Loan Default - Poisson Model

Overview

The poisson model of default uses the Poisson distribution to model the likelihood of default. The Poisson distribution is a distribution of count data. That is, the domain is the set of integers, and the distribution assigns a probability to each number.

It is typical to define default such that it only occurs once for a loan. However, the Poisson distribution will assign a finite probability for the number 2 and up. The probabilities assigned are generally quite small and immaterial, and hence, the Poisson model is still used in practice despite this discrepancy. When simulating defaults with the Poisson model, simulated counts above one are typically discarded.

Fitting the Poisson Model

The poisson model is one the exponential family of distributions, and hence can be fit using a poisson regression a generalized linear model.