Ebook Performance of Modern Techniques for Rating Model Design
Credit risk forecasting is one of the leading topics in modern finance, as the bank regulation has made increasing use of external and internal credit ratings. One of the most important examples is the package of rules for determining the required capital for the market risk in the trading book, issued by the Basel Committee on Banking Supervision.
The discussion process that led to the June 1999 BSBS proposal for a revised international accord follow this trend on importance growing attached to the credit scoring process, culminating in a more prominent proposed role for credit ratings in the determination of overall capital for banking institution, but the problems that the regulators and practioners are facing are not few.
Most of the problems that we are facing in the credit scoring are rather technical than theoretical. In an ideal (theoretical) world, probabilities of default (PDs) could directly be assigned to obligors. In such a world the model builder would know the probability distribution of future defaults within the population of borrowers. This information is, however, unknown to the model builder a priori. Due to this data restriction, however, usually a two step approach is carried out. First, based on the past information, to infer the default risk models assign a credit score for each corporate observation, which leads towards a ranking between the contemplated corporations. Second, given the ranking, corporations are mapped to an internal grade for which a PD has to be estimated. Statistical scoring methods combine and weight individual accounting ratios to produce a measure a credit risk score that discriminates between healthy and problem firms. The most widely used statistical methods are discriminant linear analysis and logistic regression.
The classic Fisher linear discriminant analysis seeks to find a linear function of accounting variables that maximizes the differences (variance) between the two groups of firms while minimizing the differences within each group. The variables of the scoring function are generally selected among a large set of accounting ratios on the basis of their statistical significance. The coefficients of the scoring functions represent the contributions (weights) of each ratio to the overall score.
Contents
1. Introduction
2. Classification problem
- 2.1. Classification theoretical framework
2.2. Classification problem and corporate rating problem
2.3. Generalization Performance
3. Data Set Description
4. Linear Classifiers
- 4.1. Linear Regressions
4.2. Gradient Descendent
4.3. Discriminant Analysis
- 4.3.1. Linear Discriminant Analysis
5. Non Linear Classifiers
- 5.1. Quadratic Discriminant Analysis
5.2. Polynomial Regression
5.3. Logistic Regression
5.4. K-Nearest Neighbors Regression
5.5. Parzen Windows density estimator
6. Neural Networks
- 6.1. Multilayer Perceptrons
- 6.1.1. Back Propagation Training with Gradient Descendent
6.1.2. Quick Propagation
6.1.3. Scaled Conjugate Gradient
6.1.4. Stochastic Learning Process
6.1.5. Pruning Optimal Brain Surgeon
6.2. Radial Basis Neural Networks
- 6.2.1. Probabilistic Neural Networks
6.3. Learning Vector Quantization
6.4. SelfOrganized Maps
7. Conclusions and Further Research
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