APPLICATION AND BEHAVIOURAL STATISTICAL SCORING MODELS

Transcription

1 APPLICATION AND BEHAVIOURAL STATISTICAL SCORING MODELS Laima Dzidzeviciute Vilnius university, Lithuania, Abstract Usually scoring models are separated to application and behavioural scoring models based on their usage, i. e. whether they will be applied for assessment of new applications or behaviour of loans already existing at a bank. However, even if application and behavioural scoring models, spheres of their usage and their development are very different, some banks develop the same common models without differentiating them to application and behavioural models. The objective of this paper is to present four approaches for application and behavioural statistical scoring models usage at banks, describe technical issues of model development for each of these approaches, analyse advantages and disadvantages of them and provide with the ways, how to join application and behavioural scores of the same obligor as time passes. Detailed comparative analysis of the advantages and disadvantages showed that the best way for banks is to construct separate application and behavioural scoring models, i.e. to choose one of the first two approaches presented in the paper because in such the case models are more accurate and representative if compared to the models developed applying other two approaches. Also, the analysis showed that banks should prefer to move to behavioural score gradually, i.e. the weight of application score should be reduced and the weight of behavioural score - increased as time passes. Keywords: Application and behavioural scoring models, score, default, result period. Introduction Usually scoring models are separated to application and behavioural scoring models based on their usage, i. e. whether they will be applied for assessment of new applications or behaviour of loans already existing at a bank. The main difference between application and behavioural scoring models is that more input variables are available for the second type. Behavioural scores are distinguished from application scores because they include characteristics representing the obligor s own payment pattern on the loan, usage activity of revolving loan and other features of obligor that are not possible to be included while developing application scoring models. Application scoring models are usually used to decide whether to grant credit to new applicants, meanwhile, behavioural scores are usually used in other spheres of a bank, i. e. to decide which of the obligors are in danger of defaulting in the near or medium-term future, to adjust credit limits, in collecting delinquent accounts (e.g. obligors with poor behavioural scores are contacted earlier in the month and the method of contact may be varied with the score), to cross-sell products to existing obligors (e.g. a bank may use a behavioural score generated for its mortgage portfolio to select borrowers for a favourable offer on a credit card), determine strategies for handling seriously delinquent accounts, in loss forecasting and so on. As behavioural scoring models include variables related to obligor s demonstrated willingness and ability to pay on the loan under consideration, behavioural scores tend to be even more predictive than application scores, which, of course, are based on data available when the loan is originated. Development of application and behavioural statistical scoring models is also different, i. e. reference dates, construction of data array needed for the development, variables included may differ significantly (Mays, 2004; McNab et al., 2003 SAS, 2006; Siddiqi, 2007; Thomas et al., 2002). Till now application and behavioural statistical scoring models were not analysed in details by researchers of Lithuania. Dzidzeviciute (2010) analysed application and behavioural scoring models only as a composite part of statistical scoring model development process. Taking into account the implementation of EU new capital adequacy directive into national legal acts of Lithuania, the need to develop statistical scoring models at Lithuanian banks increases even more. So, there is a lack of detailed theoretical analyses on this subject, i. e. various approaches of application and behavioural statistical scoring models, their advantages and disadvantages, data gathering issues in each of these approaches, possible ways to relate application and behavioural scores of the same obligor as time passes. The objective of this paper is to present four approaches of application and behavioural models usage at banks, describe technical issues of model development for each of these four approaches, analyse advantages and disadvantages of them and provide with the ways, how to join application and behavioural scores of the same obligor as time passes. The analysis presented in this paper is based on practical 1046

2 experience of the author of the paper. Technical model development issues are analysed in observance with the requirements of and definitions presented in EU new capital adequacy directive (EU, 2006) that was based on Basel 2 paper (BCBS, 2006). Chapter 1 of the paper provides with the comparison of four approaches for application and behavioural models usage as well as their advantages and disadvantages and Chapter 2 exemplary ways to relate scores derived by application and behavioural models for the same obligorthis template was created with the aim of keeping unified approach to paper typing for the Annual International Conference Economics and Management 2010 (ICEM 2010) held in Riga. The template contains predefined styles and the document text layout. The largest part of the paper is a chapter text typed in 11 points Times New Roman, aligned justified (style Normal). Approaches of application and behavioural models usage Application scoring models may be applied to new credit clients applying for a new loan and for old credit clients applying for a new loan again, meanwhile, behavioural scoring models are applied for regular reassessment of already existing loans (Dzidzeviciute, 2010). Table 1 below provides 4 approaches of different models usage. It is up to a bank which approach to choose, however, each of the approaches has its pros and cons. Table 1. Approaches of application and behavioural models usage Approach New credit clients application model Old credit clients application model Behavioural model 1st X X 2nd X X X 3rd X X 4th X 1 st approach: two models are applied, i. e. one model is applied for assessment of new applications (both for new and old credit clients), however, separate model is applied for regular behavioural scoring. 2 nd approach: three separate models are applied, i. e. one for new credit clients new applications, the second for old credit clients new applications and the third for regular behavioural scoring purposes. 3 rd approach: two models are applied, i. e. one model is applied for assessment of new credit clients applications, but for assessment of old credit clients applications and regular behavioural scoring separate model is applied. 4 th approach: one-fits-all approach, i. e. one model is applied for assessment of new credit clients applications, old credit clients applications and for regular behavioural scoring. Sub-chapters below discuss the features of 4 approaches in detail. First and second approaches When banks apply the first approach, new applications are assessed with the separate application model and regular reassessment of already existing loans is made with separate behavioural model. Developing application scoring model only the obligors 1 who received loans during certain period of time are included, and it is determined, whether during 1 year from the moment of loan granting (i. e. result period) each concrete obligor defaulted or not (Figure 1). 1 That depends on chosen level of model development, i. e. model may be developed on obligor, product or loan level. For example, model developed on obligor level would prognosticate credit risk of obligor and not of a loan. For simplicity purposes thereinafter obligor level and logistic regression form will be used for explanation. 1047

3 Variables of each included obligor that will be used as input variables into application model are determined at the time of loan granting Obligor 1 Obligor 2 Obligor n T 0,1 T0,2 T 0,n T 1,1 T 1, 2 T 1,n T result period 1 = 1 year result period n = 1 year result period 2 = 1 year It is determined, whether during 1 year after loan granting obligor defaulted or not Figure 1. Development of application scoring model For example, all obligors who received loans during period from till are included into model development, and it is determined, whether each concrete obligor defaulted 2 or not during 1 year from the date of loan granting. As obligors receive loans at different dates, each obligor will have individual reference date T 0 and individual result period (i. e. the period from reference date T 0 till T 1 during which it is assessed whether obligor defaulted or not). However, duration of these different result periods has to be the same, i. e. period from reference date T 0,1 till T 1,1 has to be the same as the period from reference date T 0,2 till T 1, 2 and etc. In accordance with the requirements of new EU capital adequacy directive this result period at banks is usually equalled to 1 year. For example, one client receives a loan on , another client on Developing application model reference dates and result periods for these two obligors will differ. For the first client reference date is and result period is from to (Figure 2), meanwhile, for the second client reference date is and result period is from to As shown in Figure 1, variables of all included obligors are determined at various reference dates T 0. Variables at reference dates T 0 may be current (e. g. age of obligor) or during the certain period till reference date T 0 (e. g. number of past due payments during last 24 months). The length of this period depends on the features of concrete included variable, e. g. it would not be reasonable to use age of obligor during last 24 months because we are interested in current age of our obligors when they apply for loans in order to assess their risk during next year, however, it would be very informative to analyse payment history during last 24 months. 2 Default shall be considered to have occurred with regard to a particular obligor when either or both of the two following events has taken place: 1) a bank considers that the obligor is unlikely to pay its credit obligations to the bank, parent bank or any of its controlled financial undertakings in full, without recourse by the bank to actions such as realising collateral (if held); 2) the obligor is past due more than 90 days on any material credit obligation to the bank, the parent bank or any of its controlled financial undertakings, excluding the cases when the exposure amount balance does not exceed LTL 100, or another amount which the bank considers insignificant (Bank of Lithuania, 2006). 1048

4 Result period of 1 year Time Loan granting date If obligor defaults during 1 year period, then dependent variable is 1, otherwise 0. Figure 2. Example of one record included developing application scoring model Separate application models at banks may be developed for new credit clients applying for a new loan first time and for old credit clients applying for a new loan at least second time. If this first approach presented in this sub-chapter is chosen by a bank, one common application model is developed both for new and old credit clients new applications. Meanwhile, developing behavioural model, reference date T 0 as well as result period is the same for all included obligors. As shown in Figure 3, variables of all included non-defaulted obligors are determined at date T 0, and it is assessed, whether during period from T 0 till T 1 obligor defaulted or not. Variables of each included nondefaulted obligor that will be used as inputs into behavioural model are determined at date T 0 It is determined, whether during period from T 0 till T 1 each concrete obligor defaulted or not Time T -n T 0 T 1 Figure 3. Development of behavioural scoring model For example, bank includes all existing non-defaulted bank s obligors as of and assess, whether during period from till each concrete obligor defaulted or not. For all these obligors reference date and result period are the same, i. e. reference date is and result period from till The second approach is very similar to the first one, the only difference is that application models are differentiated, i. e. separate application models are developed for new credit clients applications and old credit clients new applications. Development of application models is the same as shown in Figure 1, development of the third model for regular behavioural scoring is the same as shown in Figure 3. One could notice the main differences between application and behavioural models: Developing application models only new obligors who received loans during analysed period of time are included, meanwhile, developing behavioural model all existing non-defaulted obligors as of chosen reference date T 0. For this reason application model developed using only the data of 1049

5 new applications prognosticates probability of default 3 (thereinafter PD) more accurately because model reflects characteristics of these new applications. Developing application models reference date and result period, i. e. period during which it is assessed, whether obligor defaulted or not, are different for different loans depending on the date of loan granting. Meanwhile, developing behavioural model reference date and result period for all loans are the same. Third and fourth approaches Applying the third approach, development of application model for assessment of new credit clients new applications is the same as shown in Figure 1, meanwhile, development of the second model for assessment of old credit clients new applications and for behavioural scoring is the same as shown in Figure 3. If common model for old credit clients new applications and behavioural scoring is used, while developing such model, part of information for old credit clients new applications is lost. As the same reference date for all loans is used, default/non-default for old credit clients new applications would be determined not from the date of loan granting, but from chosen common reference date. So, behavioural information will overweigh application information of old credit clients and variables included into the model as well as their weights will be largely influenced by behavioural features of obligors. For example, old credit client receives a new loan on , but his/her default/non-default status will be determined not during the period from till , but from common chosen reference date, i. e. from (Figure 4). If obligor does not default during period from till , while forming data array bank will assign him/her dependent variable 0, if defaults 1. Then obligor s behaviour in the period from till is simply lost Time Non-default 0, default 1. Figure 4. Usage of reference dates developing common model If bank developed separate application model for old credit clients new applications or application model for new and old credit clients applications (see 1 st and 2 nd approaches in sub-chapter 1.1), the abovementioned problem of reference dates incompliance would be avoided. Forming data array bank would assign dependent variable 0, if obligor didn t default during one year from the date of loan granting, i. e. from till , and 1, if obligor defaulted during one year from the date of loan granting (Figure 5). Non-default 0, default Time Figure 5. Usage of reference dates developing separate application model 3 Probability of default shall mean the probability that obligor will default during one year period after assessment date. 1050

6 One could notice that: It is more accurate to assess actual obligor s PD (0 or 1) from the date of loan granting and not from the common reference date. If bank uses common reference date for new applications, then while determining dependent variable, i. e. actual PD (0 or 1), bank does not take into account the fact, whether obligor defaulted or not from the date of loan granting till common reference date (i. e. from to in exemplary Figure 4). Even if defaults/non-defaults during the above-mentioned period from the date of loan granting till common reference date were included through independent input variables (e. g. if additional independent variables such as there were defaults/there were no defaults from the date of loan granting till reference date or number of defaults during the period from the date of loan granting till reference date were used), this inclusion would influence only independent input variables ( x ) and not dependent variable (actual PD, i. e. 0 or 1 ). So, due to this fact theoretical possibility exists that obligor can default even 3 times during 10 months from till and recover every time. In such the case if obligor defaulted from till , but did not default from till , he/she would be treated as Good. If separate application model was used and default/non-default was determined starting from the date of loan granting, such obligor would be treated as Bad. Besides, if bank included his/her 3 defaults through independent variables, and obligor having these 3 defaults from till didn t default from till , bank would receive perverse results because defaults would be treated as the indicator reducing prognosticated PD. Problem is reduced using more frequent reference dates (e.g. quarterly, monthly) and completely solved using daily reference dates. However, in such the case bank s IT systems are too loaded, many overlapping data arrays are received, and as the result of that model development process is impeded. Developing common models we would probably not include the characteristics specific for application scoring models because at any point in time banks have more behavioural than application scores. For example, the concrete obligor applies for a loan on , so, this obligor receives application score only one time. If bank recalculates behavioural score of obligors quarterly, this concrete obligor will receive behavioural score 4 times a year, 8 times in two years and so on. So, as mentioned earlier at any point in time bank will have more behavioural scores than application scores. If common model is developed, behavioural information will overweigh application information and variables included into the model as well as their weights will be largely influenced by behavioural features of obligors. Applying the 4 th approach these above-mentioned problems are even more serious because meaningful part of information is lost even for new credit clients applications. In general, the fourth approach is very similar to the third one, the only difference is that separate application model for new credit clients is not used and one common model is used for all assessments for assessments of new applications and for regular reassessments of them. Developing one common application and behavioural scoring model there is no separation between old and new credit clients, all bank s existing non-defaulted obligors as of chosen reference date T 0 are included into data array. Advantages and disadvantages of various approaches Table 2 below provides with the comparison of advantages and disadvantages of 4 approaches described above. Table 2. Advantages and disadvantages of various approaches Approach Description Advantages Disadvantages Two models: one for assessment of new applications 1 st (both for new credit clients and approach old credit clients) and the second for behavioural scoring. 1. Higher representativeness than applying one model for all because characteristics of concrete sample are taken into account. 2. Higher accuracy: different reference dates are applied developing application model, i.e. facts of default/non-default are determined during one year from the date of concrete loan granting and not from the reference date that is common for all loans. 1. Necessity to apply transition from application to behavioural score. Besides, the transition from behavioural to application score is also needed after receiving a new loan because application score has to be determined again Necessity to use additional input variables developing application models. E. g. in the case of the 2 nd approach there wouldn t be a need to 4 If models are developed on loan level, then when obligor receives second loan for the first loan transition from behavioural score to application score is not needed. 1051

7 2 nd approach 3 rd approach Three models: one for new credit clients, the second for old credit clients new applications and the third for behavioural scoring. Two models: one for new credit clients applications and the second for old credit clients new applications and behavioural scoring Because of this reason the information about default/non-default during period from loan granting till reference date is not lost. 3. Larger data sample than developing separate application models (if compared with 2 nd approach) because both new credit clients and old credit clients new applications are included. 4. Less additional variables if compared to 3 rd and 4 th approaches. 1. These models are the most representative and accurate for credit risk assessment and prognostication of PD as developing models specific features of concrete obligors type are taken into account. 2. There s no need to apply additional variables that is why there s bigger possibility to include specific variables needed for each model type. 1. Developing new credit clients application model there s no need to include additional input variables such as loan age or length of credit history at the bank and etc., so it is possible to include more specific variables such as age, education, income and etc. 2. Larger data sample developing common old credit clients application and behavioural scoring model than developing separate behavioural model (the 1 st or the 2 nd approach) or separate old credit clients application model (2 nd approach). 3. Higher representativeness for new credit clients application model comparing with the 1 st or 4 th approaches because the features of concrete new clients characteristics are taken into account. 4. In common old credit clients application and behavioural scoring model internal past due information may be included. 5. Developing new credit clients application model separate reference points are taken depending on loan granting date that is why no information is lost (on the use additional variable such as loan age or length of credit history at the bank and etc. developing application model for new credit clients. Meanwhile, in the case of the 1 st approach there s a need to test such variables and after proving their significance to include into application model. In such the way the process of modelling and univariate 5 analysis is burdened. 3. As we have to include additional input variables, the possibility to include more specific variables needed for each model type is lost, e. g. if we developed separate application model for new credit clients, only specific variables such as age, education, income and etc. would be included, meanwhile, developing application model both for old and new credit clients list of variables is broader. 4. Possibility of data sample insufficiency for application model if compared to the 4 th approach. 1. Necessity to apply transition from application score to behavioural score. Besides, the transition from behavioural to application score is also needed after receiving a new loan because application score has to be determined again Higher time and IT cost both for developing and regularly validating models. 3. Possibility of data sample insufficiency both for new credit clients applications and for old credit clients new applications. 1. Non-representativeness applying common model both for old credit clients applications and behavioural scoring, especially in respect of old credit clients applications because at concrete reference point in bank s portfolio the proportion of old credit clients with old loans is relatively higher than the proportion of old credit clients with new loans. So, the features of old credit clients old loans outweigh the features of old credit clients new loans. 2. Developing common behavioural and old credit clients application model the part of information about old credit clients new loans would be lost. As for all loans the same reference date would be applied, default/nondefault for old credit clients new loans would be assessed from this reference date and not from loan granting date. The problem is analogical as applying the 4 th approach, however, not actual in the case of new credit clients applications. 3. The necessity to apply transition from application to behavioural score for new credit clients. 4. Necessity to use additional input variables 5 Univariate analysis analysis of separate independent input variables. 6 If models are developed on loan level, then when obligor receives second loan for the first loan transition from behavioural score to application score is not needed. 1052

8 4 th approach Common model for assessment of applications and for regular behavioural scoring of them is used. contrary, applying I approach, some part of information about new credit clients applications is lost). 6. There s no need to apply transition from old credit clients application score to behavioural score and vice versa. 1. Lower time and IT cost developing and validating models. 2. Applying models on obligor level, there would be no transition from score derived by application model to score derived by behavioural model. Also, if the same obligor received a loan again, there would be no transition from score derived by behavioural model to score derived by application model. 3. The largest data sample for model development. for common model, i.e. application scoring vs. behavioural scoring and etc. In such the way the process of modelling and univariate analysis is burdened. 5. As we have to include additional input variables for common model, the possibility to include more specific variables needed for each model type is lost, e. g. if we developed separate application model for old credit clients, specific variables such as loan purpose and etc. would be included, meanwhile developing common model list of variables is broader. 6. Possibility of data sample insufficiency for new credit clients application model. 1. Non-representativeness: only one model is developed using the same data sample. As at concrete reference date in bank s portfolio the number of old credit clients is always higher than the number of new credit clients, features and default/non-default information of old credit clients outweigh features and default/non-default information of new credit clients. 2. Inaccuracy: part of information for new applications would be lost because default/nondefault of newly granted loans is assessed during one year period starting from common reference date and not from loan granting date. 3. Necessity to use additional input variables, e. g. application scoring vs. behavioural scoring, obligor has internal credit history at the lending bank vs. obligor doesn t have internal credit history at the lending bank. In such the way the process of modelling and univariate analysis is burdened. 4. As bank has to include additional input variables, the possibility to include more specific variables needed for each model type is lost, e.g. if we developed separate application model for new credit clients, only specific variables such as age, education, income and etc. would be included, meanwhile, developing common model list of variables is broader. So, from the detailed analysis above one could notice that the most appropriate approaches for banks are the first two described in table 2. Statistical scoring models developed applying these two approaches are more accurate and representative if compared to the models developed applying other two approaches. If bank has sufficient data of old credit clients applying for a new loan, then the second approach is recomended. However, if there are no so many cases when old credit clients apply for a new loan again, the first approach is the most appropriate then. Chapter 2 below provides with the ways how to relate application and behavioural scores of the same obligor as time passes. Ways to relate scores derived by application and behavioural scoring models Applying the 1 st, the 2 nd or the 3 rd approaches described in Table 1 there is a necessity to relate scores derived by application and behavioural models or vice versa, i. e. to apply appropriate transition from application score to behavioural score and from behavioural score to application score. Besides, applying the 1053

9 1 st and the 2 nd approaches transition is needed even in the case of old credit client s new application. Two examplary ways how to relate different scores are presented below, i. e.: 1) In the first case during some certain defined period after loan granting date, let s say, three months, application score (and PD) would be applicable and after three months behavioural score (and PD) derived by separate model would be introduced. In next three months this behavioural score would be applicable and after that behavioural score would be recalculated again (Figure 6). Instead of three months other period may be chosen. 3 months 3 months Loan granting date application score is applied Date of the first behavioural score Date of the second behavioural score Time Figure 6. Relationship between application and behavioural score 2) Also, respective weights for PDs 7 derived by application and behavioural models may be applied (Figure 7). 1 month Loan granting date application score is applied x % weight is assigned to behavioural PD and (100-x) % weight to application PD Time Figure 7. Relationship between application and behavioural score As certain defined period of time passes, e. g. 1 month (the earliest time when it is possible to have information about obligor s payment behaviour as grace period at banks is usually one month), x% would be assigned to behavioural PD and (100-x)% to application PD. Individual loan s PD would be equal to: Individual _ PD = x behavioural _ PD + (1 x) application _ PD (1) here: t loan duration, in days. t x = (2) 360 Loan would be assigned to respective pool based on received final PD 8. For example, obligor receives a loan on and according application model individual PD of a loan is 1%. However, after 1 month bank can already have information about payments of obligor that is 7 That depends on the type of scoring model. Till now in this paper logistic regression was used for explanatory purposes. If the result of statistical scoring model is individual probability of default (e. g. logistic regression, probit regression and etc.), then this probability is used in further calculations. However, if the result of scoring model is creditworthiness score (e.g. discriminant analysis and etc.), then this score will be used further. 8 If models are applied on obligor level and obligor has more than one loan, instead of loan duration in formula (2) some adjusted indicator may be applied, let s say weighted average loan duration and so on. 1054

10 why behavioural PD also would be applied (let s say, equal to 0.5%) with weight equal to 30/360. Meanwhile, the weight of application PD (1%) would be reduced from 1 to 330/360. Individual PD as of = 1%*1 = 1% Individual PD as of = 0.5%*30/360+1%*330/360=0.96% Table 3 below provides exemplary calculation of final individual PD making the simplified assumption that monthly determined behavioural PD will not change. Table 3. Exemplary calculation of individual PD Weights Part of PD, in % Total PD, Month after in % loan granting Application Behavioural Application Behavioural The difference from previously presented approach is such that in previous approach application PD after 3 months is simply changed by behavioural PD and in this approach weight of application PD is reduced step by step according to loan duration at the bank, so there is no sudden increase or drop of PD. If bank suddenly changes PD of obligors, there may be big fluctuation of bank s specific provisions, capital requirements and other credit risk-related indicators. Meanwhile, if PD of obligors is changed gradually, step by step, transition is not so sudden and big fluctuation of bank s indicators is avoided. Conclusions This paper presented 4 approaches for the usage of application and behavioural scoring models. Detailed analysis of the advantages and disadvantages showed that the best way for banks is to construct and apply separate application and behavioural scoring models, i.e. to choose the first two approaches presented in the paper. Statistical scoring models developed applying the first two approaches are more accurate and representative if compared to the models developed applying other two approaches. If bank has sufficient data of old credit clients applying for a new loan, then the second approach is recommended. However, if there are no so many cases when old credit clients apply for a new loan again, then the first approach is the most appropriate. Also, the analysis of the ways, how to join application and behavioural scores of the same obligor showed that banks should prefer to move to behavioural score gradually, i. e. the weight of application score should be reduced and the weight of behavioural score - increased as time passes. References 1. Bank of Lithuania (2006). General Regulations for the Calculation of Capital Adequacy approved by Bank of Lithuania Board Resolution No. 138 of 9 November Valstybes zinios (Official Gazette), 2006, No Basel Committee on Banking Supervision (BCBS) (2006). International Convergence of Capital Measurement and Capital Standards: Revised Structure,

11 3. Dzidzeviciute, L. (2010). Statistinių vertinimo balais modelių konstravimo bankuose ypatumai. Lietuvos statistikos darbai, 2010 (49). 4. European Union (EU) (2006). Directive 2006/48/EC of the European Parliament and of the Council of 14 June 2006 relating to the taking up and pursuit of the business of credit institutions (recast) (OJ 2006 L 177, p. 1) 5. Mays, E. (2004). Credit Scoring for Risk Managers. The Handbook for Lenders, 3-8, McNab, H., Wynn, A. (2003). Principles and practice of Consumer Credit Risk Management, 2nd edition, The Cartered Institute of Bankers. 7. SAS (2006). Basic Credit Risk Modeling for Basel II Using SAS R. Course Notes. 8. Siddiqi, N. (2007). Credit Risk Scorecards. Developing and Implementing Intelligent Credit Scoring, John Wiley&Sons, Inc 9. Thomas, L. C., Edelman, D. B., & Crook, J. N. (2002). Credit scoring and its applications. Society for Industrial and Applied Mathematics: Philadelfia. Monographs on mathematical modeling and computation,