Defining the probability of bank debtors’ default using financial solvency assessment models

Due implementation of debtors’ financial solvency assessment models by Ukrainian banks with the aim of calculating the probability of their default (PD) is the next step towards the integration of Ukrainian banking system into global banking community, convergence of methodical approaches to assessing the credit risk with standards of international practice, possibility of using IRB-approach (an approach based on internal ratings) for calculating the regulatory requirements to capital adequacy. The analysis of approaches to bank credit portfolio segmentation according to types of debtors and debtors’ financial solvency assessment models, depending on the performed segmentation and accumulated bank statistical data, from the point of view of its suitability for Ukrainian banks, will enable the banks to choose the most suitable ones for implementation taking into account nature and complexity of operations performed. Such approaches will be more adapted to minimum capital requirements, simultaneously agreeing with national supervisory priorities. Yana Kuznichenko (Ukraine), Mariia V. Dykha (Ukraine), Natalia Pavlova (Ukraine), Serhiy Frolov (Ukraine), Olha Hryhorash (Ukraine) BUSINESS PERSPECTIVES LLC “СPС “Business Perspectives” Hryhorii Skovoroda lane, 10, Sumy, 40022, Ukraine www.businessperspectives.org Defining the probability of bank debtors’ default using financial solvency


INTRODUCTION
Risk management methods and procedures, used by European banks, are being constantly improved and developed based on approaches and standards of Basel Committee on Banking Supervision, in particular internal assessment of parameters of losses such as debtors' probability of default (PD), loss given default (LGD) and exposure at default (EAD) (National Bank of Ukraine, 2018; Bank for International Settlements, 2005; Bank for International Settlements, 2015).
Integration of the Ukrainian banking system into the world banking community, the need for ensuring the banking system reliability and prevented capital losses require the further approximation of methodological approaches to credit risk assessment to the Basel Committee on Banking Supervision principles and recommendations (National Atomic Energy Community and their member states, on the other hand" as from September 16, 2014 No. 1678/VII (LigaZakon, 2014), and advanced international practice.
The proper implementation of debtors' solvency assessment models by Ukrainian banks to calculate their default probability (PD), which is in line with advanced international practice, will allow the banks to get close to their IRB approach (internal ratings approach) to calculate regulatory capital adequacy requirements.

LITERATURE REVIEW
Matters related to approaches to assessing the debtors' solvency, the construction of models for calculating the probability of defaulted debtors (PDs) and their embedding into the bank's risk management system, including credit, are addressed by both Ukrainian and foreign scientists.
In addition, companies providing audit, taxation, consulting, corporate finance, and risk management services focus on the issues of solvency model development.
So, the Deloitte experts (Deloitte, 2016) developed the main methodological steps for creating a credit scoring model that outlines various ways of measuring the model performance (capacity and predicted power) and provides some typical specifications that help to improve it and to interpret the model in a proper way. The purpose of the credit scoring model is to classify borrowers into "good" and "bad". In practice, this means that statistical models are needed to identify a dividing line between the two categories within explanatory variables.
Edward (2012) emphasizes the negative consequences of a lack of corporate credit rating or credit bureau, which means that the bank remains dependent on its own internal data to verify the credibility of the borrower's data, which is why the ratings for the borrower conflict with other lending institutions. The authors developed a methodology based on logistic regression modeling of corporate credit, which does not require cross-referencing data. Shkodra and Ismajli (2017) analyze the components of bank credit risk in developing countries, in particular Kosovo. The research covers seven commercial banks for the 2006-2015 period. The effect of variations in credit risk exposure deter-minants is based on the use of a multidimensional panel regression model. The empirical results obtained show significant links between credit risk and variables such as ROE and ROA, inefficiency (IE), loan-to-deposit ratio (LDR), credit growth (CG) and deposit rate (DR); at the same time, variables of solvency (SR) and credit rate (CR) are not statistically significant in terms of credit risk. Gurný and Gurný (2013) assessed the default probability of American banks through statistical models of credit scoring. Given the considered models with the use of linear discriminant analysis and regression models and taking into account the statistical significance of the estimated parameters, the authors analyzed the sample of three hundred US commercial banks, which are divided into two groups (with and without default) based on historical information. Subsequently, scoring models were applied to this sample to obtain several models for assessing the default probability and determine the most appropriate model. Genriha and Voronova (2012) classify all methods for assessing credit risk, reveal all the technical problems of the application of each method in practice, and try to evaluate which method is better. The authors use a comparative analysis to show that, in addition to the most popular parametric methods of regression and discriminatory analysis, nonparametric methods can be also used. The analysis is considered based on the assistance to banks in Latvia in preventing default risks.
Blanco-Oliver et al. (2016) also develop a mixed bankruptcy model, combining parametric and non-parametric approaches that utilize logistic regression (LR) to identify bankruptcy. Next, alternative non-parametric methods are used for companies classified as "bankrupt" or "not bankrupt". The results show that mixed models provide better performance and accuracy interpretation.
Abdou, El-Masry, and Pointon (2007) conducted a somewhat similar analysis. They assess credit risk in Egyptian banks through lending models. Three statistical methods were used: discriminatory analysis, probit analysis and logistic regression. Credit scoring is based on personal loans of one bank. The results showed that all proposed models gave a better average correct classification than one used. The expenses for incorrect classification in the event of type I and II errors are also estimated.
Al-Shawabkeh and Kanungo (2017) investigated the credit risk of individual borrowers of Jordanian banks. The authors analyzed 2,755 incomplete or inactive profiles of individual loans received from Jordanian banks during the years 1999-2014. The results show that low wage loans for the unemployed are very likely to become defaulted and contribute to non-fulfillment of credit obligations by increasing the risk of lending. In addition, it has been found that unmarried, younger borrowers and a moderate amount of credit increase the likelihood of receiving bad loans. On the contrary, borrowers employed in the private sector and undereducated ones, most likely, mitigate the credit risk.
Bunker, Naeem, and Zhang (2016) investigated how the characteristics derived from bank statements issued by applicants for loans and not claimed as an application could improve the loan scoring model for a New Zealand loan company. The authors constructed two models: a base model (based solely on existing evaluation functions obtained on the loan application form) and a model based on data obtained from the bank statement. Based on two models, a combined functional model is created. The experimental results show that the combined functional model works better than each of the two basic models, and some of the bank's functions are important for improving the loan scoring model. Borio (2011) notes that the financial crisis has led to a significant rethinking of analytical approaches and policies on financial stability, while stressing that the detection of macroeconomic roots of financial instability is underdeveloped. Tasche (2008) offers a variety of tools for measuring and testing the discriminatory power of the rating system and for testing the correct classification.
In particular, Tereshchenko (2012) investigates the procedure for determining the risk indicator for a loan granted to a legal entity using a unified rating system for debtors, which is proposed for use by a national regulator for the entire banking system. The author notes that the use of the IRBapproach by banks, which is provided for by the Basel Committee on Banking Supervision, should be the next stage in reforming the Ukrainian banking regulation system. One of the steps of this reform is, in particular, a study on the assessing the debtors' solvency models, which are most suitable for use by Ukrainian banks.
Kovalenko and Nenad (2017) pay attention to the methods of credit risk management, its influence on ensuring the solvency of banks, offer directions for improving the work with problem loans as a method of credit risk management. Dolinskyi (2016) analyzes the current trends in assessing the bank's credit risk, examines the basic indicators that characterize the lending activity of banks and the level of riskiness. Sofronova (2016) and Karminskyi (2012) consider the issue of analyzing the solvency of debtors using rating systems to differentiate debtors by level of risk based on assessing the debtors' default probability, investigate the effect of financial fac-tors on the default probability, paying particular attention to expansion of the research horizon and to nonlinear variables Kazanskyi (2016) analyzes the theoretical background for building rating systems of banks in terms of consistency with Basel standards, examines both the simplest internal ratings and more complex mechanisms of rating assessments based on the probability of default, quantitative and qualitative indicators of the corporate bank customers' activity. Stezhkin (2015) analyzes the rating systems valiidation and its individual components, considers mathematical approaches to validation and conducts a comparative analysis of alternative approaches.
That is, the problem under investigation is in its infancy, therefore, needs further study.
The purpose of this article is to analyze and justify debtors' solvency assessment models, which are the most suitable for use by banks, depending on the loan portfolio segmentation and the accumulated statistics of the individual bank, in order to calculate the default probability of debtors (PD) as one of the components of calculating the credit risk that makes direct impact on the capital of banks.

KEY RESEARCH RESULTS
In Ukrainian banking, the use and calculation of loss parameters such as probability of debtor defaults (PD), loss given default (LGD) and exposure at risk (EAD) for assessing credit risk in active banking operations are subject to regulation by the National Bank of Ukraine (LigaZakon, 2018). The regulatory acts adopted by the National Bank of Ukraine in recent years, based on the principles and recommendations of the Basel Committee on Banking Supervision (National Bank of Ukraine, 2018; Bank for International Settlements, 2005; Bank for International Settlements, 2015), formed the basis for further adaptation and improvement of the standards and approaches used by banks to assess the debtor's solvency in order to calculate the PD as one of the components of calculating the credit risk, contributed to the adequacy of such assessment and acceptability in terms of international unification of credit risk assessment procedures applied by banks.
According to the National Bank of Ukraine approaches, banks determine the value of the default probability factor (PD) of debtors, guided by judgments over their own bank experience based on reliable, continuous, complete and integral statistical data of this bank (LigaZakon, 2018). As can be seen from the scheme, a clear segmentation of the bank's loan portfolio by types of debtors is a prerequisite for an adequate assessment of the debtor's solvency and the calculation of the PD parameter. In order to meet the regulatory segmentation of assets provided by the IRB approach (Bank for International Settlements, 2005; National Securities and Stock Market Commission, 2016), it is advisable for the bank to develop its own methodology, following the principles: • structuring the loan aggregates of the bank's loan portfolio based on their relevance, taking into account certain solvency factors that may vary depending on the type of debtors (for example, the solvency of public institutions is largely influenced by mactroeconomic indicators, while for legal entities this indicator is less significant); • taking into account the properties of different data sources for different types of debtors (financial statements for legal entities, collection of related data for individuals); • taking into account the difference between the average values of the PD coefficients calculated based on the data on default debtors of the respective levels of risk and depending on the type of debtor, as well as considering such differences when determining the periodicity of the solvency assessment and the level of risk inherent in each debtor segment. Table 1 shows the best way to segment the bank's loan portfolio by type of debtors in terms of both Basel II and national regulatory requirements (LigaZakon, 2018).
The next step in the proper assessment of the debtor's solvency is the choice of a bank for the assessment model for each segment of the loan portfolio.
Generally acceptable models used in international banking practice for assessing the solvency of debtors are grouped and given in Figure 2.
Let us analyze them to determine the suitability for use by Ukrainian banks for the relevant segments of the loan portfolio.
The model suitability is the result of the bank's ability to assess the debtor's solvency to meet a number of criteria, the main of which are: finding the desired value (PD); completeness, objectivity, perception, and consistency (Bank for International Settlements, 2005, 2015). No. Since the construction of heuristic models is based on subjective empirical results of previous experience, observations and assumptions about hypothetical business relations, the debtor solvency, their expedient and efficient application for a certain segment of the bank's loan portfolio depends on the completeness and quality of the data on which they are based, the adequacy of certain factors that are the basis for the evaluation analysis, their ability to adequately reflect the subjective practical experience of the experts responsible for this bank activity.

According to national regulatory requirements (National Securities and Stock Market Commission, 2016), which comply with Basel II requirements and EU Regulation
Classical rating questionnaires -suitability is ensured through the use of justified and understandable criteria for assessing the debtor's solvency through the award procedure (higher scores for higher assessment and lower scores for lower assessment).
Qualitative systems -suitability is ensured by the availability of user instructions based on business experience, which define the conditions for assigning specific ratings/classes in accordance with the solvency characteristics, which secures credit ratings from excessive dependence on the subjective perception of the user, based on the individual level of his knowledge.
At the same time, they are quite limited in terms of objectivity and job opportunities compared to statistical models.
Expert systems may be suitable provided that they are able to ensure the acceptability of the debtors' ratings/classification by simulating the expert experience in a clear and plausible manner, that is, if the developed mechanism of logical conclusion is capable of ensuring its validity. Knowledge accumulation and shaping explanations are additional features of objectivity.
Compared to classical rating questionnaires and qualitative systems, they have more rigorous structuring and greater openness for further development and improvement.
Fuzzy logic systems simulate "fuzzy logic", and are, therefore, more complex to apply, especially in retail lending and small business lending.
Statistical models, such as those formulating hypotheses concerning the potential distribution of debtors depending on their financial capacity, require the verification, approval or rejection of such hypotheses, since the financial capacity of each debtor is determined based on empirical data. Therefore, the degree of their suitability largely depends on the empirical data quality used in the development. The quality of empirical data will be considered sufficient if they: 1) comprise a rational set of primary data that provides high representativeness, accuracy of forecasting and does not lead to the final data distortion; 2) finely take into account the features of the bank debtors segment, for which the statistical model is used.
Let's consider the types of statistical models in more detail.
Multiple discriminatory analysis is suitable for determining the rating of all debtor segments with certain limitations for qualitative data, the processing of which is problematic for this type of analysis. It is most suitable for analyzing quantitative data, for example, corporate debtors financial reporting, data on operations on debtor bank accounts for various segments of the loan portfolio, financial information received from retail debtors.
The prerequisite for applying discriminatory analysis is its compliance with general mathematical requirements, in particular the normal distribution of solvency characteristics. Then the model will show maximum discriminating power.
Regression models are suitable for all segments of the bank's loan portfolio, do not have special requirements for input data, can handle all types of quantitative and qualitative solvency characteristics, provided that sufficient data is available for each segment.
Their advantage is the ability to generate meaningful, statistically justified findings regarding default debtors, interpreting the results to the PD value, which, accordingly, simplifies the model calibration procedure.
Artificial neural networks are suitable for all segments of the loan portfolio, not having specific requirements for input, can handle all types of quantitative and qualitative solvency characteristics. At the same time, they need a much larger amount of data at the development stage than other statistical models, in order to properly communicate.
This method is unsuitable for a small sample size, with suitable models of discriminant analysis and regression.
Causal models, establishing direct analytical connections with the debtor solvency based on financial theory, do not apply statistical methods for testing hypotheses regarding the empirical data set rationality.
Option pricing models are suitable for assessing companies listed on the stock exchange or financial service providers that have necessary input parameters (market value of capital, assets volatility, etc.). Also, in the case of using models (simulation) of cash flows and additional assumptions needed for modeling, they may be suitable for estimating large companies with sufficient time series of corresponding balance sheet data and whose cash flows can be reliably calculated based on planned indicators. Input parameters should be analyzed for their adequacy.
Cash flow simulation models are suitable for assessing specialized lending, since the main source of revenues for loan repayment is the proceeds from funded assets, that is, in a situation where solvency is largely dependent on future cash flows that will be generated by these assets. Also, these models can be used as the primary data processing module in option pricing models.
The criterion for the effective use of the cash flow model (simulation) is the reliable calculation of future expected cash flows and discounting conditions. In this case, having analyzed the predictive ability of past periods, it is necessary to be sure that the data set used is typical for the bank.
Hence, heuristic models can be applied to all rating segments, but in terms of discriminatory ability, statistical models, when applied to corporate and retail clients, have a significant advantage.
Statistical models require a sufficient amount of data on debtors in default at the development stage, as well as the data representativeness. For this reason, they cannot be applied to all segments of the bank's loan portfolio (for example, data on defaults of public authorities, international companies, specialized lending operations are not enough to provide sufficient statistical models). Compared to heuristic models, they have the highest discriminatory ability. This means that heuristic models can be supplemented by statistical models.
As for causal models, they are ineffective in current economic situation in Ukraine because of the fact that there are no capital markets in Ukraine and, consequently, stock exchange prices, and because of large volumes of work with uncertain outcome.
The results on the models suitability in terms of their use by Ukrainian banks are generalized in Table 3.
In practice, these models are used in their pure form very occasionally. Therefore, while combined, heuristic and statistical models will complement each other adequately.