GLMs in pricing
/ G-L-M /
The old way of finding relativities was to look at one rating variable at a time: split customers by age, compare loss ratios; then split by territory, compare again. The trouble is that variables overlap — young drivers also tend to drive certain cars and live in certain places — so a one-way analysis credits the same effect to several variables and the prices come out distorted. Generalized linear models (GLMs) solve this by estimating the effect of every rating variable simultaneously, each adjusted for all the others.
A GLM is a flexible cousin of ordinary regression, built to fit insurance data honestly. Two features make it the workhorse of modern pricing. First, the link function: pricing uses a multiplicative (log-link) structure, so the model naturally produces relativities you multiply together, matching how rating algorithms work. Second, the error distribution is chosen to match the data: a Poisson distribution for claim counts (frequency), a gamma for claim sizes (severity), or a Tweedie for pure premium directly. The model returns, for each level of each variable, a relativity that is the marginal effect holding everything else fixed — for example, 'a young driver is 1.6 times the base, after already accounting for vehicle and territory'.
GLMs transformed pricing from coarse tables into fine, internally consistent rating plans, and they remain the regulated industry standard because their coefficients are interpretable and explainable — you can show a regulator exactly why each factor is what it is. Newer machine-learning methods (gradient boosting, neural nets) often predict losses more accurately, but they are harder to explain and to defend as 'not unfairly discriminatory', so they are frequently used to inform or challenge a GLM rather than to set the filed rates outright. The honest caveat: a GLM still only finds associations in the data, not causes, and it will faithfully reproduce any bias baked into the historical data it is fed.
A frequency GLM (Poisson, log link) on auto data estimates that, holding vehicle and territory fixed, young drivers have a relativity of 1.60. A separate gamma GLM models severity; multiplying the two (or fitting a Tweedie) gives the pure-premium relativity.
A GLM estimates every variable's relativity at once, each adjusted for the rest.
A GLM finds correlations, not causes, and reproduces bias in the training data. Higher predictive accuracy from machine learning is not enough by itself — rates must also be explainable and not unfairly discriminatory.