A Bivariate Model for Correlated and Mixed Outcomes: A Case Study on the Simultaneous Prediction of Credit Risk and Profitability of Peer-to-Peer (P2P) Loans

In the peer-to-peer (P2P) lending market, current studies focus on two categories of approaches to evaluate the loans, thus providing investment suggestions to the investors: credit scoring (i.e., predicting the credit risk) and profit scoring (i.e., predicting the profitability). However, relying on a single scoring approach may bias the loan evaluation conclusion. In this paper, we propose a bivariate model based on the integration of two scoring approaches. We first formulate the loan evaluation task as a multi-target problem, in which loan_status (i.e., default or not default) is used as the discrete outcome for the credit risk measure while the annualized rate of return (ARR) is used as the continuous outcome for the profitability measure. Then to solve the multi-target problem, we design a novel loss function based on the assumption that the discrete outcome follows a Bernoulli distribution, and the continuous outcome is normally distributed conditional on the discrete output. The effectiveness of the proposed model is examined using the real-world P2P data from the Lending Club. Results indicate that our approach outperforms the sole scoring methods by identifying loans with higher profit and lower default risk. Therefore, the proposed method can serve as an alternative for loan evaluation.