A Novel Default Risk Prediction and Feature Importance Analysis Technique for Marketplace Lending using Machine Learning

Imam, Sana Hassan; Huhn, Sebastian; Hornuf, Lars; Drechsler, Rolf Article A Novel Default Risk Prediction and Feature Importance Analysis Technique for Marketplace Lending using Machine Learning Credit and Capital Markets – Kredit und Kapital Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Imam, Sana Hassan; Huhn, Sebastian; Hornuf, Lars; Drechsler, Rolf (2023) : A Novel Default Risk Prediction and Feature Importance Analysis Technique for Marketplace Lending using Machine Learning, Credit and Capital Markets – Kredit und Kapital, ISSN 2199-1235, Duncker & Humblot, Berlin, Vol. 56, Iss. 1, pp. 27-62, https://doi.org/10.3790/ccm.56.1.27 This Version is available at: https://hdl.handle.net/10419/298830 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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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. https://creativecommons.org/licenses/by/4.0/ Credit and Capital Markets 1 / 2023 A Novel Default Risk Prediction and Feature Importance Analysis Technique for Marketplace Lending using Machine Learning Sana Hassan Imam*, Sebastian Huhn**, Lars Hornuf*** and Rolf Drechsler**** Abstract Marketplace lending has fundamentally changed the relationship between borrowers and lenders in financial markets. As with many other financial products that have emerged in recent years, internet-based investors may be inexperienced in marketplace lending, highlighting the importance of forecasting default rates and evaluating default features such as the loan amount, interest rates, and FICO score. Potential borrowers on marketplace lending platforms may already have been rejected by banks as too risky to lend to, which amplifies the problem of asymmetric information. This paper proposes a holistic data processing flow for the loan status classification of marketplace lending multivariate time series data by using the Bidirectional Long Short-Term Memory model (BiLSTM) to predict “non-default,” “distressed,” and “default” loan status, which outperforms conventional techniques. We adopt the SHapely Additive exPlanations (SHAP) and a four-step ahead model, allowing us to extract the most significant features for default risk assessment. Using our approach, lenders and regulators can identify the most relevant features to enhance the default risk assessment method over time in addition to early risk prediction. Keywords: Default loan prediction, marketplace lending, time series classification, LSTM/ BiLSTM; feature importance, SHAP JEL classifications: D81, G32 * Sana Hassan Imam, Department of Informatics, University of Bremen,sanahassan@ uni-bremen.de. ** Sebastian Huhn, University of Bremen/DFKI GmbH, 28359 Bremen, Germany, h[email protected]. *** Lars Hornuf, Faculty of Business and Economics, Technische Universität Dresden, 01069 Dresden, Germany.[email protected]. **** Rolf Drechsler, University of Bremen/DFKI GmbH, 28359 Bremen, Germany, [email protected]. Acknowledgements: This research has been supported by the AI initiative of the Free Hanseatic City of Bremen and the Data Science Centre of the University of Bremen (DSC@UB). The authors thank Charlie Cai from the University of Liverpool, Nick Guest Credit and Capital Markets, Volume 56, Issue 1, pp. 27 – 62 Scientific Papers OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 28 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 I. Introduction As part of the platform revolution (Parker etal. 2016), marketplace lending has fundamentally changed the relationship between lenders and borrowers in capital markets. Marketplace lending1 enables borrowers who have been rejected by a bank to obtain funding from a large and diverse crowd of lenders over the internet. In addition, retail investors are now able to become lenders and diversify their portfolios with private and company loans, an activity that has previously been exclusive to banks (Dorfleitner/Hornuf et al. 2022). Marketplace lending has nevertheless come with its share of disadvantages since many lenders are less sophisticated than traditional banks when it comes to lending. Lenders on marketplace lending platforms often rely on easy-to-understand risk ratings rather than more sophisticated financial information (Cumming/Hornuf 2022). If there are different types of borrowers in the crowdlending market– for example good borrowers who have a high probability of repaying their loans and bad borrowers who have a low probability of repaying their loans– and lenders cannot distinguish between the two based upon the information that is provided on the platform, good borrowers will have to pay unreasonably high interest rates for their loans. According to Akerlof (1970) and Stiglitz/Weiss (1981), this is because lenders would not be able to charge interest rates commensurate with the quality of borrowers because they cannot distinguish between them. Moreover, lenders would be cautious about lending money to anyone, even good borrowers, because of the risk of bad borrowers defaulting. This would lead to a reduction in the supply of loans, making it difficult for good borrowers to obtain credit and potentially causing market failure. The presence of bad borrowers, or “lemons,” reduces the overall volume of the loan market and creates inefficiencies. This type of asymmetric information is at the expense not only of lenders but also of marketplace lending portals, which must simultaneously maximize the deal flows of both borrowers and lenders to run a successful business (Rochet/Tirole 2003). If too many marketplace loans default, the portal will ultimately collapse, similar to what recently happened with the platforms Envestio, Grupeer, and Kuetzal2. from Cornell University, Yu Li from the University of Minnesota, the anonymous referees at the 3rd Frontiers of Factor Investing Conference and 13th CEQURA Conference on Advances in Financial and Insurance Risk Management, and the anonymousrefereeat Credit and Capital Markets for their helpful comments and suggestions. 1 Because recently it is not only peers lending money to peers (peer-to-peer lending), but also institutional investors buying loans up on online marketplaces, we refer to the activity under investigation as marketplace lending (see, for example, Mohammadi/Shafi (2017) and Cumming/Hornuf (2022)). 2 We refer interested readers to the following website for scams in marketplace lending: https://rethink-p2p.de/envestio-scam/. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 29 Credit and Capital Markets 1 / 2023 Rapid changes in the world economy due to, for example, global pandemics or armed conflicts might quickly put pressure on borrowers and lenders alike (Wang/Ni 2020). As a result of the COVID-19 pandemic and the conflict in Ukraine, the global economy has suffered severe shocks. These crises and rising interest rates are likely to result in riskier and ultimately non-performing loans. Risky and distressed loans are a common feature of many financial crises. Highrisk loans are problematic because they impair bank balance sheets, depress credit growth, and delay economic recovery (Ari et al. 2020). If marketplace lending continues to grow at a rapid rate, particularly servicing high-risk loans, this segment of the credit market could become a systematic risk (Käfer 2018), for example when higher central bank interest rates increase moral hazard and default rates in the credit market (Diamond 1984). In order to foresee systematic risks in financial markets, it is important to predict not only loans in default but also those that are currently under stress. Timely detection and resolution of risky loans is difficult but essential for economic recovery and for avoiding financial crises (Ari etal. 2020). Moreover, marketplace lenders might place their capital at undue risk if lending dynamics are poorly understood and loans consequently mispriced. Distinguishing risky loans from defaulting loans and identifying the features affecting loan status can be meaningful from the lenders’ and regulator’s perspective alike (Duan 2019). Consequently, it is important to investigate the features that are most relevant in the prediction of loan default and their contribution to assessing it. Given that the existing assessments for marketplace loan defaults are inadequate and subject to unknown factors (Xu etal. 2021), the actual contribution of different features towards the assessment of loan default prediction is essential. Several studies have evaluated classification methods for loan default prediction. Xu etal. (2021) compare different classification methods such as random forests (RF), extreme gradient boosting trees, gradient boosting models, and neural networks, and conclude that RF is superior to other classification methods. However, neural networks constitute a competitive candidate. Zhu et al. (2019) evaluate classification methods such as RF, support vector machines, decision trees, neural networks, and logistic regressions (LR) for marketplace lending loan default prediction and conclude that RF performs best. Li/Chen (2020), Kumar etal. (2016), and Song etal. (2020) test different ensemble classification methods for loan default prediction and their findings reveal that the performance of ensemble learning is better than that of individual learning. All these studies investigate which classification method has the highest accuracy but do not focus on the most essential features ensuring the highest accuracy. Previous studies are limited to the classification of only two loan statuses; i. e., “non-default” and “default” and do not consider that “distressed” might serve as an early-warning indicator for systematic stress in the financial system. By stressing OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 30 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 the features and prediction of the “distressed” loan status, our work provides a new perspective and fills this research gap. To overcome the limitations of specialist knowledge, recent interest in machine learning (ML) for determining the driving factors of repayment failure has risen in the field of marketplace lending. ML techniques improve the veracity and efficiency of decision-making concerning borrower screening by platforms and risk supervision by regulators (Xu etal. 2021). Increasingly sophisticated ML methods have helped policymakers to analyze a large amount of data promptly (Xu et al. 2021). Machine learning-based classifiers, especially deep neural network-based classifiers, have outperformed the various traditional classifiers in recent research works in the domain of loan default prediction, for example, by Duan (2019) and Lee etal. (2021). These papers compare the predictive accuracy of different methods by using a certain set of features but fail to determine the best extensible features, that is, features which continue to be relevant over time, and their contribution to accurate prediction and their relevance with time. Our work examines the relevant features, ranked based on their value for predicting and lasting significance. Xu et al. (2021) emphasize feature importance and contribution. However, their study considers only a specific data set from China and is limited to a specific kind of data having the feature of borrower video verification provided by the platform. Our approach is novel in terms of identifying the importance of the extensible features and addressing the distressed status prediction. The combination of these two techniques has never been used before. To address the problem of feature importance along with time dependency, BiLSTM-based multivariate time series (MTS) classification has been applied in this work. The multivariate data set is converted into MTS to assess the extensibility of the features concerning time. To the best of our knowledge, this idea is novel, and the LSTM/BiLSTM model is implemented for the very first time in marketplace lending loan default classification. A SHapely Additive exPlanations (SHAP) model for deep neural networks (DNNs) is implemented in this article for the first time to extract the importance and extensibility of the features from this marketplace lending MTS data set. Wang/Ni (2020) address the sequential marketplace loan data as univariate and MTS, and find LSTM to be the most promising candidate for the default rate aggregation problem for marketplace lending sequential data, but only for the prediction of default rate as an aggregation problem. Similarly, Liang/Cai (2020) applies the LSTM/Gated Recurrent Unit network-based model for the loan default rate prediction for the marketplace lending sequential data. Wang/Ni (2020) and Liang/Cai (2020) conclude that LSTM is one of the most promising candidates for loan default prediction. Both of these papers performed the “default rate prediction” as an aggregated monthly rate. To the best of our knowledge, this is the first loan default prediction for individual loan classification using LSTM and BiLSTM models, OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 31 Credit and Capital Markets 1 / 2023 while the SHAP model for DNNs is used for the first time for feature ranking of the MTS marketplace lending data set. The remainder of this article is structured as follows: in Section II, we describe marketplace lending in general and the LendingClub platform in particular. In Section III, we provide a review of the literature. Then, we describe the model in Section IV, and Section V outlines the empirical results and presents robustness checks. Section VI concludes. II. Institutional Background This section presents an overview of the marketplace lending process on LendingClub. Marketplace lending has become an established form of lending to individuals or companies without the direct involvement of a commercial bank. Marketplace lending utilizes online platforms that match potential borrowers with lenders. Due to lower intermediation costs as a result of digitalization and the use of big data analytics, the platforms promise lower interest rates for borrowers and higher returns for lenders compared to commercial banks3. The lending process begins when potential borrowers submit their loan application on the marketplace lending platform, which acts exclusively as an intermediary between the potential borrower and the lender but does not extend the loan as such. The platform determines the loan interest according to the creditworthiness of the potential borrower and the loan amount. The platform usually classifies the loan based on a risk assessment into seven classes ranging from A to G (Zhu etal. 2019). If enough lenders are willing to fund the loan, the online platform informs a partner bank, which then legally extends a loan that is immediately sold to lenders. The partner bank also wires the loan amount to the borrower’s account. The marketplace lending platform manages the process as an intermediary and collects its fees from both the lender and the borrower. The borrower repays the loan to the marketplace lending platform, which subsequently returns it to the lenders. Figure 1 provides an overview of how the marketplace lending process works. Until recently, LendingClub was one of the largest marketplace lending platforms in the world. The platform is representative of the marketplace lending business model worldwide and has provided loan data to researchers4 that has been used in previous empirical studies (e. g., Tang 2019). LendingClub was founded in 2006 and brokered loans over the internet, allowing borrowers to obtain unsecured personal loans ranging from USD1,000 to USD40,000. The 3 We refer interested readers to the following website for details: https://bit.ly/3TG wzTM. 4 We refer interested readers to the following website for LendingClub details: https:// bit.ly/3cNa4M8. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 32 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 usual loan period in our sample was three years. Lenders could browse the loan listings on the LendingClub website and select loans to invest in based on the information provided about the borrower, loan size, loan quality, and loan purpose. After investing, lenders earned an annuity payment from the interest on these loans. LendingClub made money by charging borrowers an origination fee and investors a service fee. Over time, LendingClub experienced increasing difficulty in attracting lenders, in 2020, acquired Radius Bank, and finally announced that it will ultimately shut down its marketplace lending platform. However, to the best of our knowledge, LendingClub continues to operate the marketplace model alongside an underwriting business. According to LendingClub, the marketplace model primarily helps to gain size in a bull market, while the underwriting business serves as a hedge in a bear market5. III. Literature Review 1. Machine Learning This section presents an overview of the ML techniques implemented in this article: recurrent neural networks, LSTM, BiLSTM, SHAP, and principal component analysis. 5 See for example: bit.ly/3KqWBZ9. /ŶŝƚŝĂůĂƉƉůŝĐĂƚŝŽŶĂŶĚĨƵŶĚŝŶŐ >ŽĂŶŶŽƚĞƚƌĂŶƐĨĞƌ ŽƌƌŽǁĞƌ >ĞŶĚŝŶŐWůĂƚĨŽƌŵ ;ĞŐ>ĞŶĚŝŶŐůƵďͿ >ĞŶĚĞƌ/ŶǀĞƐƚŽƌ WĂƌƚŶĞƌĂŶŬ;ĞŐ tĞďĂŶŬͿ >ŽĂŶŶŽƚĞƉƵƌĐŚĂƐŝŶŐ >ŽĂŶƌĞƉĂLJŵĞŶƚ >ŽĂŵŶŽƚĞ;ϱͿ /ƐƐƵĞƐƚŚĞĂĐƚƵĂů ůŽĂŶ;ϰͿ >ŽĂŶ ŶŽƚĞ;ϴͿ WƵƌĐŚĂƐĞƐƚŚĞůŽĂŶŶŽƚĞ using investor’s cash (7) /ŶĨŽƌŵƐƚŚŝƌĚͲ ƉĂƌƚLJďĂŶŬƚŚĂƚ ďŽƌƌŽǁĞƌŝƐ ǀĞƌŝĨŝĞĚ ŝŶǀĞƐƚŽƌƐŚĂǀĞ ĐŽŵŵŝƚƚĞĚ;ϯͿ ;ϭϬͿ ƉƉůŝĞƐĨŽƌĂ ůŽĂŶ;ϭͿ ŽŵŵŝƚƐƚŽĂ ďŽƌƌŽǁĞƌ;ϮͿ 'ŝǀĞƐĐĂƐŚƚŽƚŚĞ ƉůĂƚĨŽƌŵ;ϲͿ /ŶǀĞƐƚŽƌƌĞĐĞŝǀĞƐ ůŽĂŶŶŽƚĞ;ϵͿ ;ϭϭͿ Source: Bakker (2015). Figure 1: Marketplace Lending Process OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 33 Credit and Capital Markets 1 / 2023 a) Recurrent Neural Network The conventional feed-forward artificial neural network (ANN) comprises an input layer, an output layer, and several hidden layers. The input layer accepts the input, the hidden layers process it, and the output layer produces the results using an activation function (Abiodun et al., 2019). Typically, ANNs demonstrate only limited performance on sequential data such as time series because the connections within a network are set between layers only. The recurrent neural network (RNN) is an extension of the ANN with the ability to manage variable-length sequential input. In RNNs, the connection is between the layers and also with the neurons within the layers, which allows for remembering the past. The disadvantage of RNNs is the vanishing and exploding gradient problem. LSTM solves this problem by introducing another cell state along with input and output gates using an additional gate (the forget gate) (Sherstinsky 2020). b) Long Short-Term Memory Models LSTM-based models are an extension of RNNs, usually implemented for time series classification or regression problems. LSTM models are designed to preserve and learn the long-term dependencies of the inputs. Furthermore, they have the ability to remember the information over an extended period, with the ability to decide between preserving or ignoring the memory information. An LSTM model captures important input features and preserves this information over a long period of time. The decision of keeping or forgetting the information is based on the weights assigned during the training process and through the gates. An LSTM model typically consists of three gates: the forget, input, and output gates. The forget gate makes the decision of keeping or eliminating the existing information, the input gate specifies the duration for which the new information will be kept in the memory, and the output gate controls whether the preserved value in the cell contributes to the output. These models are able to address the vanishing gradient problem with the help of the forget gate. Figure 2 shows the LSTM structure unit. A drop layer follows the LSTM model to avoid the over-fitting problem, and a dense layer is followed by an output layer. The details are discussed in the subsection IV.7. Hyper-parameters Selection. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 34 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 The architecture of the LSTM can be represented by the following six formulas: ( ) 1 () gate t i t i t i Input i W X R h b σ - = ++ ( ) 1 () gate t f t f t f forget f W X R h b σ - = ++ ( ) ( ) 1state t c t c t c Cell C tanh W X R h b - = ++  ( ) ( ) 1gate t o t o t o Output O W X R h b σ - = ++ 1 ttt tt C fC iC - =+   () tt t h O tanh C= where σ represents the gate activation function, which is Sigmoid, tanh is a hyperbolic tangent function,  represents element-wise multiplication. Wi. Wf, Wc and Wo are input weight matrices. Ri, Rf, Rc and Ro are the recurrent weight matrices. Xt is the input, ht is the current block output and ht–1 is the previous block Śƚ y н σ ƚĂŶŚ ď ď ď н н н ƚͲϭ ŚƚͲϭ yƚ Śƚ ƚ ĞůůƐƚĂƚĞ ,ŝĚĚĞŶƐƚĂƚĞ /ŶƉƵƚ KƵƚƉƵƚ EĞdžƚĐĞůůƐƚĂƚĞ y y н ď ƚĂŶŚ σσ ƌŽƉ>ĂLJĞƌ /ŶƉƵƚ>ĂLJĞƌ ĞŶƐĞ>ĂLJĞƌ KƵƚƉƵƚ>ĂLJĞƌ EŽŶͲĞĨĂƵůƚ ŝƐƚƌĞƐƐĞĚ ĞĨĂƵůƚ >^dD>ĂLJĞƌ >^dDĐĞůů Figure 2: Structure of LSTM OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 41 Credit and Capital Markets 1 / 2023 busi ness,” “total received principal (€),” “outstanding principal by investor (€),” and “interest rate.” Table 1 provides detailed descriptions of each feature. Appendix Table A2 provides the descriptive statistics of the selected features. Table 1 Selected Features with Description Feature Name Description Type Loan amount (€) The listed amount of the loan applied by the borrower. If at some point in time, the credit department reduces the loan amount, then it will be reflected in this value. Numeric Installment (€) The monthly payment owed by the borrower if the loan originates. Numeric Grade LendingClub-assigned loan grade. Numeric Application type Indicates whether the loan is an individual application or a joint application with two co-borrowers. Nominal Funded amount (€) The total amount committed to that loan at that point in time. Numeric Open account Number of open credit lines in the borrower’s credit file. Numeric Total payment (€) Payments received to date for total amount funded. Numeric Total received interest (€) Interest received to date. Numeric Verification status Indicates if income was verified by LendingClub, notverified, or if the income source was verified. Nominal Term The number of payments on the loan. Values are in months and can be either 36 or 60. Nominal Fico range The boundary range the borrower’s FICO at loan origination belongs to. There are two ranges (High and Low) for upper and lower ranges. Nominal Annual income (€) The self-reported annual income provided by the borrower during registration. Numeric Employment length of borrower Employment length of the borrower in years. Possible values are between 0 and 10. Nominal Delinquency in 2years The number of 30+ days past-due incidences of delinquency in the borrower’s credit file for the past 2years. Nominal (continue next page) OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 42 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 Feature Name Description Type Home ownership The homeownership status provided by the borrower during registration or obtained from the credit report. The homeownership status can be rent, own, mortgage, and other. Nominal Purpose car or small business or renewable energy A category provided by the borrower for the loan request. Nominal Dti A ratio calculated using the borrower’s total monthly debt payments on the total debt obligations, excluding mortgage and the requested LC loan, divided by the borrower’s self-reported monthly income. Numeric Total received principal (€) Principal received to date. Numeric Outstanding principal by the investor (€) Remaining outstanding principal for a portion of the total amount funded by an investor. Numeric Interest rate Interest rate on the loan. Numeric Table 2 Loan Class Definition Class Name Loan Types Labels Non-default Fully Paid/ Non-Default/ Issued 0 Distressed In Grace Period/ Late (16–30 days)/ Late (31–120 days) 1 Default Default/ Charged Off 2 3. Time Series Analysis Time series is a sequence of observations based on discrete occurrences equally spaced in time. The issue date of the loan is used to determine the start date of the time series. During the time series data pre-processing, it is important to check the stationarity property of the time series. If the time series is non-stationary, it is required to first convert it into a stationary time series. For a stationary time series, the mean and variance must be constant with respect to time. For this, an ADF test is performed. (Table 1 continued) OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 43 Credit and Capital Markets 1 / 2023 Table 3 ADF Test for Stationarity Example Features ADF-statistics p-value Critical Values Conclusion 1 % 5 % 10 % Loan amount –6.842 <0.001 –3.679 –2.968 –2.623 Stationary Installment –3.241 0.002 –3.711 –2.981 –2.630 Stationary Grade –5.248 <0.001 –3.677 –2.962 –2.523 Stationary Open account –4.702 0.008 –3.711 –2.976 –2.633 Stationary Note: A p-value > 0.5 indicates that the test does not reject Ho, i. e. the series is non-stationary, while a p-value <0.5 indicates that the test accepts H1, i. e. the series is stationary. According to Yang/Shahabi (2005), if all the univariate time series in a multivariate time series item are stationary, then the MTS item is also stationary. The data set used in this article is also an MTS. The ADF test is applied for each individual univariate variable/feature of the time series. In our data set all the variables are stationary with respect to time. The mean and variance of these univariate variables are constant with respect to time. Some of the variables are presented in Table3 as examples. Trends and seasonality for each variable are also verified, and it is observed that no specific trend or seasonality associated with any of the selected feature variables exists. 4. Model Generation The following section illustrates the BiLSTM structure and discusses the LSTM and BiLSTM implementation, the hyper-parameters selection, tuning, and model performance evaluation. Appendix Figure A3 comprises a pseudo-code to explain the adopted algorithm with all the steps and details of implementations of the proposed procedure. In the first block train, test data splitting is applied. In the second block, LSTM/BiLSTM implementation with all hyper-parameter tuning is conducted. With class weight adjustment, cost-sensitive analysis is performed in order to mitigate the data imbalance problem. Feature importance is graphically visualized in the last block with the help of the SHAP library implementation. 5. Model Training and Summary When the data set is imbalanced, the classifier predicts the majority class primarily, and the predictive accuracy of the minority class declines (Ye etal. 2018). There are many methods for handling the problem of data imbalance, such as OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 44 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 under-sampling, over-sampling, and cost-sensitive analysis. Cost is a penalty associated with misclassification. Some research has noted that over-sampling and under-sampling possess significant drawbacks compared to cost-sensitive analysis (Xia etal. 2017). In this study, the number of non-defaulters (majority class) is significantly higher than the number of defaulters (minority class). A weighted cost matrix is introduced in the proposed model training phase to reduce the effect of the imbalanced data set on the loan default prediction. This matrix increases the cost of misclassifications associated with defaulters. Therefore, due to the high penalty for misclassification, the classifier strives to make correct predictions of defaulters (minority class) to minimize the cost, hence improving the predictive accuracy for the defaulters class (Ye etal. 2018). During the model’s training, two parameters are used for mitigating the effect of the imbalanced data set by introducing the penalty of misclassification: class weight and sample weight. The class weights are calculated based on the ratio of the majority class to the minority class. A ratio of 1 to 10 assigns a weight of 10 to the minority (ratio 1 class) and a weight of 1 to the majority class. During the training phase, these weights are multiplied with the loss function to impose a high penalty on the classifier for wrongly classifying a minority class. The aim of the classifier is to reduce the overall cost of misclassification. Similarly, the sample weights are used when weights are assigned for each sample of the whole data set based on the imbalanced data set. Each sample is element-wise multiplied with this corresponding sample weight matrix. The model summary for the training of the proposed model is described in Table 4. Table 4 Model Summary of LSTM/BiLSTM Layer type Output shape parameter# Input Layer (None, None, No. of features) 0 LSTM/BiLSTM (None,128) 75776 Dropout (None,128) 0 Dense (None,2) 258 Output Layer (Dense) (None,2) 6 Total trainable parameters 76040 Note: The table reports the shape and number of parameters of input, output, dropout, and LSTM/BiLSTM layers. The table also indicates the total number of trainable parameters used for model training. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 45 Credit and Capital Markets 1 / 2023 6. Challenges during Training Over-fitting and under-fitting problems prevail even after adopting model classification and prediction algorithms. Thus, the over-fitting problem is addressed by the dropout layer and L2 regularization methods. The dropout layer sets the weights of the nodes to zeros at a certain ratio, thereby reducing the effect of the over-fitting problem. The L2 regularization slows down the weight update process, heavily reducing the over-fitting problem. For tackling the under-fitting problem, the learning rate and the number of epochs constitute the most important hyper-parameters that have to be deliberately adjusted to improve the performance of the proposed algorithm. The Adam optimizer8 is selected following a grid search principle9 since it performs better than other optimizers for the indented algorithm. Consequently, the updating speed of the inner parameters of the model is determined by the learning rate of the Adam optimizer. The model is able to achieve good performance when an appropriate learning rate is applied. The number of epochs is set to a large number to avoid under-fitting. 7. Hyper-parameters Selection Table 5 presents the complete list of selected hyper-parameters. Adam, RMSprop, ADAdelta, and SDG10 are the optimizers tested in the training phase, and the Adam optimizer performed the best among them. The learning rates of 0.1, 0.01, 0.001, and 0.0001 are tested and with a 0.001 learning rate, the model is converging at a moderate pace. The dropout rates of 0.05, 0.1, 0.2, and 0.5 are also tested and 0.1 has been selected after several simulations. 8. Evaluation Matrices for Model Performance As opposed to standard evaluation metrics, imbalanced classification problems typically rate errors with minority classes more highly than errors with majority classes. Suppose we have a data set of 100 patients, of which 8 are cancer patients, and the rest of 92 is healthy. In this example, we have an imbalanced data set, as the majority class is about nine times bigger than the minority class. 8 An optimization algorithm that is used in neural networks to update network weights iteratively. 9 We refer interested readers to the following website for details of grid search technique: https://scikit-learn.org/ stable/modules/grid_search.html. 10 We refer interested readers to the following website for details of deep learning optimizers: https://www.analyticsvidhya.com/blog/2021/10/a-comprehensive-guide-ondeep-learning-optimizers/. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 46 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 Here the majority class is “healthy,” and the minority class is “cancer.” So, it is crucial to detect the 8 cancer patients accurately. False negatives, in this case, would be a life-threatening condition. Sensitivity/Recall is the ability of a test to identify patients with a disease correctly. While specificity is the ability of a test to correctly identify people without the disease or the ability to avoid false positives. These two parameters are important in imbalanced data set classification along with the AUC-ROC curve score.11 On the basis of the threshold matrix for imbalanced classification, we use the following four evaluation parameters to evaluate the model’s characteristics and performance. Accuracy: Accuracy is the proportion of the correctly predicted labels (true positives (TP) and true negatives (TN)) among all our predictions (TP, TN, false positives (FP) and false negatives (FN)) 12. TP TN Accuracy TP TN FP FN + =+ ++ Sensitivity/Recall: Recall addresses the question: “Among all the positive labels in the data set, how many of them are correctly captured by the model?” TP Recall / Sensitivity TP FN =+ 11 Different types of threshold matrices for imbalanced classification and when to apply them can be found on the following website: https://machinelearningmastery.com/ tour-of-evaluation-metrics-for-imbalanced-classification/. 12 https://tinyurl.com/4ukftyky. Table 5 Hyper-parameters of LSTM and BiLSTM Hyper-parameters LSTM BiLSTM Hidden layers 2 3 Nodes 128,128 128,128,128 Optimizer Adam Adam Activation function SoftMax SoftMax Learning rate 0.001 0.001 Epochs 500 500 Dropout rate 0.1 0.1 L2 regularization Recurrent layers l2(0.01) Recurrent layers l2(0.01) Note: The table reports the shape and number of parameters of input, output, dropout, and LSTM/BiLSTM layers. The table also indicates the total number of trainable parameters used for model training. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 47 Credit and Capital Markets 1 / 2023 Precision: Precision addresses the question: “Among all the positive labels predicted by the model, how many are indeed positive?” TP Precision TP FP =+ Specificity: Specificity measures the proportion of correctly identified negative labels among all the negative labels (TN + FP). Specificity also is a key ingredient in the ROC curve. TN Specificity TN FP =+ 9. Data Division and Cross Validation For time series cross-validation, the validation data set is evaluated on the “future” observations immediately following the training data set in time rather than random observations. In particular, we apply an expanding window cross-validation technique. The expanding window is also referred to as “time series split,” in which the training set is divided at each iteration in a way that the validation set is always ahead of the training split (Assaad/Fayek 2021). This method is called the nested walk forward or expanding window method, where Train Test Training Test Test Test Test Validation Outer Loop Inner Loop Nested Cross-Validation Note: Our study employs an expanding window cross-validation with the data set partitioned into 5 distributed sets, equating to a 5-split iteration procedure. The average accuracy values of the 5 splits were used to evaluate the models’ overall performance. Figure 5: Expanding Window Time Series Cross-Validation OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 48 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 the validation set is also defined inside the training set.13 Nested cross-validation provides an almost unbiased estimate of the true error (Varma/Simon 2006). The data set is divided into five-time splits and accuracy is calculated for each split, as shown in Figure 5. V. Results The empirical analysis was performed on a SLURM-based HPC cluster with a machine equipped with three Nvidia V100S 32GB, 256GB memory, and 2 AMD EPYC ROME 7272 system. The algorithm is written in Python (v3.7.2) using TensorFlow and Keras (v2.7.0). The LSTM and BiLSTM models are implemented and evaluated against traditional classifiers. The most important step before the implementation of LSTM/BiLSTM is hyper-parameter tuning since this step highly affects the accuracy scores. By applying the grid search approach via maximizing the accuracy of the data set, the values of the hyper-parameters are adjusted, as described in Table5. The number of nodes is set to 128. The parameter “mini-batch size” is set to 20, with a validation step of 20, following the grid search ranging from 10 to 100, as described in the subsection IV.7. Hyper-parameters Selection. The number of steps per epoch is set to 10, and the number of epochs is adjusted to 500, to ensure the algorithm’s convergence. Figure 6 and Figure7 show the training and validation curves for model accuracy 13 We refer interested readers to the following website for details of time-series nested cross-validation: https://www.angioi.com/time-nested-cv-with-sklearn/. dƌĂŝŶŝŶŐ ƵƌǀĞ sĂůŝĚĂƚŝŽŶ ƵƌǀĞ Figure 6: Training and Validation Accuracy Curves OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 49 Credit and Capital Markets 1 / 2023 and loss function. The loss function is set to be “binary cross entropy” and “categorical cross entropy” for the binary and the multi-class classification, respectively. The data set is divided into five-time splits and in each split, the algorithm runs for 500 epochs as shown in Table 6. It is observed that with the increase in the training samples, the corresponding accuracy increases in each time split, consequently yielding an accuracy of 93 % for multi-class and 95 % for binary class prediction. This article focuses on the four evaluation criteria (Recall, Specificity, Precision, and Accuracy) to evaluate and compare the classifiers’ performance. Recall (or Sensitivity) is the important evaluation parameter because the concern is how many default/distressed loans are classified correctly by the classifier amongst all the default/distressed loans. LSTM, BiLSTM, RF, ExtraTree classifier, logistic regression, decision tree, and XGBoost classifier are tested for the loan default and distressed classification. Note that the class weight assignment for data balancing is performed in the training parameters of the classifiers. LSTM and BiLSTM perform better than the other classifiers in terms of Precision and Recall for binary as well as for multi-class classification, as illustrated in the confusion matrix for loan default classification presented in Figure 8. Table7 proves that both LSTM and BiLSTM perform better than all traditional sĂůŝĚĂƚŝŽŶ ƵƌǀĞ dƌĂŝŶŝŶŐ ƵƌǀĞ Note: Model accuracy increases while error decreases. Accuracy and error approach a constant value after around 300 iterations. Figure 7: Training and Validation Loss Curves OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 50 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 classifiers, with an accuracy of 95 % and 93 % for the binary and multi-class loan status prediction. Figure 9 shows the Receiver operating curve ROC for the BiLSTM algorithm for the classification of three classes. Figure 10 shows the ROC for all tested classifiers (RF, DT, ExtraTree, LR, and XGB classifier) on the LendingClub time series data set. 1. Feature Importance by SHAP A novel time series one-step-ahead prediction approach is applied for the MTS-based marketplace lending data set. The BiLSTM model has been trained one step ahead, and the SHAP feature importance summary is plotted on this basis. Analogously, SHAP feature importance has been calculated for two-step, three-steps, and four-steps-ahead prediction, as shown in Figure 11. The following 14 features that remain consistently important with one-step-ahead prediction are extracted: “loan amount (€),” “installment (€),” “grade,” “funded amount (€),” “total payment (€),” “term 36 months,” “interest rate,” “verification status ,” “employment length of borrower,” “outstanding principal by investor (€),” “total  Note: Confusion matrices show the performance of the classifier algorithm on the test data set. The figure shows that the BiLSTM performs best in binary and multi-class classification. Figure 8: Confusion Matrix LSTM/BiLSTM OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 57 Credit and Capital Markets 1 / 2023 Kaveri, V. /Narang, D. (2020): Peer to Peer Lending in India under COVID-19 Scenario. Vinimaya Vol. 41(1), 5 – 19. Kim, J. Y./Cho, S. B. 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OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 59 Credit and Capital Markets 1 / 2023 Table A1 Eliminated Attributes Category Eliminated variables Attributes that cannot be used for prediction ID, member ID, employment title, url, loan description, loan title Attributes with more than 50 % missing values months since borrower’s last delinquency, months since last major derogatory, months since recent bank card delinquency, months since recent revolving delinquency, open installment account since 6 months, open installment account since 12 months, open installment account since 24 months, months since recent installment account opened, total balance of installment accounts, installment loan utilization, months since last record, open revolving trades since 12months, open revolving trades since 24months, max current balance, open account since 6 months, all utilization, finance inquiry, total finance trades, inquiry last 12m Redundant attributes annual income joint, dti joint, verified status joint Attributes that are filled after the borrower starts torepay policy code, payment plan, outstanding principal, outstanding principal by investors OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 60 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023 Table A2 Descriptive Statistics of Selected Features Feature Name nmean std min 25 % 50 % 75 % max loan amount (€) 1587613 15912.63 9872.05 1000 8000 14000 21550 40000 installment (€) 1587613 466.71 283.92 7.61 257.75 391.5 627.55 1719.83 grade 1587613 1.47 1.19 0 1 1 2 6 application type 1587613 0.09 0.29 0 0 0 0 1 funded amount (€) 1587613 15912.61 9872.05 1000 8000 14000 21550 40000 open account 1587613 12.37 5.91 1 8 11 15 104 total payment (€) 1587613 11909.70 9878.53 0 4556 9014.86 16452.51 70826.17 total received interest (€) 1587613 2401.12 2573.70 0 738.04 1543 3137.72 33337.57 verification status 1587613 0.61 0.49 0 0 1 1 1 term 36months 1587613 0.69 0.46 0 0 1 1 1 term 60months 1587613 0.31 0.46 0 0 0 1 1 fico range high 1587613 706.70 34.20 664 679 699 724 850 fico range low 1587613 702.70 34.20 660 675 695 720 845 annual income (€) 1587613 85730.00 90555.89 14 50000 71000 100000 10999200 employment length of borrower 1587613 3.59 3.22 0 1 2 6 10 delinquency in 2 years 1587613 0.29 0.85 0 0 0 0 35 home ownership mortgage 1587613 0.50 0.50 0 0 0 1 1 home ownership own 1587613 0.11 0.31 0 0 0 0 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 Default Risk Prediction and Feature Importance 61 Credit and Capital Markets 1 / 2023 Feature Name nmean std min 25 % 50 % 75 % max home ownership rent 1587613 0.39 0.49 0 0 0 1 1 purpose car 1587613 0.01 0.10 0 0 0 0 1 purpose house 1587613 0.01 0.08 0 0 0 0 1 purpose medical 1587613 0.01 0.11 0 0 0 0 1 purpose renewable energy 1587613 0.00 0.02 0 0 0 0 1 purpose small business 1587613 0.01 0.10 0 0 0 0 1 dti 1587613 20.59 14.19 –1 13.56 19.29 25.92 999 total received principal (€) 1587613 9355.36 8537.10 0 3000 6529.99 12983.73 40000 outstanding principal by investor (€) 1587613 5258.53 8064.72 0 0 0 8460.71 40000 interest rate 1587613 13.03 5.10 5.31 8.81 12.4 16.02 30.99 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35 62 Sana Hassan Imam, Sebastian Huhn, Lars Hornuf, Rolf Drechsler Credit and Capital Markets 1 / 2023  Figure A3: Algorithm of LSTM/BiLSTM OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.56.1.27 | Generated on 2023-07-20 09:24:35