A Novel behavioral scoring model for estimating probability of default over time in peer-to-peer lending
Introduction
Peer-to-peer (P2P) lending is the practice of providing loans to individuals or businesses through online platforms that match lenders directly with borrowers, bypassing the need for a traditional financial intermediary, such as a bank. By operating fully online, P2P lending incurs lower overhead costs than do traditional bank loans, often resulting in higher returns for lenders and lower interest rates for borrowers. Thus P2P lending is especially attractive to individuals and small businesses (Guo et al., 2016). P2P lending has undergone phenomenal development in recent years and has now become an important alternative to loan services provided by traditional financial institutions in countries such as the U.S. and China (Bachmann et al., 2011). However, P2P lending also faces great challenges. The information asymmetry inherent to P2P lending—in which lenders know limited information about borrowers while borrowers know considerably more about their own risk levels—attracts riskier borrowers and misleads lenders to fund them, leading to higher default rates compared with bank loans (Chen and Han, 2012).
Financial institution business performance is heavily dependent on the management of credit risk. Credit scoring models are important tools for decision support systems in the financial industry, and have been widely applied to make decisions concerning whether to grant credit to new applications (Crook et al., 2007, Wang et al., 2012). Although credit scoring models can effectively filter out most risky borrowers, some borrowers still default even after their loan application has been approved. Therefore, most financial institutions subsequently apply behavioral scoring models to monitor borrowers’ repayment behaviors, especially in P2P lending (Alves and Dais, 2015). An accurate behavioral scoring model for borrowers is extremely valuable in the P2P market.
Both credit scoring and behavioral scoring are a process of determining how likely borrowers are to default with their repayment, that is, predicting the probability of default (PD). Credit scoring is defined as a connection between two snapshots of the state of the borrower indicating the characteristics at the time of application and the state of the loan at a later date respectively (Savvopoulos, 2010). (See Panel (a) in Fig. 1). The future performance (i.e., the performance of repayment behavior) is indicated as a static PD for the entire loan.
In a behavioral scoring model, the borrowers’ future performance depends not only an initial snapshot of their risk condition at the time of application but also on their recent performance; thus, contrary to credit scoring, the PD takes a dynamic property (Alves and Dais, 2015). By adding information about the borrower’s past performance such as the number of successful loans, failed loans and paid-off loans, the traditional behavioral scoring model replaces the first snapshot by a description of the dynamics of the borrower’s performance (Panel (b) in Fig. 1), but the second snapshot remains. Given the dynamic property of repayment behavior, a more appropriate behavioral scoring model should be able to utilize the past behavior to estimate subsequent repayment performance over a future time interval, not just at a specific future time (Panel (c) in Fig. 1). Thus, to develop dynamic behavior scoring one needs to estimate the dynamic PD over time, namely predicting not only whether but also when the borrowers are likely to default. Especially, this framework can offer guidance in a timely manner and improve the effectiveness of post-loan risk management and control. Experience has shown that early intervention can both effectively minimize the arrears and reduce the number of accounts that become bad debts and the resulting losses (Sarlija et al., 2009).
In the present paper, we propose a novel behavioral scoring model based on a mixture random forest ensemble to predict the PD over time. First, we propose a mixture random forest (MRF) model based on survival analysis to predict the PD over time. The proposed MRF model consists of two components: the incidence component, which is modeled by a random forest, predicts whether a borrower will default, and the latency component, which is modeled by a random survival forest, predicts the survival time (i.e., the time of the occurrence if it were to occur) of a borrower conditional on the borrower being susceptible to default. The two components are combined by a conditional probability formula to estimate the PD over time. In contrast to an ordinary behavioral scoring model, which poses a classification problem in which each loan is classified as default or non-default, the proposed mixture random forest model outputs a two-dimensional matrix of the probabilities of default over time (i.e., the PD at different times). Second, after obtaining the MRF model, we consider using a combination of models to reduce the variance and improve the stability.
An ensemble is a supervised learning paradigm in which multiple base learners are combined to form an improved learner. The trained ensemble represents a single hypothesis that is not necessarily contained within the hypothesis space of the models from which it is built. Thus, ensembles have greater flexibility to represent various functions. This flexibility can, in theory, enable ensembles to obtain relatively higher classification accuracies compared to a single model (Twala, 2010). In this paper, we utilize tree-based ensemble methods (i.e., a random forest and a random survival forest) to improve the performances of the incidence and latency components. The averaging ensemble, which is a simple and effective model combination strategy, is used to improve the robustness of the proposed model.
We evaluated our proposed ensemble mixture random forest (EMRF) model on a real-world dataset collected from a major P2P platform in China. We compare our proposed model with a standard mixture cure model (Tong et al., 2012), the Cox proportional hazards model and logistic regression in terms of both their discrimination performances (the ability to risk-rank borrowers accurately over time) and their calibration performances (the accuracy of the probability of the default estimates themselves over time).
The remainder of this paper is organized as follows. In Section 2, relevant previous studies on behavioral scoring and P2P lending are presented. In Section 3, we propose an averaging ensemble model based on a mixture random forest for behavioral scoring. We describe the experimental design in Section 4 and report on the results in Section 5. Finally, we conclude the paper by summarizing our contributions and discussing future research directions in Section 6.
Section snippets
Credit assessment models
In the scope of credit risk management, two types of scoring models have been widely used to make decisions on new loan applications and to monitor borrowers’ repayment behaviors; the former model is known as a credit scoring model (also known as an application scoring model) while the latter model is known as a behavioral scoring model (Kao et al., 2012, Alves and Dias, 2015). Credit scoring and behavioral scoring models are commonly built on accepted loan applicants; however, credit scoring
Proposed methodology
We next discuss how the ensemble mixture random forest model (EMRF) assessment process is implemented. The process of predicting the PD over time including variables preprocessing is illustrated in Fig. 2. Specifically, we start by using the weight of evidence (WOE) transformation to coarsely classify the original variables. In the WOE transformation, all variables are converted into orderly discrete variables, in which the order is based on the default rate of the categories in each variable.
Empirical evaluation
The empirical evaluation was performed on a PC with a 3.20 GHz Intel Core i5-3470 CPU and 12 GB of RAM using the Windows 7 operating system. The data mining toolkit from R version 3.31 was used for the experiment. R is a free software environment for statistical computing and graphics.
Dynamic repayment process
Before examining the discrimination and calibration performance of each model, we first provide an example to illustrate how the dynamic PD reflects the dynamic repayment process. Fig. 5 displays the predicted PD over time compared to the actual repayment process. The solid lines depict the predicted PD of four models (i.e., EMRF, MCM, Cox PH and LR) over time. The dotted lines (“0″ and “1″ denote “non-default” and “default”, respectively) depict the actual repayment process, indicating that
Conclusion
Behavioral scoring has gradually become an essential tool for financial institutions in today’s credit marketplace, which requires highly automated decisions, especially in the P2P market. To monitor the repayment behavior and evaluate the creditworthiness of existing customers, traditional behavioral scoring models have used a variety of classification methods to predict a static PD over a future period. Because borrowers’ repayment behavior is a dynamic process, in this paper, we proposed a
Acknowledgement
This work was funded by the National Natural Science Foundation of China (Grant Nos. 71731005, 71571059) and the Humanities and Social Sciences Fund Research Planning of the Ministry of Education (Grant No. 15YJA630010).
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