Improving credit risk assessment in P2P lending with explainable machine learning survival analysis

Bone-Winkel, Gero Friedrich; Reichenbach, Felix Article — Published Version Improving credit risk assessment in P2P lending with explainable machine learning survival analysis Digital Finance Provided in Cooperation with: Springer Nature Suggested Citation: Bone-Winkel, Gero Friedrich; Reichenbach, Felix (2024) : Improving credit risk assessment in P2P lending with explainable machine learning survival analysis, Digital Finance, ISSN 2524-6186, Springer International Publishing, Cham, Vol. 6, Iss. 3, pp. 501-542, https://doi.org/10.1007/s42521-024-00114-3 This Version is available at: https://hdl.handle.net/10419/316976 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) Digital Finance (2024) 6:501–542 https://doi.org/10.1007/s42521-024-00114-3 1 3 ORIGINAL ARTICLE Improving credit risk assessment inP2P lending withexplainable machine learning survival analysis GeroFriedrichBone‑Winkel1· FelixReichenbach2 Received: 4 March 2024 / Accepted: 17 May 2024 / Published online: 12 June 2024 © The Author(s) 2024 Abstract Recent research using explainable machine learning survival analysis demonstrated its ability to identify new risk factors in the medical field. In this study, we adapted this methodology to credit risk assessment. We used a comprehensive dataset from the Estonian P2P lending platform Bondora, consisting of over 350,000 loans and 112 features with a loan volume of 915million euros. First, we applied classical (linear) and machine learning (extreme gradient-boosted) Cox models to estimate the risk of these loans and then risk-rated them using risk stratification. For each rating category we calculated default rates, rates of return, and plotted Kaplan– Meier curves. These performance criteria revealed that the boosted Cox model outperformed both the classical Cox model and the platform’s rating. For instance, the boosted model’s highest rating category had an annual excess return of 18% and a lower default rate compared to the platform’s best rating. Second, we explained the machine learning model’s output using Shapley Additive Explanations. This analysis revealed novel nonlinear relationships (e.g., higher risk for borrowers over age 55) and interaction effects (e.g., between age and housing situation) that provide promising avenues for future research. The machine-learning model also found feature contributions aligning with existing research, such as lower default risk associated with older borrowers, females, individuals with mortgages, or those with higher education. Overall, our results reveal that explainable machine learning survival analysis excels at risk rating, profit scoring, and risk factor analysis, facilitating more precise and transparent credit risk assessments. Keywords P2P lending· Explainable AI· Cox model· Credit risk· SHAP· Survival analysis JEL Classification G10· G21· G32· G33· G51 * Felix Reichenbach f.reichenbac[email protected] 1 Technische Universität Berlin, Straße des 17. Juni 135, 16023Berlin, Germany 2 Chair ofFinance andInvestment, Technische Universität Berlin, Straße des 17. Juni 135, 10623Berlin, Germany 502 Digital Finance (2024) 6:501–542 1 3 1 Introduction Driven by technological advancements, Peer-to-Peer (P2P) lending meets a growing demand for alternative financing and personal loans (Suryono etal., 2019). These loans are typically unsecured (De Roure etal., 2016) and lenders bear the risk of default. Most major P2P lending platforms set interest rates based on their internal rating models. On these platforms, accurate risk assessment is crucial: If the platform overestimates the risk of a loan, the borrower might be able to get a cheaper loan elsewhere. If the risk is underestimated, lenders might not be able to recover their investment in case of default and might not invest via the platform again. However, the lack of credit history and collateral makes it difficult to assess the creditworthiness of borrowers using traditional credit risk assessment methods (Bavoso, 2020). Machine Learning (ML) is a promising technology that could prove key to more accurate risk evaluation (Zhang etal., 2015). While many studies have been conducted on the topic of credit risk assessment using ML, most focus on predicting binary default, rather than default timing. Moreover, ML is often seen as a “black box”—powerful at risk-classification, but not well suited for analyzing the economic impact of individual risk factors. Accordingly, this (perceived) trade-off between explanatory and predictive performance limits the usefulness of ML methods in risk management (Van Liebergen, 2017). However, recent developments in explainable ML demonstrate that the two are not necessarily at odds, with ML survival analysis methods identifying both known and novel risk factors for breast cancer survival (Liu etal., 2023; Moncada-Torres etal., 2021). Our study applies this promising methodology to credit risk assessment in P2P lending. We use a dataset from the Estonian platform Bondora consisting of over 350,000 loans and 112 features with a volume of €915 million at the end of 2023. Using classical and extreme gradient-boosted Cox models, we predict the risk of P2P loans. Subsequently, we assign risk ratings using risk stratification. We show that the ratings based on the ML model (i.e., the boosted Cox model) significantly outperform both Bondora’s risk rating and the rating based on the classical model (i.e., the linear Cox model).1 We also discuss the practical implications for risk screening, setting fairer interest rates and the potential profit opportunities for investors when using these models. Then, we open the “black box” of ML by using Shapley Additive Explanations (SHAP) to explain and compare the models (Lundberg & Lee, 2017). Here, we examine the differences between the classical and ML Cox model and evaluate how the ML model can be used to identify risk factors in P2P lending. Our analysis uncovers risk factors that align with those identified in prior studies, while also unveiling novel relationships with nonlinear and interaction effects. 1 While it could be argued that “classical” (linear) Cox models are also a form of ML, we follow Ley etal. (2022) in distinguishing between the two: Classical models are defined by the user (top-down), whereas ML models are defined by the algorithm (bottom-up and driven by the data). AppendixB provides a more detailed discussion of this issue. 503 1 3 Digital Finance (2024) 6:501–542 In summary, we demonstrate that with superior predictive and explanatory performance, explainable ML survival analysis is not only a useful tool for credit scoring but also for the examination of credit risk factors. The study is structured as follows. Section2 presents the theory, reviews the existing research on risk assessment methodologies, and outlines the contribution and objectives of our study. Section3 then introduces the datasets and our methodical approach.2 Section4 presents the model’s performance and explanations, which we interpret and discuss in Sect.5, followed by Sect.6 that concludes the study. 2 Theoretical background andliterature In the following subsections, we briefly review the literature on credit risk modeling in P2P lending and explainable ML. Furthermore, we identify the research gap and discuss the objectives and contribution of this study. 2.1 Credit risk modeling inP2P lending As outlined in the introduction, accurate risk assessment is essential for platforms, borrowers, and lenders. However, a review by Suryono etal. (2019) underscores that risk assessment poses a major challenge in P2P lending due to large information asymmetry, lack of credit history, gender discrimination, and low loan success rates. The review further identifies ML methods and big data as potential solutions to these issues. Investigating credit risk is a well-established field of research and has been studied extensively using binary classification. Binary classification aims to predict whether a borrower will default. It has been studied widely on P2P lending datasets using statistical (e.g., Emekter etal., 2015; Serrano-Cinca et al., 2015), ML (e.g., Jiang etal., 2018; Xu etal., 2021; Zhou etal., 2019), and rarely using explainable ML methods (e.g., Ariza-Garzón etal., 2020; Bussmann etal., 2021). In practice, like most studies, banks typically use binary classification to calculate the probability of default for credit scoring (Dömötör etal., 2023). While their exact method is not disclosed, Bondora’s ratings are based on expected loss, which also takes into account the likelihood of recovery after default (Bondora, 2023c).3 Survival analysis offers an alternative approach that has some advantages over traditional classification methods: First, survival analysis takes into account the time duration until a loan defaults. This is not done when analyzing the default status alone. However, time to default plays a crucial role in return on investment and 2 AppendixB offers a more detailed exposition of the models, performance metrics, risk rating, and explainable ML, serving as an accessible guide for practitioners and researchers keen on applying this innovative methodology. 3 These ratings are based in part on sensitive data that lenders legally cannot access. This includes prior loan applications, and information from credit bureaus, population registries, banks, and tax authorities (Bondora, 2023c). By encoding information unavailable to lenders in ratings, Bondora could reduce uncertainty between lenders and borrowers. However, if the ratings do not accurately reflect a loan’s risk profile, it can lead to mispricing through too high or too low interest rates. 504 Digital Finance (2024) 6:501–542 1 3 expected loss: With later defaults, the exposure at default and thus investment at risk is lower. This is particularly important in the case of fixed-rate loans, where the outstanding payments for investors are much higher when the loan defaults on the first payment as opposed to the last payment. Second, survival analysis also enables including loans in the training dataset that have not yet reached maturity through censoring. This can be a significant advantage, especially for long maturities, as it allows for the use of more recent data. A third advantage is that researchers can use survival functions to examine the influence of characteristics on solvency over time, which may provide insights into possible underlying causes. This is promising in practice, e.g., when evaluating loans in secondary markets, borrower characteristics may have a different effect after a certain period of time. While statistical survival analysis models like linear Cox regression are used in some studies on P2P lending datasets (e.g., Emekter etal., 2015; Serrano-Cinca etal., 2015), few ML-based survival analysis studies exist (Suárez-Ramírez etal., 2022; Tan etal., 2019) and none of these use explainable ML methods. Nevertheless, when proposing a novel ML survival-analysis method (Bai etal., 2022) demonstrate that ML-based survival analysis can outperform statistical survival analysis methods in default classification. 2.2 Explainable machine learning andcontribution The scarcity of ML survival analysis studies in recent literature may be caused by seemingly conflicting goals of their methodologies: While popular survival analysis methods like linear Cox regression are commonly used for their interpretability in risk factor assessment (Emekter et al., 2015; Reichenbach & Walther, 2021; Serrano-Cinca etal., 2015), ML methods focus on predictive accuracy and are more difficult to interpret. Even the most precise predictions from a ML Cox model may not be very useful if they are not interpretable. Recent research addresses this issue with the model agnostic and scalable explainable ML method SHAP (Lundberg and Lee, 2017; Lundberg etal., 2019, 2020; Mitchell et al., 2022). This method enables the explainability of ML Cox models, unveiling much more complex nonlinear relationships and interaction effects than the linear models could capture. This combination of methods yielded breakthrough results in clinical research, identifying both clinically confirmed and potentially novel risk indicators for breast cancer survival (Liu et al., 2023; Moncada-Torres etal., 2021) using explainable ML survival analysis. To the best of our knowledge, explainable ML survival analysis has not yet been applied to P2P lending. This study aims to address this research gap by presenting explainable ML-based survival analysis as a useful tool for both credit scoring (i.e., classification using risk ratings) and the (inferential) analysis of different risk factors (e.g., debt-to-income, age, education) in P2P lending. Thus, we seek to contribute to both the literature on credit scoring techniques and the analysis of risk factors of individual borrowers. 505 1 3 Digital Finance (2024) 6:501–542 Concerning the Bondora dataset used to test the methods, previous studies found room for improvement in credit risk scoring (e.g., Dömötör etal., 2023; Lyócsa etal., 2022; Teply & Polena, 2020), and signs for asset mispricing on the secondary market (Caglayan etal., 2020). However, as discussed above, the data has not been extensively studied using interpretable ML and survival analysis methods. 3 Data andmethods In this section, we briefly present the data and methods used in this study. For readers not familiar with survival analysis, ML, or SHAP, we recommend reading our more detailed introduction to these methods in Appendix B, where we introduce classical (Cox) models, their predictions and how these can be generalized using ML methods. We also explain how SHAP values are used to explain ML predictions. The methodology of our study consists of 6 major steps: (1) preprocessing, (2) sampling, (3) training of the models, (4) rating assignment, (5) performance measurement and (6) analysis of risk factors. These are illustrated by Fig.1 and are discussed in the following subsections after the presentation of the datasets. 3.1 Datasets We use two datasets provided by Bondora (2023a) for our analysis. These are updated daily and were last retrieved on January 3, 2024. The loan dataset contains data on all loans originated on the Bondora platform, including over 350,000 loans from Estonia, Finland, and Spain. Its 112 features provide details on the borrowers’ demographics, financials, and borrowing history, as well as risk ratings calculated by Bondora and information on the loan terms and outcome (see AppendixA for a full table with Bondora’s definitions). With loans ranging from 2009 until the end of 2023, the total cash volume of all loans sums up to 915 million Euros. The loans in the dataset have varying maturities, the most common being 5 and 3years. Our study focuses on 3-year-loans as the duration is short enough, in light of the limited data timespan available, to allow for the splitting of training, validation, and test data in a temporal order. The fixed loan duration ensures comparability between borrowers when analyzing the risk factors using survival analysis (see AppendixB.1). The following data and plots address this subset. As seen in Fig. 2 the majority of loans were originated after 2017. The overall risk structure of the portfolio appears to have shifted towards less risky loans after 2019. This may be explained by Bondora’s shift to hands-off4 investment from 2016 to 2020 (Bondora, 2016). The lower amount of loans since 2020 may be due to the COVID-19 pandemic and a focus on higherquality lenders. 4 Today, Bondora exclusively offers investments into a single platform-managed portfolio at a fixed annual rate of return. 506 Digital Finance (2024) 6:501–542 1 3 In addition, we use Bondora’s repayments dataset (Bondora, 2023a), which contains all payments received by investors (over 6.2million in total) to calculate the loans’ internal rate of return (IRR). In contrast to the return on investment, the IRR takes into account the time of payment and therefore indicates Fig. 1 Overview of the main preprocessing, training and evaluation steps 507 1 3 Digital Finance (2024) 6:501–542 the actual rate of return realized by the investors. The results of this analysis are presented in Sect.4.1. 3.2 Preprocessing As seen in Fig.1, we preprocessed the data for model training in 10 steps. To achieve better comparability, we train both models on the same datasets. As such, these steps follow the stricter requirements of the linear model by excluding missing values. Benefiting the interpretability of both models, we reduce high dimensionality, co-dependencies and sparsity of the data, leading to simpler models and thus simpler SHAP explanations. Next, we present the preprocessing steps in more detail: First, we removed 37 features not available at the time of the auction to avoid target leakage.5 This includes data about the loan status, secondary market, and debt collection process. To identify these features, we consulted the Bondora auction Application Programming Interface (API) documentation (Bondora, 2023b) and the Bondora website (Bondora, 2023a). We then removed another 16 features not available due to data protection laws after June 1, 2017 (e.g., private information like marital status and employment position, but also financials like debt-to-income (DTI)). Furthermore to avoid overfitting, we dropped features not relevant to the analysis, like the loan ID, loan number, username, and features about the exact timing of the listing like the payment day, listing time, weekday, and month. As a fourth step, we modeled some features found relevant in prior literature that are not present in the data and added control variables: DebtToIncomeModeled measures the ratio between monthly income and monthly liabilities plus loan Fig. 2 Number of 3-year-loans by origination year and risk rating 5 Target leakage occurs when data not available in the real world is used to train a model (Kaufman etal., 2011). 508 Digital Finance (2024) 6:501–542 1 3 payments.6 RepaymentRatio measures the previous repayment amounts divided by the previous loan amounts.7 Next, we removed features with a high percentage of missing values: DateOfBirth, City, and County were missing for all borrowers, likely because they were retracted from the public data. Additionally, we removed the country-specific credit scores from external rating agencies due to missing data (between 41 and 91%). This left us with a few features with less than 2% missing. For these, we removed data points with any missing values. This affected 2.85% of the remaining borrowers. For categorical features, we removed unused and extremely rare categories (less than 0.1% of the borrowers), i.e., the only remaining homeless and 41 Slovakian borrowers. Note that this step may introduce bias to the benefit of improved comparability between the models and could be skipped for the boosted model. Then, we merged the two categories “income unverified” and “income unverified, cross-referenced by phone” due to a very low number of loans in the latter category (less than 1%). As a significant portion of Estonian borrowers is Russian-speaking, this population was separated from the other Estonian borrowers as “EE_Ru”. For other country codes, the language spoken was more homogenous, and other languages were too rare to draw any conclusions. After that, the features “Language” and “Country” were removed from the dataset and replaced by the new feature “Country_Lang”. We renamed categorical features encoded as numbers (as seen in AppendixA) to strings to improve readability in the plots and remove false ordinality. Additionally, we renamed NewCreditCustomer to NewBondoraCustomer, as this reflects the meaning of the feature better, and corrected spelling mistakes. Furthermore, we use one-hot encoding for the categorical variables when fitting the linear models. Onehot encoding creates a new column for every categorical value (e.g., Rating_AA, Rating_A ,…, Rating_HR). The new columns contain a 1 if the loan has the corresponding rating and a 0 otherwise. To avoid multicollinearity, we dropped the first category of each feature in these models. Finally, we added two variables needed for survival analysis. That is the survival time (SurvivalTime) and an event indicator (Defaulted). In our analysis of the Bondora dataset, we define survival time and the default indicator as follows. Survival time is the time in days between the loan origination and the first of the following events: default (defaulted), end of the loan term (not defaulted), and end of the observation period (not defaulted), i.e., the split date for training and validation sets or the date of the report for the testing set. In other words, we investigate how long a subject can observably meet the loan’s conditions without default. Crucially, 7 However, some loans had no data on previous repayments. This could be due to the loans being still active or the data being unavailable. On top, some loans had no previous loans. For these variables, the ratio was not calculable and was set to 0. To control for this, we added variables for unknown previous repayments, namely NanEarlyRepayment and NanRepaymentHistory. 6 Loan payments appear not to be included in Bondora’s monthly liabilities variable. This calculated ratio appears to deviate from the DTI ratio calculated by Bondora for data prior to 2017. This deviation is likely caused by the exclusion of some liabilities and income sources from the dataset for data protection reasons. Unfortunately, the exact calculation of the DTI ratio, income, and liabilities are not disclosed by Bondora. 515 1 3 Digital Finance (2024) 6:501–542 bars on the right. The vertical dispersion of the boosted SHAP values is explained by feature interaction effects. We will dissect these for selected features later. Figures6 and7 show the SHAP values for the boosted and linear Cox model for three selected features from the demographics category, Country_Lang, Education Age. The full dependence plots for all 21 features in the categories demographics, financials, and borrowing history are presented in AppendixF. Fig. 6 SHAP values for the features Country_Lang (left) and Education (right). The blue dots represent the predictions of the boosted model, while the lines are the coefficients of the linear model, with their statistical significance indicated by the color bar on the right (colour figure online) Fig. 7 SHAP values for the feature Age. The blue dots represent the predictions of the boosted model, while the slope of the line is determined by the coefficient of the linear model. Its statistical significance is indicated by the color bar on the right (colour figure online) 516 Digital Finance (2024) 6:501–542 1 3 Country. The most impactful demographic feature is the country and language of the borrower. For this feature, the Shapley values of the linear and boosted Cox model appear to be quite similar in magnitude and direction, except for the centering difference. While the boosted model is centered on the average contribution of all feature values, the linear model is centered on the first feature value dropped in one hot encoding (i.e., EE). This results in slightly higher values for the linear model. The linear model’s SHAP values are equal to the coefficients of the linear Cox regression (see AppendixE). Both models show that Estonian-speaking Estonians have the lowest risk, followed by Russian-speaking Estonians and Finnish borrowers. Spanish borrowers exhibit the highest default risk (HR ∗e1.2 ≈3.22). Education. One of the more intuitive features in the demographics category is the educational level of the borrower. While the boosted model finds a monotonically decreasing risk with higher education, the linear model only finds a significant impact on risk for the highest educational level (HR ∗e−0.2 ≈0.82). Age. The linear model identified age as a significant risk factor to the p=10−2 level (blue line), and found that the risk decreased monotonically with age. For example, a borrower aged 60 (𝜙age ≈−0.04) would have around 92% the risk of a borrower aged 20 (𝜙age ≈0.04) with HR =e−0.04∕e0.04 ≈0.92. By definition, the slope of the line corresponds to the coefficient of the linear Cox regression (−0.002) and has its x-intercept at approximately 40years, which is the average age of borrowers. In the boosted model the risk of default also generally decreases with age. However, young borrowers between 20 and 25 and borrowers older than 60 have a higher risk than the linear model would predict. While these SHAP dependence plots visualize the individual feature’s contributions, some features may interact with other features in the model, leading to vertical dispersion in the plots (e.g., for Country_Lang and Education). These can be investigated further using SHAP interaction values, as shown in the following section. 4.3 Model explanations: SHAP feature interactions The SHAP interaction effects estimate how much the SHAP value of a feature changes when combined with another feature. Subtracting all interaction effects from the total effects results in the more focused main effect of a feature. This main effect is often more interpretable than the total effect, as it is not influenced by interaction effects and thus shows less vertical dispersion. In the plots below, we present the main effect and the two most important interaction effects (which are our two examples from the last section, Country_Lang and Age) for the categorical feature with the most vertical dispersion, HomeOwnershipType. For the interaction effects, the dots in the scatter plots are colored by the value of the interacting variable. Here, red indicates a higher and blue indicates a lower value. The coloring is illustrated with the color bars on the right. Compared to the total SHAP value (see Appendix F), the main effect for the homeownership type in Fig.8 shows less vertical dispersion. 517 1 3 Digital Finance (2024) 6:501–542 Looking at the interaction with the country (and language for Estonians), as seen in Fig.9, borrowers living with their parents or in furnished apartments are deemed Fig. 8 SHAP values for the main effect of HomeOwnershipType. The main effect is calculated by subtracting all interaction effects from the total effect (for HomeOwnershipType, see AppendixF) Fig. 9 SHAP values for the interaction effect of HomeOwnershipType and Country_Lang. The dots are colored by the value of Country_Lang (color bar on the right) (colour figure online) 518 Digital Finance (2024) 6:501–542 1 3 less risky in Finland and Spain, while the opposite is true for Estonians. The inverse relationship is found for the other categories, except for owners. Here, Spanish borrowers are deemed more risky, followed by Estonians and Finns. Figure10 shows the interaction with age. The risk decreases for older borrowers most notably in the categoriesMortgage and Owner, while increasing for LivingWithParents and TenantFurnished. In summary, these interaction effects reveal more interpretable feature contributions on credit risk for less clear effects such as HomeOwnershipType. These interaction effects are derived from the boosted model without any manual modeling. 5 Discussion The principal goal of this study was to evaluate the utility and performance of explainable ML survival analysis within the P2P lending sector, with a particular focus on its potential to improve risk assessment and risk indicator analysis compared to linear models. 5.1 Model performance Our results show that the ML model outperformed the linear model. This applies to both Harrell’s c-index and the more conservative IPCW c-index. While the differences appear slight for the c-indices, the following results on practical rating performance demonstrate that the boosted model performed significantly better Fig. 10 SHAP values for the interaction effect of HomeOwnershipType and Age. The dots are colored by the value of Age (color bar on the right) (colour figure online) 519 1 3 Digital Finance (2024) 6:501–542 at risk assessment. For an in-depth analysis of the c-index results, including their limited significance in practice and further robustness checks, see AppendixC. The boosted model achieved the best risk differentiation across the rating groups and vastly outperformed Bondora’s rating. The Kaplan–Meier survival estimates revealed that the boosted model was the only model with non-crossing survival curves ordered correctly by risk ranking (Fig.5). Here, it had the largest margins between groups, the smallest confidence bands and also the largest span between the highest and lowest risk groups, indicating a superior ability to discriminate loans by risk. When looking at the tabular results including defaultand IRR rate, compared to Bondora, the boosted model showed a more ordinal, even distribution and wider spread of the IRR between the rating groups from 15.63 to −40.69% for the boosted-, and 3.91 to −36.26% for Bondora’s ratings. Investing an equal amount in boosted “AA” rated loans would have outperformed the Bondora-rated “AA” loans by almost 19% p.a. (IRR of 15.63% compared to −3.20%). Moreover, the boosted “AA” rated loans were less risky, at a default rate of 14.45%, in contrast to 17.26% for the Bondora “AA” group. These results were especially striking when considering the risk-group sizes. The boosted model assigned more than four times as many loans as Bondora to the “AA” rating (713 vs 168). This favorable risk-return profile could be further enhanced by targeting mispriced loans (predicted low risk and high interest rates). Future research could investigate the model’s potential for identifying mispriced loans on the secondary market. On the opposite spectrum, ML survival analysis ratings could aid in the screening of high-risk borrowers, addressing a major challenge for P2P platforms. The boosted model rated almost twice as many borrowers as F, returning − 40.69% annually compared to Bondora’s F group at −36.26%. Screening out these highrisk borrowers would benefit investors, platforms and lower-risk borrowers alike, as argued in the theory section. In addition, boosted survival analysis can enable fairer interest rates on P2P platforms. Multiple crossing survival curves and poor predictiveness of time-to-default indicated that the Bondora ratings may not be well-calibrated. This could cause unfair interest rates, as detailed in Sect.2. If the interest rates on loans were fairly pricing risk, they should compensate for it. However, we found a different picture, e.g., the average interest rate of the boosted “AA” group (27.77%) was almost three times that of Bondora’s “AA”-group (9.52%), despite the boosted-“AA” group’s lower default rate. Moreover, we observed a low correlation between default risk and interest rates. The rating-performance differences may be attributed to the fact that Bondora’s ratings encode expected loss rather than expected time-to-default. However, expected loss is linked to expected time-to-default, as argued in the theory section (Sect.2). Furthermore, the boosted ratings outperformed Bondora’s ratings regardless of the used performance measures (i.e., c-index, differentiation based on Kaplan–Meier curves, mean IRR and mean default rate). Hence, the interest rates may be set inaccurately and borrowers should get quotes from multiple platforms to promote fairer pricing. While the boosted model outperformed the linear model, the linear model exhibited decent risk-rating performance, except for “C” having a significantly higher 520 Digital Finance (2024) 6:501–542 1 3 default rate (49.17%) than D (39.58%, AppendixD). We will address the model differences in the next section. In summary, the application of boosted survival analysis to rate loans originated in 2020, utilizing historical performance data available to an investor by the end of 2019, demonstrated effective results. Our findings suggest that, within our dataset, boosted ML survival analysis models emerged as a promising tool for improving credit risk assessment, supporting investors’ decision-making, advancing risk screening and promoting fairer interest rates. 5.2 Model explanations Another objective of this study was to investigate whether explainable ML survival analysis can be beneficial to risk indicator analysis in P2P lending. With SHAP explanation values, we explained and compared both linear and boosted Cox models using feature dependence plots (Sect.4.2). Overall, the boosted model extracted at least as much information from the data as the linear model. In our data, where the linear model identified significant effects, the boosted model consistently found similar effects (see AppendixF for a full display of all feature contributions). Unsurprisingly, these similar findings are mostly in line with prior research. To name a few: Borrowing risk reduced with age (e.g., Albert & Duffy, 2012; Kurnianingsih etal., 2015), male gender indicated higher risk (e.g., Lin et al., 2017), while having a mortgage reduced risk (e.g., Serrano-Cinca etal., 2015). Furthermore, the boosted model uncovered more detailed and new relationships between borrower information and default risk. For example, all grades of education were well differentiated by the boosted model, with higher education decreasing risk. This is in line with prior research (e.g., Chen etal., 2018; Lin etal., 2017). In contrast, the linear model only found a significant impact on risk for the highest educational level, and no significance for the intermediate levels. The same applied for homeownershiptype (Fig.12b), where the boosted model clearly distinguished LivingWithParents (higher risk), and Owner (lower risk) in addition to the categories identified significant by the linear model (Mortgage, lower risk and TenantFurnished, higher risk). While the higher risk for borrowers living with their parents makes intuitive sense (indicates lower assets), the lower risk for homeowners is supported by prior research (e.g., Serrano-Cinca etal., 2015). Furthermore, some variables impacted the boosted model where the linear model did not find significance at all. The relationship with DTI (Fig.13b) found by the boosted model is a known factor in risk prediction (Emekter etal., 2015; Serrano-Cinca etal., 2015) and was not identified by the linear model. In addition to the more detailed linear effects, the boosted model found both known and novel non-linear and interaction effects exploratively. For example, credit risk decreased sharply for younger borrowers with age, flattening out until the age of 55 years and then increasing slightly again. As mentioned, research confirms this general trend of the models, as risk aversion increases with higher age (e.g., 521 1 3 Digital Finance (2024) 6:501–542 Albert & Duffy, 2012; Kurnianingsih etal., 2015). Additionally, evidence points towards a nonlinear and domain-specific relationship between risk-taking and age, with increased risk-taking in early adulthood (e.g., Rolison etal., 2014; Willoughby etal., 2021), which was also picked up by the boosted model. On top, the newly quantified risk increase for borrowers at 55years may be explained by lower income due to retirement, increased medical costs and reduced life expectancy. Analyzing interaction effects also unveiled novel risk indicators and helped us dissect the vertical dispersion of primary effects. For HomeOwnershipType, we found that tenants living with their parents or in a furnished apartment were deemed less risky when younger (Fig.10), which intuitively makes sense. The interaction with the country (Fig.9) indicates that the model may be able to account for systemic and cultural differences. To the best of our knowledge, these particular interaction effects have not been identified exploratively in prior research. Especially in the European market, analyzing cultural and systemic differences (e.g., due to different retirement systems) might be valuable for credit risk assessment. Finally, one advantage of the classical model is that it can test for statistical significance. However, in the cases where the ML-SHAP values were less dense, the linear models often found the feature value to be less or even insignificant (white coloring). This indicates that SHAP feature importances (average absolute SHAP values) may be consistent with statistical significance, which was also found by Bussmann etal. (2021). Overall, the boosted model not only found the same significant risk factors as the linear model but also found more detailed and even new relationships between risk factors and default risk. This included nonlinear and interaction effects that are not quantifiable in linear models in the same explorative way.16 This is in line with prior research on this methodology in oncology (Moncada-Torres etal., 2021), supporting the argument that explainable machine learning survival analysis can reveal known and potentially novel risk factors in risk research. 5.3 Limitations andimplications Further research is required to test these methods more widely. While we were able to achieve exceptional results on the Bondora dataset, future studies should test the reliability of the models by applying them to different datasets and split dates. For the latter, we suggest a rolling window approach, as this would allow the adaptability and validity of the models to be tested. Here, the US Lending Club dataset could be suitable. The lending club dataset is widely used in prior research and has a much larger number of completed loans ranging over a longer period. The Bondora dataset did not allow for this at the time of writing due to the limited available observation period combined with the need for completed loans to calculate the IRR. However, it can be revisited in the future, as the dataset grows and more loans are completed. For our purposes, to assess risk rating ability and risk-factor analysis the dataset we 16 While interaction effects can be quantified in linear Cox regression, they need to be carefully modeled by hand based on domain knowledge and prior research. This can be very resource-consuming, especially with many features. 522 Digital Finance (2024) 6:501–542 1 3 used is well-suited. Especially for the latter, as seen in the explanations, the dataset provided valuable hypotheses into cultural differences important for risk assessment in the European P2P market (this insight would not be possible on the US Lending Club dataset). Furthermore, the good performance of the ML models on the test set despite the changed risk profile (changes in rating distribution in Fig.2) indicated that the models are likely robust and can be used for future loans. As discussed in more detail in Appendix C, we also applied random sampling and rated 5-year loans, which resulted in even higher performance for the ML models and qualitatively similar results for the SHAP values. Additionally, simply removing borrowers with missing and sparse values from the dataset can introduce bias to the model. This is especially problematic if the missingness is systematic and should be investigated to avoid bias against demographics (e.g., in our case, the excluded homeless and Slovakian borrower). While our decision to compare the models lead to following the more restricted preprocessing steps of the linear model, the boosted model can be trained (and predict) on incomplete and sparse datasets in future use. Furthermore, not all of the explained relationships, as shown in AppendixF, were straightforward. Some required further investigation (e.g., using interaction effects), and some contradicted intuition. For example, we found a risk decrease with larger liabilities and an increase with larger income. We suspect that this is caused by collinearities, e.g., with DTI.17 This indicates that explainable ML findings need to be validated, as Shapley values explain the model, and not the data directly. If the model finds complex mathematical relationships that obscure the true underlying risk factors, explanations may be incapable of identifying meaningful risk indicators that are intuitive, straightforward, and supported by theory. Developing a model with useful explanations may require some trial and error—especially through regularization and adequate data prepossessing, including feature selection and modeling of variables likely relevant in reality. Nevertheless, spurious relations are not only found in ML models but also in linear models. To overcome this issue, a hypothesis-based approach is commonly used with linear models. For explainable ML methods matching quantitative with qualitative theory is equally important, although its explorative approach allows deriving hypotheses directly, which should be verified with existing theory. 6 Conclusion In this study, we used classical and ML survival analysis to predict defaultriskin P2P lending using a European dataset with over 350,000 loans. We compared the performance of the models in rank correlation, classification, and credit risk rating. We then opened the ML models’ black box using SHAP to explain the performance differences and identify credit risk indicators. 17 While liabilities do not contain the applied amount, the DTI ratio does. At a fixed DTI ratio, larger liabilities may indicate a lower relative loan amount to a borrower’s financial situation. Additionally, DTI may typically decrease with higher incomes, and thus, high DTI at larger incomes may indicate higher risk. 523 1 3 Digital Finance (2024) 6:501–542 Our results demonstrated that ML survival analysis performs exceptionally well in credit scoring, significantly outperforming the platform’s risk ratings. For investors, our ratings revealed a profit opportunity through targeting high-interest loans with low estimated risk. On the platform side, more accurate risk assessments could promote fairer pricing and improve the screening process, ultimately reducing overall risk and increasing portfolio performance. Using SHAP, we were able to explain the models decision making and discover both novel and known credit risk factors. This yielded compelling and intuitive hypotheses, establishing promising avenues for future research. Altogether, the methodology’s exceptional performance results, combined with its meaningful explanations, confirmed its ability to improve credit-risk ratings through more accurate while transparent credit risk assessments. With analogous findings in oncology that validate explainable ML survival analysis’ ability to generate knowledge, we are confident that this approach can further the understanding of time-to-event data across various domains. This methodology could spark a new wave of survival analysis research, including the reexamination of studies previously conducted with linear survival analysis methods. Appendices A Bondora dataset feature descriptions The following table shows an excerpt of the features presented in the loan dataset, grouped by categories. The features were selected based on public availability and relevance for the analysis. Bondora excluded 16 features due to data protection regulations starting on June 1, 2017. The excluded features include information about family status, employment, loan usage, and financial details like sources of income, free cash, and debt-to-income (DTI) ratio (Table2). B Detailed explanation ofthemethodology This appendix explains the survival analysis models used in this study in more detail and demonstrates how classical models can be generalized to allow for more complex models using Machine Learning (ML). Finally, we introduce the methods used to evaluate and explain the models. B.1 Survival analysis Statistical survival analysis investigates the timing of an event of interest. This event can be anything that occurs over time, like death, failure of a machine, or credit default. 524 Digital Finance (2024) 6:501–542 1 3 Table 2 Data features of the Bondora loan dataset Group Name Description Application and contract details AppliedAmount The amount borrower applied for originally ContractEndDate The date when the loan contract ended FirstPaymentDate First payment date according to initial loan schedule LoanDate Date when the loan was issued Bondora rating details ExpectedLoss Expected Loss calculated by the current Rating model ExpectedReturn Expected Return calculated by the current Rating model HomeOwnershipType 0 Homeless 1 Owner 2 Living with parents 3 Tenant, pre-furnished property 4 Tenant, unfurnished property 5 Council house 6 Joint tenant 7 Joint ownership 8 Mortgage 9 Owner with encumbrance 10 Other LossGivenDefault Gives the percentage of outstanding exposure at the time of default that an investor is likely to lose if a loan actually defaults. This means the proportion of funds lost for the investor after all expected recovery and accounting for the time value ... ProbabilityOfDefault Probability of Default refers to a loan’s probability of default within a one-year horizon. Rating Bondora Rating issued by the Rating model Borrower demographics Age The age of the borrower when signing the loan application Country Residency of the borrower Education 1 Primary education 2 Basic education 3 Vocational education 4 Secondary education 5 Higher education EmploymentStatus 1 Unemployed 2 Partially employed 3 Fully employed 4 Self-employed 5 Entrepreneur 6 Retiree Gender 0 Male 1 Woman 2 Undefined LanguageCode 1 Estonian 2 English 3 Russian 4 Finnish 5 German 6 Spanish 9 Slovakian NewBondoraCustomer (renamed from NewCreditCustomer) Did the customer have a prior credit history in Bondora 0 Customer had at least 3 months of credit history in Bondora 1 No prior credit history in Bondora VerificationType Method used for loan application data verification 0 Not set 1 Income unverified 2 Income unverified, cross-referenced by phone 3 Income verified 4 Income and expenses verified Credit and borrowing history AmountOfPreviousLoansBeforeLoan Value of previous loans NoOfPreviousLoansBeforeLoan Number of previous loans 531 1 3 Digital Finance (2024) 6:501–542 between the predicted and the actual value. This way, each tree tries to correct the error of the previous trees. The trees can then be combined using simple (weighted) addition. The XGBoost package used in this study is an implementation of a boosted regression tree. XGBoost uses ML principles like regularization to prevent overfitting, and achieves breakthrough performance in speed and memory usage using (“extreme”) optimization methods (Chen & Guestrin, 2016). B.5 Model explanation using SHAP Even though ML methods are powerful tools for prediction, they are often considered black boxes (Van Liebergen, 2017). For example, the resulting XGBoost models used in this analysis consist of up to 2594 trees with a maximum depth of up to 10 node layers. With over a million nodes (2594 ∗29), it is difficult to gauge how the model makes its predictions from the model parameters. Instead, we can explain the model by looking at the feature contributions to the model output. That is the difference in the prediction of the model with and without that feature. This is quite simple in the linear case. For example, the feature contributions of a feature xj in the model f(x)=𝛽0+𝛽1x1+ ⋯ +𝛽pxp is simply the product of its coefficient 𝛽j and its value xj, minus the expected value of this product: For more complex ML models like gradient boosting, this is not as straightforward. In our example, the effect of income on the time to default could be dependent on other variables, like the country of the borrower. These interaction effects are often present in ML models, where the impact of a feature on model output may depend on the values of other features. So how can we consider these interaction effects when estimating the contribution of each feature to the model output? One solution to this problem stems from cooperative game theory. Shapley values (Shapley, 1952) are a unique solution to the problem of fairly distributing the gain (e.g., pay-off) of a cooperative game among its players. In a cooperative game, the interactions between the players are important. One player who works well in a team may improve the productivity of the whole team more than a player who struggles working in a team. Shapley’s values take these effects into account by comparing the achievements of the whole team with and without each player. Every player is then assigned a Shapley value that represents their marginal contribution to the outcome (e.g., the estimated additional pay-off that the team achieved with, compared to without the player). Thus, adding up all Shapley values yields the total gain of the game. We can use this solution for our problem of explaining ML predictions by distributing the prediction contributions (pay-off) optimally among the features (players). See (Lundberg etal., 2019) for details on this estimation in the XGBoost case. Shapley Additive Explanations (SHAP) can estimate pair-wise feature contributions as well, yielding the interaction effects of any feature pair. By removing these interaction values from the SHAP value of a feature, we can isolate (7) 𝜙j(x)=𝛽jxj−E(𝛽jxj). 532 Digital Finance (2024) 6:501–542 1 3 the main effect. The main effect is often easier to interpret, while the interaction effects can help understand how a feature interacts with other features in a model. We will use this approach for two features in the results section. To explain the overall decision-making of a model and not just single predictions, we can calculate the SHAP values of a large sample and analyze the global relationship of feature values and model output (Lundberg etal., 2020). In our study, we use SHAP dependence plots to visualize our models. While other methods (e.g., LIME, Ribeiro etal., 2016) can also be used to explain ML models, SHAP has several properties desirable for this analysis: Most importantly, the SHAP framework is model agnostic. This means that it can be applied to explain and compare the predictions of any model, independent of the model’s inner workings. Additionally, it is the only method that can satisfy three desirable explanation attributes: local accuracy (single explanations capture the difference between expected model output and the prediction), missingness (missing features get an attribution of zero), and consistency (if a changed model increases the impact of a feature, its SHAP value will not decrease). Providing this unique solution to these criteria, Lundberg and Lee’s SHAP framework unified six popular additive model explanation methods, including LIME, at the time of its publication. Furthermore, SHAP is well-optimized for some ML models. The XGBoost implementation uses graphical processing units to estimate SHAP values (Lundberg etal., 2019). This provides a significant speedup compared to other methods and makes it feasible to calculate SHAP values for large datasets (Lundberg etal., 2020) like the Bondora dataset used in this study. C Model performance: c‑index This appendix takes a closer look at the performance of the models using the concordance index (c-index). We begin by discussing its calculation and meaning. Harrell’s c-index (Harrell et al., 1982) measures the rank correlation between predicted risk scores and the actual survival times. It is defined as the ratio of concordant pairs to comparable pairs. Two observations are comparable when we can determine whether one of the observations has a shorter survival time than the other. A pair of comparable observations is concordant when the observation with the shorter survival time also has a higher predicted risk score. In other words, the c-index is the probability that the model correctly predicts the survival order of two randomly chosen loans. A c-index of 0.5 would indicate model randomness, while a c-index of 1.0 would indicate perfectly right and a c-index of 0.0 perfectly wrong predictions. While the c-index is a popular metric for evaluating survival models, it has some limitations. With larger numbers of censored observations, the c-index becomes too optimistic (Uno etal., 2011). To account for this issue, Uno etal. (2011) propose the Inverse Probability of Censoring Weighting (IPCW) c-index that takes the censoring distribution of the data into account. As we have active, censored loans in our dataset, we additionally use this estimator to evaluate the models. 533 1 3 Digital Finance (2024) 6:501–542 Figure11 presents Harrell’s c-index and the more conservative censoring independent IPCW c-index for all models. The results indicate that the boosted models perform better than the linear models. In addition, the inclusion of the Bondora rating only slightly improves performance. This suggests that the ratings do not encode much additional information useful to the models. Furthermore, the IPCW c-index is slightly lower than the regular c-index for all models. This is expected, as the IPCW c-index is a more conservative measure when a large number of subjects is censored. In general, it is worth noting that although the c-index for all models is significantly higher than 0.5 (i.e. not random), it is still relatively low (<0.7). The reasons for this are twofold. First, while sampling the test after the training data provides a more realistic setting, the portfolios strongly fluctuating risk profile and an overall shift toward less risky loans may be challenging to account for the models. As a robustness check, we reran the models with random sampling, 5-year loans and monthly time periods, which resulted in a c-index above 0.75. Second, by definition, the c-index is highly sensitive to slight differences in survival time. While in practice, a difference in loan survival time of one day likely does not matter, it can lower the c-index if the loan risks are not ranked in the same order. This again illustrates that the importance of these indicators should not be overstated. In our case, the metrics in the main analysis (Sect.4.1) are likely to be more relevant to stakeholders. As a further robustness check, we tested the performance of ML AFT models instead of Cox models. Notably, both performed very similarly. However, we did observe that the AFT model was more difficult to tune as two additional parameters regarding the survival distribution needed to be set. This slowed optimization convergence significantly. The similar performance supports the idea that the models Fig. 11 Harrell’s c-index (left) and the IPCW c-index (right) of the models. “Lin_” prefixes linear models, while “Bst_” prefixes the boosted models. Additionally, a “1” denotes models that do not use the Bondora rating variables for their prediction (which is true for all models discussed in the main text). A “2” denotes models that also use the Bondora rating. We use the python package lifelines (DavidsonPilon, 2023) to estimate the c-indices 534 Digital Finance (2024) 6:501–542 1 3 are similarly restricted because they cannot model time-varying effects. As the proportional hazards assumption of the Cox model may be violated, further research could investigate whether less restrictive models could perform better in this context. For example, instead of setting the survival time of early repayment to the loan duration, repayments could be predicted and modeled as a competing risk. Other classical models that performed well on loan data (Dirick etal., 2017) could be implemented and tested as ML models, and advanced ML-models like boosted survival trees (Bai etal., 2022) may yield improved results. Overall, the performance results support the findings of prior literature that ML models can perform at least as well as linear survival analysis models (MoncadaTorres etal., 2021) while showing good results when used as classification models (Bai etal., 2022). D Model performance: linear rating model See Table3. E Coefficients ofthelinear Cox models The following table presents the results of the linear Cox model. Stars indicate the statistical significance of the coefficients. The table shows the coefficients of the two linear models (with and without Bondora ratings) and the standard errors in parentheses (Table4). Table 3 Mean values grouped by linear Cox ratings The table includes the number of loans, the mean amount, interest rate, default rates and IRR for each group. Loan status for the default rate and IRR is based on the approach of Dömötör etal. (2023). The HR thresholds are shown in parentheses Rating Count Amount Interest (%) Defaults (%) IRR (%) AA: (−inf, 0.55] 858 2005.78 28.20 15.85 13.23 A: (0.55, 0.65] 906 2364.26 28.77 24.72 10.55 B: (0.65, 0.75] 1020 2589.93 28.90 34.51 6.45 C: (0.75, 0.97] 907 2518.62 30.73 49.17 −0.69 D: (0.97, 1.51] 768 2848.00 37.55 39.58 −3.25 E: (1.51, 2.1] 1412 2961.59 39.38 57.01 −18.95 F: (2.1, inf] 331 2791.44 50.01 77.64 −47.04 535 1 3 Digital Finance (2024) 6:501–542 Table 4 Cox proportional hazard model coefficients Parameters Cox_1 Cox_2 IncomeTotal −0.0 (0.0) −0.0 (0.0) DebtToIncomeModeled 0.0 (0.0005) 0.0 (0.0) LiabilitiesTotal 0.0 (0.0) −0.0 (0.0) ExistingLiabilities 0.0106* (0.0033) −0.0 (0.0) AppliedAmount 0.0*** (0.0) 0.0 (0.0) AmountOfPreviousLoansBeforeLoan 0.0 (0.0) −0.0 (0.0) PreviousRepaymentsBeforeLoan 0.0* (0.0) 0.0 (0.0) RepaymentRatio −0.7338*** (0.0533) −0.5419*** (0.0395) PreviousEarlyRepaymentsBefoleLoan 0.0* (0.0) 0.0 (0.0) NoOfPreviousLoansBeforeLoan −0.0353*** (0.0075) −0.0285*** (0.0058) PreviousEarlyRepaymentsCountBeforeLoan −0.1977*** (0.0403) −0.06* (0.0262) Country_Lang_EE_Ru 0.1866*** (0.0332) 0.0696* (0.0343) Country_Lang_ES 0.9406*** (0.0416) 1.1699*** (0.0276) Age −0.0007 (0.0009) −0.002* (0.0009) Country_Lang_FI 0.7053*** (0.0331) 0.888*** (0.0269) Gender_male 0.1497*** (0.0252) 0.0757* (0.0243) Gender_undefined 0.1895*** (0.0424) 0.0938* (0.0425) Education_Basic 0.0205 (0.0497) 0.0478 (0.0434) Education_Vocational −0.1239** (0.0343) −0.0 (0.0) Education_Secondary −0.0875* (0.0318) −0.0 (0.0) Education_Higher −0.3069*** (0.0328) −0.2082*** (0.0207) EmploymentDurationCurrentEmployer_Retiree 0.1291* (0.0543) 0.0157 (0.0424) EmploymentDurationCurrentEmployer_TrialPeriod 0.0355 (0.1262) 0.0 (0.0003) EmploymentDurationCurrentEmployer_UpTo1Year 0.0171 (0.0457) 0.0 (0.0001) EmploymentDurationCurrentEmployer_UpTo2Years 0.0161 (0.0586) −0.0 (0.0001) EmploymentDurationCurrentEmployer_UpTo3Years 0.0116 (0.062) −0.0 (0.0001) EmploymentDurationCurrentEmployer_UpTo4Years −0.0346 (0.0716) −0.0 (0.0002) EmploymentDurationCurrentEmployer_UpTo5Years 0.0293 (0.0447) 0.0 (0.0001) EmploymentDurationCurrentEmployer_ MoreThan5Years −0.0484 (0.0431) −0.0624* (0.0204) HomeOwnershipType_LivingWithParents −0.014 (0.0409) 0.0 (0.0001) HomeOwnershipType_Council house −0.1425 (0.1014) −0.0 (0.0003) HomeOwnershipType_TenantNotFurnished −0.0821 (0.0645) −0.0 (0.0002) HomeOwnershipType_TenantFurnished 0.0868* (0.0384) 0.1076*** (0.026) HomeOwnershipType_Joint tenant 0.0502 (0.0877) 0.0 (0.0003) HomeOwnershipType_Joint ownership 0.0673 (0.0684) 0.0 (0.0002) HomeOwnershipType_Mortgage −0.28*** (0.043) −0.1727*** (0.0319) HomeOwnershipType_Owner, encumbrance −0.476** (0.135) −0.2549* (0.115) HomeOwnershipType_Owner −0.1273** (0.0373) −0.0794* (0.0247) VerificationType_income 0.0376 (0.0454) −0.0204 (0.0404) VerificationType_income and expenses −0.0269 (0.0206) 0.0 (0.0) NewBondoraCustomer_True −0.0246 (0.0279) 0.076* (0.0268) NanRepaymentHistory_True −0.2317*** (0.0273) −0.1922*** (0.027) 536 Digital Finance (2024) 6:501–542 1 3 Table 4 (continued) Parameters Cox_1 Cox_2 NanEarlyRepayment_True −0.3377*** (0.028) −0.2455*** (0.0246) Interest 0.0021* (0.0007) ExpectedLoss 0.0211 (0.2302) ExpectedReturn −0.5082* (0.2032) ProbabilityOfDefault 1.2587*** (0.115) LossGivenDefault −0.3897*** (0.0475) Rating_A 0.0235 (0.0577) Rating_B −0.0065 (0.0478) Rating_C 0.0792 (0.0457) Rating_D 0.276*** (0.046) Rating_E 0.2142*** (0.0502) Rating_F 0.2208*** (0.0567) Rating_HR 0.0201 (0.0755) Observations 31517 31517 c_cph train 0.711838 0.701238 c_cph test 0.665275 0.659625 LR 5973.63661 4449.765007 LR_p 0.0 0.0 * p < 0.01; ** p < 0.001; *** p < 0.0001 Fig. 12 SHAP values—demographics 537 1 3 Digital Finance (2024) 6:501–542 F Dependence plots forall features In this appendix, the dependence plots for all features of the categories demographics, financials, and borrowing history are presented. Within categories, the plots are ordered by the magnitude of their mean absolute SHAP value (i.e., feature importance). Demographics Overall the Shapley values of the linear and boosted Cox model appear to be quite similar in magnitude and direction for the demographic feature contributions(Fig.12), except for centering differences (e.g., for country). Additionally, the boosted model shows vertical dispersion, the largest overall for the homeownership type indicating interaction effects. The faint visibility in some categories for the boosted model (e.g., TrailPeriod) is caused by the small count present in the training set. In these cases, the linear models found the feature to be less or even insignificant (blue coloring). The boosted model found a nonlinearity for the feature interaction with age. Financials For the financials, the differences between the linear and boosted models are more apparent. The boosted model found nonlinear relationships where the linear models found no significant relationship at all (Fig. 13a–c). Existing liabilities were found to decrease risk until 3–5 liabilities, and then increase risk slightly (Fig.13e). The verification type (Fig.13f) had a small impact on the risk, with a slight decrease for verified borrowers. Borrowing history Regarding the borrowing history, the models again find similar relationships (Fig.14a, d, f, g). However, again there are two features not found Fig. 13 SHAP values—financials 538 Digital Finance (2024) 6:501–542 1 3 very significant in the statistical model but quite important in the boosted model (Fig.14b and c). Author contributions The initial idea and concept of the study was developed by GBW under the guidance of FR. GBW conducted the initial literature research, analyzed the data, built the prediction and rating models, calculated the Shapley values, and prepared all figures using Python and CUDA. GBW wrote the first draft of the paper as part of a thesis, which FR supervised. Subsequently, FR contributed to the further development of the methodology, in particular regarding financial aspects, and the final draft. Both authors reviewed and approved the final manuscript. Funding Open Access funding enabled and organized by Projekt DEAL. Data availability All datasets used in this study were obtained from publicly available data sources (see references in Section3). Fig. 14 SHAP values—borrowing history 539 1 3 Digital Finance (2024) 6:501–542 Declarations Conflict of interest The authors declare no competing interests. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 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