Credit Scoring Using Binary Quantile Regression

Abstract

This paper presents an application of binary quantile regression to the problem of credit scoring. Credit scoring techniques are extensively employed by financial institutions in an effort to predict credit worthiness of loan applicants. Commonly used parametric models like logit and probit discrimination assume that the probability of a “bad” loan (default) is given by P(D = 1|X) = F(X′β), where D is the indicator of default, X is a vector of costumer characteristics, and F is a known distribution function. In an effort to better control risk, a number of recent studies propose using semiparametric single index models, as well as, nonparametric alternatives like neural networks and classification trees.

In this paper we compare probit discrimination to quantile regression discrimination using a matched sample of 1000 loans issued in Germany, 300 of which defaulted. The total sample is split into an estimation random subsample of 800 loans, and a validation subsample of 200 loans. Quantile regression discrimination implies that for the τ-th conditional quantile of credit risk, P(D = 1|X) = 1 − τ when the τ-th quantile index X′α(τ) is approximately zero. Given scaled estimates of α(τ) over a grid of τ’s in (0,1), we are able to classify loans over the corresponding probability grid p = 1 − τ in (0,1). We find that quantile regression discrimination compares favorably to probit and heteroskedastic probit discrimination both in the estimation as well as in the validation datasets.