A model that performs well only on the training data may be overfitted.

Testing on a later period can be particularly useful because it shows how the model responds to changes over time.

Deviance and information criteria

Deviance measures the difference between the fitted model and the observed data.

Information criteria, such as the Akaike Information Criterion, balance model fit against complexity.

These measures can help compare different model versions, but they should not replace judgement. A small improvement in fit may not justify a much more complicated pricing structure.

Residual analysis

Residuals represent the differences between actual and predicted outcomes.

Patterns in residuals may suggest:

• Missing variables
• Incorrect variable shapes
• Missing interactions
• Poor fit in particular segments
• Changes over time
• Extreme observations

Residuals should be examined across key variables, product segments, time periods and business channels.

Calibration

A calibrated model produces predictions that align with observed outcomes.

Calibration should be examined:

• Across the whole portfolio
• By risk band
• By product
• By channel
• Over time
• For new and renewal business

A model may appear accurate overall while overpricing one segment and underpricing another.

Discrimination

Discrimination measures how well the model separates lower-risk and higher-risk policies.

A model may rank risks effectively but produce predictions at the wrong overall level. Equally, it may be well calibrated overall but fail to differentiate between policies.

Both calibration and discrimination are important.

Stability testing

The model should be tested across:

• Different time periods
• Business segments
• Geographic areas
• Distribution channels
• New and renewal portfolios

The estimated effects should also be challenged by changing assumptions or removing influential observations.

A model that changes dramatically after a small adjustment may be too unstable for production use.

GLMs compared with machine learning

​Machine-learning techniques can identify complex relationships that may be difficult to specify manually within a GLM.

Common methods include:

• Decision trees
• Random forests
• Gradient boosting
• Neural networks

These approaches may offer improved predictive performance, particularly where there are many variables, nonlinear relationships and complex interactions.

However, they may also create additional challenges around:

• Interpretation
• Governance
• Implementation
• Monitoring
• Data leakage
• Communication with underwriters

GLMs often remain easier to explain and translate into practical rating structures.

The choice should not be framed as GLMs versus machine learning in every situation. Hybrid approaches are increasingly useful.

Machine learning can be used to:

• Identify possible nonlinear relationships
• Detect interactions
• Challenge an existing GLM
• Create new risk scores
• Identify areas of poor model performance

These findings can then be incorporated into a controlled GLM structure.

The appropriate approach depends on the insurer’s data, products, technology, governance capabilities and modelling objectives.

A simplified GLM insurance pricing example

Consider a fictional motor insurer building a claim-frequency model.

The insurer starts with:

• A Poisson distribution
• A log link
• Policy duration as the exposure measure

The selected variables are:

• Driver age
• Vehicle group
• Region
• Annual mileage

The model produces these simplified factors.

Driver age

• 40–59: 1.00
• 25–39: 1.10
• 18–24: 1.55
• 60 and over: 1.18

Vehicle group

• Standard: 1.00
• Low power: 0.85
• High power: 1.30

Region

• Region A: 1.00
• Region B: 1.08
• Region C: 1.20

Annual mileage

• Under 5,000 miles: 0.82
• 5,000–10,000 miles: 1.00
• More than 10,000 miles: 1.25

Assume the base claim frequency is 0.04.

For a driver aged 25–39, with a high-powered vehicle, living in Region B and driving more than 10,000 miles:

0.04 × 1.10 × 1.30 × 1.08 × 1.25 = approximately 0.077

Now consider a driver aged 40–59, with a low-powered vehicle, living in Region A and driving under 5,000 miles:

0.04 × 1.00 × 0.85 × 1.00 × 0.82 = approximately 0.028

The first risk has an expected claim frequency around 2.75 times higher than the second.

Suppose a separate severity model predicts:

• £6,000 average severity for the first risk
• £4,500 for the second risk

Expected claims costs are:

• First risk: 0.077 × £6,000 = £462
• Second risk: 0.028 × £4,500 = £126

These amounts would form part of the technical price before expenses, commission, reinsurance, capital and profit are added.

Common implementation problems

The quality of the statistical model is only one part of a successful pricing project.

Poor data quality

Missing values, inconsistent coding and inaccurate exposure or claims records can undermine the model.

The data should be reconciled and understood before model development begins.

Data leakage

Using information that would not be available when the price is calculated can make a model appear unrealistically accurate.

All variables should be checked against the live pricing process.

Changes in portfolio mix

Historical data may not reflect the risks the insurer now writes or intends to target.

Changes in channels, products, underwriting rules and customer groups should be considered during development.

Overfitting

Adding too many variables, interactions or categories may improve historical fit while weakening performance on new data.

Out-of-sample testing and stability analysis are essential.

Large claims

A small number of severe losses can dominate model results.

Possible treatments include:

• Capping claims
• Modelling large losses separately
• Applying separate loadings
• Reviewing influential observations

Implementation limitations

The live rating system may not be able to reproduce all the model’s transformations and interactions.

Implementation requirements should be considered from the beginning, not after model development has finished.

Weak underwriter engagement

Underwriters can provide important context about data, claims, customer behaviour and changing risks.

Engagement helps challenge both the statistical results and existing underwriting assumptions.

Uncontrolled overrides

Pricing adjustments may be necessary, but they should be recorded and monitored.

Frequent overrides may indicate missing variables, a weak model, commercial pressure or poor user confidence.

Lack of ongoing monitoring

A GLM can deteriorate as claims inflation, customer behaviour and the portfolio change.

Monitoring should cover:

• Actual versus expected claims
• Performance by rating factor
• Portfolio mix
• Conversion and retention
• Underwriting overrides
• Profitability

Pricing models should be treated as living tools rather than one-off projects.

Frequently asked questions

What does GLM stand for in insurance?

GLM stands for Generalised Linear Model. It is a statistical framework used to estimate relationships between insurance outcomes and risk characteristics.

What are GLMs used for in insurance?

They are commonly used to model claim frequency, claim severity, aggregate claims cost, claim probability, renewal and other pricing outcomes.

Which GLM is used for claim frequency?

Poisson GLMs are widely used. Negative binomial models may be considered when claim counts show greater variation than a Poisson model can accommodate.

Which GLM is used for claim severity?

Gamma GLMs with a log link are common for positive and right-skewed claim amounts. Other distributions may be appropriate depending on the data.

Why use separate frequency and severity models?

Different variables may affect how often claims happen and how much they cost. Separate models provide greater insight into each component of expected risk.

Are machine-learning models better than GLMs?

Not automatically. Machine learning may identify more complex patterns, while GLMs are generally easier to interpret, validate and implement.

Can a GLM calculate the final insurance premium?

A GLM can estimate expected claims cost or another component of the technical price. The final premium may also include expenses, commission, reinsurance, capital, profit, tax and commercial adjustments.

How MatBlas can help

MatBlas helps insurers develop, review and improve their pricing frameworks.

Our actuarial and software specialists can support organisations with:

• Developing bespoke pricing models
• Reviewing existing GLMs and rating structures
• Improving model validation and governance
• Translating models into practical pricing tools
• Streamlining pricing and underwriting workflows
• Training actuaries, underwriters and insurance professionals
• Developing insurance-specific actuarial software

To discuss your organisation’s insurance pricing requirements, contact the MatBlas team.

Ana Mata

Managing Director and Actuary