What are generalized linear models (GLMs) and when are they used in finance?

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AcadiFi · Accepted Answer

Generalized linear models (GLMs) extend ordinary least squares regression to handle response variables whose distribution isn't normal. An OLS regression assumes the dependent variable is continuous and normally distributed around its mean. But many financial phenomena aren't — default/no-default is binary, claim counts are discrete, loss severities are skewed and nonnegative. A GLM has three components: (1) Random component — specifies the distribution of Y from the exponential family (normal, binomial, Poisson, gamma, etc.). (2) Systematic component — linear predictor η = Xβ, just like OLS. (3) Link function — g(μ) = η connecting the expected value to the linear predictor. Different link functions suit different distributions. ```mermaid flowchart LR X[Features
X beta] --> LP[Linear
Predictor eta] LP --> LF[Link
Function g] LF --> M[Mean
mu] M --> D[Distribution
Family] ``` Examples in finance: (1) Logistic regression — binomial distribution + logit link — used for default prediction, fraud detection. (2) Poisson regression — Poisson distribution + log link — claim frequency modeling in insurance. (3) Gamma regression — gamma distribution + log link — loss severity modeling. (4) Probit regression — binomial + inverse normal link — credit scoring. GLMs are fit via maximum likelihood estimation rather than OLS. Key advantages over linear regression for non-normal data: proper handling of bounded outcomes (probabilities), non-negativity constraints, variance-mean relationships (heteroskedasticity built in), and ability to model counts. In the new CFA curriculum, GLMs are key building blocks for machine learning applications in finance. Understanding how to interpret coefficients (log-odds in logit, rate ratios in Poisson) is critical.

What are generalized linear models (GLMs) and when are they used in finance?

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