This thesis is concerned with statistical aspects of credit scoring, the process of determining how likely an applicant for credit is to default with repayments. In Chapters 1-4 a detailed introduction to credit scoring methodology is presented, including evaluation of previous published work on credit scoring and a review of discrimination and classification techniques. In Chapter 5 we describe different approaches to measuring the absolute and relative performance of credit scoring models. Two significance tests are proposed for comparing the bad rate amongst the accepts (or the error rate) from two classifiers. In Chapter 6 we consider different approaches to reject inference, the procedure of allocating class membership probabilities to the rejects. One reason for needing reject inference is to reduce the sample selection bias that results from using a sample consisting only of accepted applicants to build new scorecards. We show that the characteristic vectors for the rejects do not contain information about the parameters of the observed data likelihood, unless extra information or assumptions are included. Methods of reject inference which incorporate additional information are proposed. In Chapter 7 we make comparisons of a range of different parametric and nonparametric classification techniques for credit scoring: linear regression, logistic regression, projection pursuit regression, Poisson regression, decision trees and decision graphs. We conclude that classifier performance is fairly insensitive to the particular technique adopted. In Chapter 8 we describe the application of the k-NN method to credit scoring. We propose using an adjusted version of the Eucidean distance metric, which is designed to incorporate knowledge of class separation contained in the data. We evaluate properties of the k-NN classifier through empirical studies and make comparisons with existing techniques.

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Ph.D. (Mathematical Statistics) / This thesis considers the modelling and prediction of consumer credit risk events. We model consumer credit risk events (like a missed payment, a repayment or a default) by means of a discrete, real time, staggered entry counting process. Merton s (1974) structural approach is the foundation of numerous credit-risk models, as well as the Basel capital accords. The underlying assumptions of this approach are that both liability and asset levels are observable to some extent and that default, which occurs if liability levels are larger than asset levels, can occur only once. These assumptions are inappropriate for consumer credit risk, where asset and liability levels are not observable and multiple defaults may occur. We nd that the so-called reduced-form models initially developed by Artzner and Delbaen (1995) and Jarrow and Turnbull (1995), which impose no structure on the default event, are better suited to model and predict consumer credit risk. All reduced-form models can be represented as counting processes. Counting processes are continuous in nature, so we discretize these processes before applying them to the regularly spaced, discrete monthly data. We show that the use of survival analysis tech- niques such as Cox s (1972) proportional hazard model, which is a special case in counting processes, are not well suited to model credit risk. This is because survival analysis is mostly concerned with the prediction of the time until a single event occurs. Accordingly, in survival analysis the time domain used is event time . Hence, all observations need to be aligned to some starting time. We prefer to work in calendar time and are concerned with the timing (in calendar time) of multiple events. We identify and implement a dynamic, discrete statistical model based on calendar time that accounts for staggered entries, multiple entries into and exits from the portfolio, as well as multiple default events on an account level. This approach, from Arjas and Haara (1987), makes use of both idiosyncratic and systematic covariates, which facilitates stress-testing. This approach has, to our knowledge, never been applied to credit risk before and we apply it to a mortgage loan portfolio of a major bank in South Africa.

The thesis covers aspects of the law relating to letters of credit. It deals with the operation of letters of credit with particular reference to the doctrine of strict compliance, the principle of independence, the fraud exception and conflict of laws. According to the principle of independence, banks must make payment in terms of the letter of credit irrespective of any dispute that may exist between the buyer and the seller in an underlying contract or other contracts. Although the principle of independence is clearly established, it is not absolute. An exception occurs in the case of fraud. Thus, if the seller has committed fraud, such as tendering forged documents, the buyer can instruct the bank not to make payment in terms of the credit. If the bank refuses to dishonour the letter of credit, the buyer can apply to a court to interdict the bank from making payment. In South African law the buyer must establish that the seller was party to fraud in relation to the documents presented to the bank for payment before the court can grant an interdict. This thesis also examines the standard of proof of fraud required in letters of credit transactions and proposes a standard of proof which will not unduly favour the seller whose good faith is in dispute. The fast growing technology of computers and telecommunications is rapidly changing the methods of transacting business by paper documentation and letter of credit transactions are no exception. At present the buyer can apply to the bank to issue a letter of credit through the computer and banks also communicate letter of credit transactions through computer networks. However, the beneficiary still has to present documents to the bank for payment in paper form. It is proposed that the Uniform Custom and Practice For Documentary Credits (UCP) be amended to provide for fully computerised letters of credit transactions. Another objective of the thesis is to examine the doctrine of strict compliance. In terms of the doctrine of strict compliance documents presented under the credit must comply strictly with the requirements set out in the credit. If banks are satisfied that the documents presented by the seller strictly conform with the requirements of the credit they are obliged to make payment as required by the credit. It is proposed that the doctrine of strict compliance should not be applied strictly. In other words, the banks should make payment in terms of the credit if the discrepancy in the documents is trivial. The thesis also covers conflict of laws issues. As the UCP does not have rules dealing with conflict of laws, most jurisdictions have developed their own rules to be applied by the courts in cases of conflict of laws. The thesis examines the different rules of conflict of laws as developed and practiced by different jurisdictions.

The influence of the Nation Credit Act should not be underestimated as it has shifted the focus from contractual freedom between parties to protecting consumers. The Act changed the entire approach when contracting parties enter into credit agreements from initially doing so spontaneously, to now contracting with the utmost care whilst taking the protection of consumers into account. The Act provides specific protection for consumers by enabling those who seek debt relief measures, to apply for a debt review order to restructure their debt by means of a court order or negotiation talks with credit providers. Although protection of consumers is much needed in today’s economic climate the reality of the matter is that a valid agreement came into being between the consumer and the credit provider and by protecting the consumer and not enabling the credit provider to enforce its rights against a consumer brings an imbalance in the contractual relationship between the two parties. This dissertation focuses on the balancing of rights between the consumer and credit provider in the event where the consumer applies for debt review and the credit provider terminates the debt review in order to enforce the agreement. Initially two schools of thought, with contradicting viewpoints, were formed with regards to this issue by means of case law and addressed the question whether the consumer or the credit provider’s rights should be the determining factor when it comes to the enforcement of a credit agreement. The Supreme Court Appeal gave legal certainty on how the rights of the two parties need to be balanced by focussing on procedural correctness, good faith and honouring the agreement between the parties and giving absolute discretion to the courts in weighing the parties’ rights and bringing them into balance. Debt review is an improvement on previous debt relief measures in South Africa and especially in today’s economic climate the debt review procedure enables consumers to financially survive over-indebtedness, however, the relief brought to consumers by the debt review process is not absolute as credit providers’ rights need to be taken into account to balance the financial relationship between the two parties and will always have to take into account that a valid agreement came into being between a credit provider and consumer. Although the Act assists consumers who find themselves in an over-indebted situation by possible restructuring of obligations, the credit provider’s rights will have to be taken into account. Although protection of the consumer is priority section 3(d) of the Act states that one of the purposes of the Act is to promote equity in the credit market between the credit provider and consumer and balancing their respective rights and responsibilities. Only by means of balancing the rights of consumers and credit provider’s we will establish a sound credit market. Copyright / Dissertation (LLM)--University of Pretoria, 2012. / Mercantile Law / unrestricted

This thesis aims to chart and explain the evolution of credit practices and the law’s reaction to them vis-à-vis the protection of borrowers between 1700 and 1974. The cat-and-mouse game played out between the credit industry and the legislature, and the longstanding tension between the credit needs of the commercial community and those of the small private borrower are of central importance. This thesis is primarily historical rather than theoretical; it seeks to describe and explain legal developments over time. But, in order to illuminate this development, the law will be viewed through the lens of a simple analytical framework based on the dichotomy between public law regulation, on the one hand, and the private law of contract, on the other. Viewed through this lens, it should be possible to position the law at any given stage of its development at a particular point on a scale of ‘regulatoriness’. The framework within which these rules were originally developed was, of course, neither intentionally nor self-consciously theoretical, but that is not to say that a theoretical framework lacks utility in legal historical inquiry.

Credit scoring is a mechanism used to quantify the risk factors relevant for an obligor’s ability and willingness to pay. Credit scoring has become the norm in modern banking, due to the large number of applications received on a daily basis and the increased regulatory requirements for banks. In this study, the concept and application of credit scoring in a South African banking environment is explained, with reference to the International Bank of Settlement’s regulations and requirements. The steps necessary to develop a credit scoring model is looked at with focus on the credit risk context, but not restricted to it. Applications of the concept for the whole life cycle of a product are mentioned. The statistics behind credit scoring is also explained, with particular emphasis on logistic regression. Linear regression and its assumptions are first shown, to demonstrate why it cannot be used for a credit scoring model. Simple logistic regression is first shown before it is expanded to a multivariate view. Due to the large number of variables available for credit scoring models provided by credit bureaus, techniques for reducing the number of variables included for modeling purposes is shown, with reference to specific credit scoring notions. Stepwise and best subset logistic regression methodologies are also discussed with mention to a study on determining the best significance level for forward stepwise logistic regression. Multinomial and ordinal logistic regression is briefly looked at to illustrate how binary logistic regression can be expanded to model scenarios with more than two possible outcomes, whether on a nominal or ordinal scale. As logistic regression is not the only method used in credit scoring, other methods will also be noted, but not in extensive detail. The study ends with a practical application of logistic regression for a credit scoring model on data from a South African bank. Copyright / Dissertation (MSc)--University of Pretoria, 2010. / Mathematics and Applied Mathematics / unrestricted

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<p>Credit risk is the risk of losses due to the failure to fulfil the obliged payment from a debtor or a counterparty. It is one of the three major components of risks that a bank faces as defined in the new Basel Accord. The credit risk literature has experienced similar rapid growth as the credit market itself. There are currently four different approaches to analyzing credit risk: structural, reduced-form, incomplete information and hybrid models. Even though there are large volumes of published research papers and books on credit risk, our understanding and management skills in this area are still very limited as evidenced by the recent crash of the subprime market. This thesis combines three working papers on credit risk modeling and aims at adding some insights and contributions to the current credit risk literature.</p><p>In the first paper, we propose to randomize the initial condition of a generalized structural model, where the solvency ratio instead of the asset value is modeled explicitly. This initial randomization assumption is motivated by the fact that market players cannot observe the solvency ratio accurately. We find that positive short spreads can be produced due to imperfect observation on the risk factor. The two models we have considered, the Randomized Merton (RM)-II and the Randomized Black-Cox (RBC)-II, both have explicit expressions for Probability of Default (PD), Loss Given Default (LGD) and Credit Spreads (CS). In the RM-II model, both PD and LGD are found to be of order of √T, as the maturity T approaches zero. It therefore provides an example that has no well-defined default intensity but still admits positive short spreads. In the RBC-II model, the positive short spread is generated through the positive default intensity of the model. Because explicit formulas are available, these two Randomized Structure (RS) models are easily implemented and calibrated to the market data. This is illustrated by a calibration exercise on Ford Motor Corp. Credit Default Swap (CDS) spread data.</p> <p>In the second paper, we introduce the inverse-CIR (iCIR) intensity model of credit risk. A multi-firm intensity-based model is constructed where negative correlations are built through the negative correlation between the Cox-Ingersoll-Ross (CIR) process and its inverse. This parsimonious setting allows us to form rich correlation structures among short spreads of different firms, while keeping nonnegative conditions for interest rates and short spreads. The bond prices are given by explicit expressions involving confluent hypogeometric functions. This model can be regarded as an extension of the Ahn & Gao (1999) one factor iCIR model on interest rates to a multi-factor framework on credit risk.</p> <p> In the third paper, we derive several forms of the equity volatility as a function of the equity value, from the structural credit risk literature. We then propose a new jump to default model by taking the equity volatility to be of the form implied by the models of Leland (1994) and Leland & Toft (1996). This model involves a process we call the Dual-Jacobi process and which has explicit formulae for its moments. Gram-Charlier expansions are then applied to approximate bond and call prices. Our model generalizes Linetsky (2006) by incorporating a local volatility which is bounded below by a positive constant. This local volatility will decrease to a positive constant for increasing stock prices, making the stock process asymptotic to Geometric Brownian Motion (GBM). In this sence, our model is more realistic than Constant Elasticity of Variance (CEV) models.</p> / Thesis / Doctor of Philosophy (PhD)

Final qualification work (master thesis) investigates the theoretical and methodological framework for an integrated approach to the organization of credit process in commercial banks at the modern stage. The need for research is that effective organization of the credit process helps to avoid many risks and maximize the profit of the disbursed loan funds. The relevance of the research lies in the fact that lending to individuals and legal entities is one of the main sources of income of commercial Bank. In a rapidly changing banking environment to work on the current principles and types of lending getting more difficult, because the competitors appear more attractive offers. But the Bank such as Sberbank, it is necessary not only to follow the trends, but also to be attentive to all risks, maintaining a balance between the availability of credit and guarantee their repayment. / Выпускная квалификационная работа (магистерская диссертация) посвящена исследованию теоретической и методологической базы для комплексного подхода к организации кредитного процесса в коммерческом банке на современном этапе. Необходимость научного исследования заключается в том, что эффективная организация кредитного процесса помогает избежать возникновения многих рисков и обеспечить максимальную прибыль от выданных в кредит денежных средств. Актуальность научного исследования заключается в том, что кредитование физических и юридических лиц является одним из основных источников доходов коммерческого банка. В условиях динамично меняющейся банковской среды работать по сложившимся принципам и видам кредитования становится сложнее, т.к. у конкурентов появляются все более привлекательные предложения. Но такому банку, как Сбербанк, необходимо не только следовать тенденциям, но и внимательно относиться ко всем рискам, соблюдая баланс между доступностью кредитов и гарантией их возвратности.