My Second Master's Thesis Topic:
CREDIT RISK ASSESSMENT FOR A SMALL BUSINESS,
USING MULTIDIMENSIONAL MEMBERSHIP FUNCTIONS: DESIGN AND APPLICATIONS
The thesis was written in the Research Unit of Artificial Intelligence
under the supervision of Andrzej Piegat, Ph. D., Professor and Dean of
Faculty of Computer Science and Information Technology,
Technical University of Szczecin, Poland.
If you are interested in any parts of this work and would like to cooperate with me on further research, please contact me.
Last revised: September, 2004 HOME PAGE
The evaluation of credit risk is a substantial issue for all of the financial institutions all over the world. The main problem of the topic is the fact that the credit analyst needs to analyze and assume a large number of differently valuated factors in a short time, yet the human brain is capable of evaluating only a very small set of factors. For these more advanced problems computer systems are used. The situation is further complicated because every case is different or new even for very experienced evaluators. In addition, many cases, which have been already successfully solved, cannot be legally transferred to other departments of the same institution because of data security. Many expert systems were developed to support solving this kind of situations but the constantly changing business environment continues to require more advanced solutions. The author decided to concentrate his interests in the area of small business credits, facing the problem of implementation allowing transferring knowledge gained from the secret data to solve other cases of credit risk estimation, especially emphasized by bank authorities.
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The thesis has the five-chapter structure. The purpose of this work is to investigate the potential of the artificially intelligent classification methods for the improvement of the bank credit allowance procedures. In the first part the author characterized the problem, focusing mainly on the explanation of the credit application assessment and the key issues occurring in this area. In addition the author decided to present a general framework of the entire computer system for the credit worthiness estimation, where the aspect solved by this thesis needs to be applied. In the second chapter, the data characterization is included. It starts from the description of received samples, by the data normalization process, to end at the significance analysis. The third chapter includes the proposition of Kohonen’s neural network, which according to the belief of the author, could be successfully applied in the analyzed area. There is a fuzzy system application for the same problem placed in the chapter four. In chapter five, being the last part of presented thesis, the author compares the received results for both of the built models, trying to chose the better of these two applications for the credit applications assessment problem. In this part the author placed also all conclusions, which came to his mind as the result of the accomplished work.
The purpose of the work presented in this thesis was to investigate the potential of employing the artificially intelligent classification methods for the improvement of the credit allowance procedures applied by the bank officers towards the clients coming from the small business sector.
Both of the utilized modeling techniques let to indicate the input variables, which are important for the credit worthiness assessment: Financial Indices (X1), Selling Ability (X2), Expansion Prospects (X3), Management (X4), Future market needs (X6) and the one input which should be omitted, when the loan application is considered – Credit guarantees (X5). According to both of the employed models, the question about credit guarantees, given to the credit applicants (at least to the borrowers from the small business sector) does not reflect correctly the assurances of credit return and should be removed from the system, to improve its’ work accuracy. It might be that the bank officers like to think that extended credit guarantees given by the borrowers additionally assure the return of their funds. However according to the results achieved by the author, it might be worth to consider the opinion, that
if the applicant have no money to pay the financial obligations (such as the credit rates), the fact that the bank may occupy its (or someone else) belongings does not change at all the bad financial situation of the borrower and its inability to return the borrowed monies. The bank’s insistence on the guarantees seems to be irrational especially in the cases of atypical credits, when the fact that the applicant accepts to have the target guarantee on the unusual equipment he/she is going to buy for the borrowed monies, does not improve the risk profile of the loan. In the case of the borrower’s bankruptcy the bank has practically no chance to re-sell the occupied equipment, to receive the invested funds back.
In both of the employed techniques the best models had very similar and rather low (below 5%) error level, which may additionally assure of the usefulness of the analyzed methods for the credit allowance dilemma. Although none of the created models was working perfectly, both of them can be definitely used as the decision support systems, especially because of the fast applicant classification ability.
Moreover both of the created solutions work on the basis of the relations between values of considered inputs, using normalized data instead the exact numeric values. This feature could be successfully utilized by the bank evaluators, especially in the context of the difficulties of the knowledge transformation, often entirely blocked by the data security procedures. The presented systems that gained the knowledge about credit applications in the one of bank departments, could be effectively used as the decision support tools in the others of the bank departments, for example located in the different cities, without the risk of personal information leaks. The same model can be successfully employed in many locations and/or bank departments, as long as the structure of the client profiles remains similar (which usually is the case for the borrowers coming from the small business sector).
As not a bank professional, the author had problems with distinguishing the right proportions between some descriptive values of input variables, and had to employ the linear scaling (e.g. the difference between grades "Very good" and "Good" is identical, as between "Good" and "Sufficient" in all of the presented models). Since the ratios between the given grades have great values for the model accuracy, and do not have to be really linear, it is strongly recommended to achieve the extended help of the bank professionals in this matter when the more advance models are going to be built.
TABLE OF CONTENTS .............................................................................................. 2
INTRODUCTION......................................................................................................... 4
1 DESCRIPTION OF THE DILEMMA ..................................................................... 5
1.1 CHARACTERIZATION OF CREDIT RISK AREA ...........................................5
1.2 CREDIT ALLOWANCE PROCEDURE.................................................................6
1.2.1 Credit scoring .........................................................................................................9
1.2.2 Critical issues ..................................................................................................11
1.3 PROPOSAL OF THE SYSTEM.............................................................................12
2 DATA ANALYSIS............................................................................................... 15
2.1 DESCRIPTIVE CHARACTERIZATION..............................................................15
2.1.1 Characterization of inputs .............................................................................................15
2.1.2 Output analysis............................................................................................................16
2.2 SAMPLES PREPARATION.....................................................................................17
2.2.1 Data normalization..........................................................................................................17
2.2.2 Separation of samples for the training and testing sets ............................................17
2.3 SIGNIFICANCE OF VARIABLES..........................................................................18
2.3.1 Mean value curves..........................................................................................................18
2.3.2 Arc-angle significance index Sa ....................................................................................21
2.3.3 Dispersive significance index I3 ....................................................................................22
2.4 RESULTS RECEIVED...............................................................................................24
2.4.1 The influence of the input variables on the credit granting .......................................24
2.4.2 Dependences between the input variables..................................................................29
3 NEURAL NETWORKS FOR CREDIT CLASSIFICATION.................................. 39
3.1 KOHONEN SELF-ORGANIZING MAPS ...........................................................39
3.2 APPLYING KOHONEN NETWORK TO THE PROBLEM .........................42
3.2.1 Characterization of applied network.............................................................................42
3.2.2 Error measurement.........................................................................................................45
3.3 RESULTS RECEIVED...............................................................................................46
3.3.1 Experiments results .......................................................................................................46
3.3.2 The best model architecture..........................................................................................49
4 FUZZY SYSTEM FOR CREDIT CLASSIFICATION........................................... 51
4.1 FUZZY C-MEANS METHOD ..................................................................................51
4.2 APPLYING FUZZY C-MEANS TO THE PROBLEM ....................................54
4.3 RESULTS RECEIVED...............................................................................................56
4.3.1 Estimation of the initial cluster centers .......................................................................56
4.3.2 Experiments results .......................................................................................................72
CONCLUSIONS........................................................................................................ 75
INDEX OF FIGURES ................................................................................................ 77
INDEX OF TABLES................................................................................................... 79
INDEX OF EQUATIONS ........................................................................................... 80
LITERATURE............................................................................................................ 81
APPENDIX A – THE DATA SAMPLES ..................................................................... 83
APPENDIX B – RESULTS OF THE SAMPLES QUALIFICATION PERFORMED
WITH THE KOHONEN NETWORK........................................................................... 87
FOR THE TESTING SET......................................................................................... 90
APPENDIX C – RESULTS OF THE SAMPLES QUALIFICATION PERFORMED
WITH THE FUZZY C-MEANS ALGORITHM............................................................. 91