Preface xi
About the authors xiii
1 The emergence of credit ratings tools 1
2 Classifications and key concepts of credit risk 5
2.1 Classification 5
2.1.1 Default mode and value-based valuations 5
2.1.2 Default risk 6
2.1.3 Recovery risk 7
2.1.4 Exposure risk 8
2.2 Key concepts 8
2.2.1 Expected losses 8
2.2.2 Unexpected losses, VAR, and concentration risk 9
2.2.3 Risk adjusted pricing 13
3 Rating assignment methodologies 17
3.1 Introduction 17
3.2 Experts-based approaches 19
3.2.1 Structured experts-based systems 19
3.2.2 Agencies’ ratings 22
3.2.3 From borrower ratings to probabilities of default 26
3.2.4 Experts-based internal ratings used by banks 31
3.3 Statistical-based models 32
3.3.1 Statistical-based classification 32
3.3.2 Structural approaches 34
3.3.3 Reduced form approaches 38
3.3.4 Statistical methods: linear discriminant analysis 41
3.3.5 Statistical methods: logistic regression 54
3.3.6 From partial ratings modules to the integrated model 58
3.3.7 Unsupervised techniques for variance reduction and variables’ association 60
3.3.8 Cash flow simulations 73
3.3.9 A synthetic vision of quantitative-based statistical models 76
3.4 Heuristic and numerical approaches 77
3.4.1 Expert systems 78
3.4.2 Neural networks 81
3.4.3 Comparison of heuristic and numerical approaches 85
3.5 Involving qualitative information 86
4 Developing a statistical-based rating system 93
4.1 The process 93
4.2 Setting the model’s objectives and generating the dataset 96
4.2.1 Objectives and nature of data to be collected 96
4.2.2 The time frame of data 96
4.3 Case study: dataset and preliminary analysis 97
4.3.1 The dataset: an overview 97
4.3.2 Duplicate cases analysis 103
4.3.3 Missing values analysis 104
4.3.4 Missing value treatment 107
4.3.5 Other preliminary overviews 109
4.4 Defining an analysis sample 114
4.4.1 Rationale for splitting the dataset into an analysis sample and a validation sample 114
4.4.2 How to split the dataset into an analysis sample and a validation sample 114
4.5 Univariate and bivariate analyses 116
4.5.1 Indicators’ economic meanings, working hypotheses and structural monotonicity 117
4.5.2 Empirical assessment of working hypothesis 130
4.5.3 Normality and homogeneity of variance 137
4.5.4 Graphical analysis 140
4.5.5 Discriminant power 145
4.5.6 Empirical monotonicity 157
4.5.7 Correlations 160
4.5.8 Analysis of outliers 162
4.5.9 Transformation of indicators 164
4.5.10 Summary table of indicators and short listing 177
4.6 Estimating a model and assessing its discriminatory power 184
4.6.1 Steps and case study simplifications 184
4.6.2 Linear discriminant analysis 185
4.6.3 Logistic regression 210
4.6.4 Refining models 216
4.7 From scores to ratings and from ratings to probabilities of default 229
5 Validating rating models 237
5.1 Validation profiles 237
5.2 Roles of internal validation units 239
5.3 Qualitative and quantitative validation 241
5.3.1 Qualitative validation 242
5.3.2 Quantitative validation 249
6 Case study: Validating PanAlp Bank’s statistical-based rating system for financial institutions 257
6.1 Case study objectives and context 257
6.2 The ‘Development report’ for the validation unit 258
6.2.1 Shadow rating approach for financial institutions 258
6.2.2 Missing value analysis 259
6.2.3 Interpreting financial ratios for financial institutions and setting working hypotheses 260
6.2.4 Monotonicity 263
6.2.5 Analysis of means 263
6.2.6 Assessing normality of distributions: histograms and normal Q–Q plots 263
6.2.7 Box plots analysis 266
6.2.8 Normality tests 267
6.2.9 Homogeneity of variance tests 269
6.2.10 F-ratio and F-Test 270
6.2.11 ROC curves 270
6.2.12 Correlations 270
6.2.13 Outliers 270
6.2.14 Short listing and linear discriminant analysis 272
6.3 The ‘Validation report’ by the validation unit 274
7 Ratings usage opportunities and warnings 285
7.1 Internal ratings: critical to credit risk management 285
7.2 Internal ratings assignment trends 289
7.3 Statistical-based ratings and regulation: conflicting objectives? 291
7.4 Statistical-based ratings and customers: needs and fears 295
7.5 Limits of statistical-based ratings 298
7.6 Statistical-based ratings and the theory of financial intermediation 305
7.7 Statistical-based ratings usage: guidelines 310
Bibliography 315
Index 321
