Tsybusova Karina

Faculty School of Economics and Management

Department of Economic Cybernetics

Speciality Economic Cybernetics

Simulation of customer credit commercial bank under incomplete information

Scientific adviser: Ph. D., Assoc. Donets Alex

Abstract

Contents

• Introduction
• Relevance of a subject
• Purpose and research problems
• Subject and object of research
• System of an assessment of solvency of the borrower and its information support
• Analysis of models of an assessment of solvency of the borrower
• 1. Assessment of solvency of the borrower by means of a decision tree
• 2. Assessment of solvency of the borrower by means of Altmanʼs model
• 3. Assessment of solvency of the borrower with use of the device of fuzzy logic
• Conclusions
• List of sources

  Introduction

  Careful selection of borrowers, the analysis of conditions of issuance of credit, continuous control of a financial condition of the borrower, of ability to extinguish the credit are one of fundamental components of financial wellbeing of the credit organizations. The solvency analysis in a large number of banks is made by experts who rely, generally on the experience and intuition that can lead to entering into the solution of not having sufficient bases of subjective reasons. In a real situation of opinion of analysts often differ, especially if the controversial questions having a set of alternative decisions are discussed. When developing methods of an assessment level to solvency natural persons the approach which is based on calculation of a rating of the borrower was widely adopted. Basis in this approach is the initial polling questionnaire which data reflect socially-economic situation and ability of the client of timely return of the credit. The scoring system in this case carries out the quantitative, semantic analysis and questionnaire data processing. Modification of the polling questionnaire attracts need of adjustment or essential modernization of all system. This circumstance limits possibility of adaptation the scoring of models to socially-economic conditions in Ukraine. Therefore, similar approach doesnʼt allow to develop universal system of the automated analysis of solvency.

  Relevance of a subject

  The problem of timely return of the credits is actual for the majority of banking institutions. Its decision considerably depends on quality of an assessment of solvency of potential borrowers. Relevance of a subject of work is defined by need of development of the formalized technique improvement of modern approaches to an assessment of solvency of natural persons and algorithms, realizing a technique in the form of the system supporting adoption of objective decisions.

  Purpose and research problems

  The purpose of work is development mathematical and tools of increase of efficiency adoptions of objective decisions in the analysis of solvency of natural persons on the basis of methods of fuzzy logic.

  Goals defined the following problems of work:

  1. The analysis of domestic and foreign approaches to an assessment of solvency of natural persons on purpose uses of positive achievements and elimination of shortcomings.

  2. Studying and systematization of the mathematical models developed so far and methods which it is possible to use in problems of classification of borrowers.

  3. Use of the methodological device of fuzzy logic for an assessment of quality of credit history of borrowers.

  4. Creation of the models reflecting specifics of the analysis of economic and social situation of private clients.

  5. Research of applied opportunities of offered models and procedures.

  6. Development of methods of calculation of economic effect of realization of the actions focused on optimization of quality of a credit portfolio of the bank organization.

  7. Program realization of the developed mathematical apparatus.

  Subject and object of research

  Object of research : credit portfolio of natural persons of the bank organization.

  Object of research : mathematical apparatus of modeling and analysis of solvency of private clients.

  System of an assessment of solvency of the borrower and its information support

  Now in the world there is no uniform standardized system of an assessment of solvency. Solvency is the complex legal and financial characteristic presented by a financial and non-financial performance, allowing to estimate its opportunity in the future completely and in time, provided in the credit agreement, to pay off according to the debts before the creditor, and also defining degree of risk of bank when crediting the specific borrower. Banks use various systems of the analysis of solvency of the borrower. The list of the indicators used for the analysis of a financial condition of the borrower, and order of their calculation are defined by the credit organization independently depending on branch, a field of activity of the borrower, analysis tasks, with all available information. At assignment of a credit rating banks range borrowers on various classes. The necessary quantity of classes is defined by bank independently.

  One of the most important stages in the organization of process of crediting is the assessment of solvency and solvency of the client. Viability of bank often depends on the correct assessment. The wrong assessment can lead to a credit non-return that is in turn capable to break bank liquidity and eventually to result in bankruptcy of the credit organization.

  Analysis of models of an assessment of solvency of the borrower

  Modern practical approaches to methodology of the analysis of solvency of borrowers in commercial banks are based on complex application of financial and non-financial criteria. We will consider classification of methods and models of an assessment of solvency of borrowers of commercial banks (fig. 2).

  
  

  Fig. 1. Models of an assessment of solvency of the borrower

  Classification models allow to break into groups (classes) and are the auxiliary tool when determining possibility of satisfaction of the credit demand. Two models are rather well shined in literature: ball (rating) assessment and forecasting of bankruptcies. Rating models divide borrowers on bad and good, and models of forecasting try to differentiate bankrupt firms and the steady companies. The rating assessment of the enterprise – the borrower pays off on the basis of the received values of financial coefficients and is expressed in points. Points are estimated by multiplication of value of any indicator by its weight in an integrated indicator.

  1. Assessment of solvency of the borrower by means of a decision tree

  The scheme a tree decisions is very similar to the scheme a tree probabilities. It use, when it is necessary to make some decisions in the conditions of uncertainty, when each decision depends on an outcome previous or outcomes of tests. Making a tree decisions, it is necessary to draw trunk and branch, problems displaying structure. Trees from left to right settle down. Branches designate possible alternative decisions which can be are accepted, and the possible outcomes resulting these decisions. On the scheme we use two types of branches: the first – the dashed lines connecting squares of possible decisions, the second – the continuous lines connecting circles possible outcomes. Square knots designate places where the decision is made, round knots – emergence of outcomes. As making the decision canʼt influence emergence of outcomes, it needs to calculate only probability them emergence.

  When all decisions and their outcomes are specified a tree, each of options, and miscalculates at the end its monetary income is put down. All expenses caused by the decision, are put down on corresponding of a branch. Prompt development of information technologies, in particular, progress in methods of collecting, storage and processing data I allowed many organizations to collect huge data files which need to be analyzed. Volumes of these data are so great that opportunities of experts any more donʼt suffice that generated demand for methods automatic research (analysis) of data which constantly increases every year. Trees of decisions – one of such methods of the automatic analysis of data. Trees of decisions is a way of representation I governed in hierarchical, consecutive structure, where to everyone to object there corresponds the only knot giving the decision.

  The scope of trees of decisions is wide now, but all tasks solved by this device can be united in the following three classes:

  1. Description of data: trees of decisions allow to store information on data in a compact form, instead of them we can store a tree of decisions which contains the exact description of objects.

  2. Classification: trees of decisions perfectly cope with problems of classification, reference of objects to one of in advance known classes. The target variable has to have discrete values.

  3. Regression: if the target variable has continuous values, trees of decisions allow to establish dependence of a target variable on independent (entrance) variables. For example, problems of numerical forecasting (a prediction of values of a target variable) belong to this class.

  For creation of a tree on each internal knot it is necessary to find such condition (check) which would break the set associated with this knot on subsets. As such check one of attributes has to be chosen. The general rule for a choice of attribute can be formulated as follows: the chosen attribute has to break a set so that received as a result of a subset consisted of the objects belonging to one class, or were most approached to it. the amount of objects from other classes (of impurity) in each of these sets was as little as possible.

  Trees of decisions are the fine tool in systems of support of decision – making, the intellectual analysis of data (data mining). The structure of many packages intended for the intellectual analysis of data, already included methods of creation of trees of decisions. In areas where the mistake price is high, they will serve as excellent help of the analyst or the head. Trees of decisions are successfully applied to the solution of practical tasks in following banking area for an assessment of solvency of clients of bank at delivery of the credits.

  2. Assessment of solvency of the borrower by means of Altmanʼs model

  Calculation and analysis of dynamics of the financial resources which are at disposal of the enterprise, in total amount and in a section of the main groups allow to draw only the most general conclusions about it property status. The following analytical procedure is the vertical analysis: other representation of a form of account, in details of balance, in the form of relative indicators. Such representation allows to see specific weight each article of balance in the general result. Obligatory element of the analysis – dynamic ranks of these sizes, by means of which it is possible to trace and predict structural changes in structure of assets and sources of their covering.

  Can estimate the Financial condition of the organization from the point of view of short – term and long-term prospect. In the first case criterion of an assessment-liquidity and solvency of the enterprise, that is ability in due time and in full to make calculations for short-term obligations. Examples of similar operations-calculations with workers on compensation, with suppliers for the received inventory items and the rendered services, with bank according to loans, etc.

  The Assessment of stability of activity of the enterprise in long-term prospect is connected by p with the general financial structure the organizations, degree of its dependence on external creditors and investors, conditions on which are attracted and external sources of means are served.

  There are various techniques of the analysis of a financial state. In our country by experience of economically developed countries the technique based on calculation and use in the existential gains ground analysis of system of coefficients. Indicators can be calculated directly according to accounting reports. However it is more convenient to transform balance by aggregation of articles and their regrouping: in an asset-on extent of decrease liquidities of assets, in a passive-extent of increase of maturity dates of obligations. Such approach is more convenient as in the computing plan, and from a position of understanding of logic of calculation.

  

  Fig. 2. The package of accompanying documents
  (animation: 8 frames, 3 cycles of repeating, 42 kilobytes)

  For a bank-creditor financial solvency of borrower is important so far as he bargains in time to get the sum and percent back given out as a credit on it. Solvency is ability (presence of possibility) and readiness (presence of desire) of legal or physical entity in good time and in full to pay off the bills of debt.

  Difference from it solvency is ability and readiness in good time and in full to liquidate the credit debts (capital amount of debt and percents). Solvency – a concept is more narrow, than solvency. To decide to give out a credit this borrower, a bank is enough to make sure in his solvency, not necessarily examining a question in more wide plan. A borrower gives in a bank the copies of next accompanying documents, presented on (Fig. 2).

  3. Assessment of solvency of the borrower with use of the device of fuzzy logic

  Now, in the conditions of crisis of the banking system, one of actual tasks the assessment is solvency of the bank clients which decision promotes receiving the maximum profit from the concluded bargains on granting the credits and exception of possibility of financial losses. Existing techniques of an assessment of solvency of borrowers in the majority are based on the analysis of the expert estimates which bring a certain subjective error in the estimation mechanism. The device of the theory of the indistinct sets, been the basis for the model developed in this work, allows to find the solution of this problem in the conditions of uncertainty, and also weak structure of estimated indicators, without resorting to application of expert estimates.

  The Main advantage of use of this device consists in possibility of creation of quantitative estimates for linguistic variables, and also effective display dependences between these variables in the form of indistinct rules.

  For the solution of a problem of an assessment of a financial solvency of the borrower with use of the device of fuzzy logic it is developed also the model of an indistinct logical conclusion in the environment of MATLAB is realized. The realization of indistinct modeling in the environment of MATLAB is enabled with use of a package of the Fuzzy Logic expansion Toolbox in which tens functions of fuzzy logic, an indistinct conclusion and classification, with opportunity are realized their integration in Simulink. Convenient FIS-the editor who contains all necessary tools for is used realization of the functional display entrances – exits on the basis of an indistinct logical conclusion. Systems of an indistinct logical conclusion will transform values of entrance variables of management process during week-end variables on the basis of use of indistinct rules.

  In this work the indistinct model with the following entrance variables was developed:

  • profitability of the cumulative capital;
  • coefficient of the current liquidity;
  • coefficient of financial independence.

  Output variable:

  • assessment of level of solvency.

  The received assessment is a basis for decision-making by the management of bank on granting credit to potential clients. In all entrance variables terms are distributed on function Gaussʼs accessories which most precisely describes dynamics of change of an assessment of input parameters.

  Algorithm of an indistinct conclusion of Mamdani – one of possible versions of the decision considered in this to problem work. As the main stages of this method it is possible to allocate the following sequence operations: fazzifikation of input parameters; creation of the knowledge base; definition of the resultant indistinct sets; defazzifikation.

  
  

  Fig. 3. Scheme of an indistinct logical conclusion

  In quality term-set of the first entrance variable Profitability of the Cumulative Capital the set is used: T1 = {Bad, Normal, Excellent} Numerical value of a variable [0,1].

  In quality the term-sets of the second entrance variable Coefficient of the Current Liquidity is used by p a set: T2 = {Bad, Normal, Excellent}. Numerical value of a variable belongs to an interval [0,3].

  In quality the term-sets of the third entrance variable Autonomy Coefficient is used by a set: T3 = {Bad, Normal , Excellent}. Numerical value of a variable belongs to an interval [0,1].

  In an output variable terms are distributed by p on triangular function of accessory since this function most fully describes change of an assessment of output parameter. In quality Assessment variable term-set solvency use a set: M = {Bad, Normal, Excellent}. Numerical value day off variable [0,100].

  After the announcement of entering variables fazzifikation procedure – assignment to variables of terms is carried out (linguistic values) from a term-sets, according to their numerical values and accessory functions. Defazzifikation – procedure the return this, is result of its performance transformation of the linguistic values of an output variable in the numerical.

  

  Fig. 4. General view of model

  

  Fig. 5. Function of accessory of the variable Profitability of the Cumulative Capital

  

  Fig. 6. Function of accessory of the variable Autonomy Coefficient

  

  Fig. 7. Function of accessory of the variable Solvency Assessment

  

  Fig. 8. Visualization of a surface entrances – exits

  At creation of base of rules that its main objective in this model, is establishment of weight coefficient of each entrance indicator according to the D. Durant method is considered. On the basis of a linguistic assessment, this model forms an accurate numerical assessment of input parameter according to its function of distribution. Then using the received numerical values of all entering variables, by means of base of rules, the total assessment of solvency of the client is removed.

  The conducted researches showed that complex use of system of an indistinct logical conclusion in systems supports of decision-making by banks for an assessment of level of solvency, promotes speed and accuracy increase decision – making due to automation of processing of arriving semistructured information. Model simplifies processing of indistinct linguistic information and doesnʼt demand direct participation of the expert.

  Conclusions

  The developed technique of an assessment of solvency and quality management of a credit portfolio can be applied in various bank organizations realizing programs for crediting.

  World and domestic banking practice allowed to allocate criteria of solvency of the client: character of the client, ability to borrow means, ability to earn means during the current activity for debt repayment (financial opportunities), the capital, providing the credit, a condition in which business deal, control (a legislative basis of activity of the borrower, compliance of character of the loan to standards of bank and supervision bodies) is made. The enterprise and in the American technique is versatily estimated. Here such indicators as profitability of firm which are somewhat capable to compensate dependence of the enterprise on borrowed funds are allocated. Also in techniques of the American banks the greatest interest is given to qualitative characteristics, such as character of the borrower, ability to borrow means. Control of activity of the borrower is still made. In this work the device of fuzzy logic for an assessment of a financial solvency of clients is used when granting the bank credit, MATLAB realized by means. MATLAB allows to define at existence of rather big base degrees of the importance of these or those factors at an assessment of solvency of borrowers that it is possible to use subsequently in the analysis of the new borrower, and also the hidden communications which not always can be allocated logically.

  Decade of activity of commercial banks in Ukraine yet doesnʼt allow to speak about existence of enough of the internal information necessary for an effective assessment of solvency of the borrower. In such conditions use of external independent sources of information is expedient. Domestic banks have to rely more on external sources of information, and in case of lack of those to initiate their emergence.

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