A joint scoring model for peer-to-peer and traditional lending: a bivariate model with copula dependence

We analyse the dependence between defaults in peer-to-peer lending and credit bureaus. To achieve this, we propose a new flexible bivariate regression model that is suitable for binary imbalanced samples. We use different copula functions to model the dependence structure between defaults in the two credit markets. We implement the model in the R package BivGEV and we explore the empirical properties of the proposed fitting procedure by a Monte Carlo study. The application of this proposal to a comprehensive data set provided by Lending Club shows a significant level of dependence between the defaults in peer-to-peer and credit bureaus. Finally, we find that our model outperforms the bivariate probit and univariate logit models in predicting peer-to-peer default, in estimating the value at risk and the expected shortfall.