GIACOMO DE LAURENTIS, Department of Finance and SDA Bocconi School of Management, Bocconi University, Italy.RENATO MAINO, Lecturer, Bocconi University and Turin University, Italy.LUCA MOLTENI, Department of Economics and SDA Bocconi School of Management, Bocconi University, Italy.

• Preface xiAbout the authors xiii1 The emergence of credit ratings tools 12 Classifications and key concepts of credit risk 52.1 Classification 52.1.1 Default mode and value-based valuations 52.1.2 Default risk 62.1.3 Recovery risk 72.1.4 Exposure risk 82.2 Key concepts 82.2.1 Expected losses 82.2.2 Unexpected losses, VAR, and concentration risk 92.2.3 Risk adjusted pricing 133 Rating assignment methodologies 173.1 Introduction 173.2 Experts-based approaches 193.2.1 Structured experts-based systems 193.2.2 Agencies’ ratings 223.2.3 From borrower ratings to probabilities of default 263.2.4 Experts-based internal ratings used by banks 313.3 Statistical-based models 323.3.1 Statistical-based classification 323.3.2 Structural approaches 343.3.3 Reduced form approaches 383.3.4 Statistical methods: linear discriminant analysis 413.3.5 Statistical methods: logistic regression 543.3.6 From partial ratings modules to the integrated model 583.3.7 Unsupervised techniques for variance reduction and variables’ association 603.3.8 Cash flow simulations 733.3.9 A synthetic vision of quantitative-based statistical models 763.4 Heuristic and numerical approaches 773.4.1 Expert systems 783.4.2 Neural networks 813.4.3 Comparison of heuristic and numerical approaches 853.5 Involving qualitative information 864 Developing a statistical-based rating system 934.1 The process 934.2 Setting the model’s objectives and generating the dataset 964.2.1 Objectives and nature of data to be collected 964.2.2 The time frame of data 964.3 Case study: dataset and preliminary analysis 974.3.1 The dataset: an overview 974.3.2 Duplicate cases analysis 1034.3.3 Missing values analysis 1044.3.4 Missing value treatment 1074.3.5 Other preliminary overviews 1094.4 Defining an analysis sample 1144.4.1 Rationale for splitting the dataset into an analysis sample and a validation sample 1144.4.2 How to split the dataset into an analysis sample and a validation sample 1144.5 Univariate and bivariate analyses 1164.5.1 Indicators’ economic meanings, working hypotheses and structural monotonicity 1174.5.2 Empirical assessment of working hypothesis 1304.5.3 Normality and homogeneity of variance 1374.5.4 Graphical analysis 1404.5.5 Discriminant power 1454.5.6 Empirical monotonicity 1574.5.7 Correlations 1604.5.8 Analysis of outliers 1624.5.9 Transformation of indicators 1644.5.10 Summary table of indicators and short listing 1774.6 Estimating a model and assessing its discriminatory power 1844.6.1 Steps and case study simplifications 1844.6.2 Linear discriminant analysis 1854.6.3 Logistic regression 2104.6.4 Refining models 2164.7 From scores to ratings and from ratings to probabilities of default 2295 Validating rating models 2375.1 Validation profiles 2375.2 Roles of internal validation units 2395.3 Qualitative and quantitative validation 2415.3.1 Qualitative validation 2425.3.2 Quantitative validation 2496 Case study: Validating PanAlp Bank’s statistical-based rating system for financial institutions 2576.1 Case study objectives and context 2576.2 The ‘Development report’ for the validation unit 2586.2.1 Shadow rating approach for financial institutions 2586.2.2 Missing value analysis 2596.2.3 Interpreting financial ratios for financial institutions and setting working hypotheses 2606.2.4 Monotonicity 2636.2.5 Analysis of means 2636.2.6 Assessing normality of distributions: histograms and normal Q–Q plots 2636.2.7 Box plots analysis 2666.2.8 Normality tests 2676.2.9 Homogeneity of variance tests 2696.2.10 F-ratio and F-Test 2706.2.11 ROC curves 2706.2.12 Correlations 2706.2.13 Outliers 2706.2.14 Short listing and linear discriminant analysis 2726.3 The ‘Validation report’ by the validation unit 2747 Ratings usage opportunities and warnings 2857.1 Internal ratings: critical to credit risk management 2857.2 Internal ratings assignment trends 2897.3 Statistical-based ratings and regulation: conflicting objectives? 2917.4 Statistical-based ratings and customers: needs and fears 2957.5 Limits of statistical-based ratings 2987.6 Statistical-based ratings and the theory of financial intermediation 3057.7 Statistical-based ratings usage: guidelines 310Bibliography 315Index 321

GIACOMO DE LAURENTIS, Department of Finance and SDA Bocconi School of Management, Bocconi University, Italy.RENATO MAINO, Lecturer, Bocconi University and Turin University, Italy.LUCA MOLTENI, Department of Economics and SDA Bocconi School of Management, Bocconi University, Italy.

• Preface xiAbout the authors xiii1 The emergence of credit ratings tools 12 Classifications and key concepts of credit risk 52.1 Classification 52.1.1 Default mode and value-based valuations 52.1.2 Default risk 62.1.3 Recovery risk 72.1.4 Exposure risk 82.2 Key concepts 82.2.1 Expected losses 82.2.2 Unexpected losses, VAR, and concentration risk 92.2.3 Risk adjusted pricing 133 Rating assignment methodologies 173.1 Introduction 173.2 Experts-based approaches 193.2.1 Structured experts-based systems 193.2.2 Agencies’ ratings 223.2.3 From borrower ratings to probabilities of default 263.2.4 Experts-based internal ratings used by banks 313.3 Statistical-based models 323.3.1 Statistical-based classification 323.3.2 Structural approaches 343.3.3 Reduced form approaches 383.3.4 Statistical methods: linear discriminant analysis 413.3.5 Statistical methods: logistic regression 543.3.6 From partial ratings modules to the integrated model 583.3.7 Unsupervised techniques for variance reduction and variables’ association 603.3.8 Cash flow simulations 733.3.9 A synthetic vision of quantitative-based statistical models 763.4 Heuristic and numerical approaches 773.4.1 Expert systems 783.4.2 Neural networks 813.4.3 Comparison of heuristic and numerical approaches 853.5 Involving qualitative information 864 Developing a statistical-based rating system 934.1 The process 934.2 Setting the model’s objectives and generating the dataset 964.2.1 Objectives and nature of data to be collected 964.2.2 The time frame of data 964.3 Case study: dataset and preliminary analysis 974.3.1 The dataset: an overview 974.3.2 Duplicate cases analysis 1034.3.3 Missing values analysis 1044.3.4 Missing value treatment 1074.3.5 Other preliminary overviews 1094.4 Defining an analysis sample 1144.4.1 Rationale for splitting the dataset into an analysis sample and a validation sample 1144.4.2 How to split the dataset into an analysis sample and a validation sample 1144.5 Univariate and bivariate analyses 1164.5.1 Indicators’ economic meanings, working hypotheses and structural monotonicity 1174.5.2 Empirical assessment of working hypothesis 1304.5.3 Normality and homogeneity of variance 1374.5.4 Graphical analysis 1404.5.5 Discriminant power 1454.5.6 Empirical monotonicity 1574.5.7 Correlations 1604.5.8 Analysis of outliers 1624.5.9 Transformation of indicators 1644.5.10 Summary table of indicators and short listing 1774.6 Estimating a model and assessing its discriminatory power 1844.6.1 Steps and case study simplifications 1844.6.2 Linear discriminant analysis 1854.6.3 Logistic regression 2104.6.4 Refining models 2164.7 From scores to ratings and from ratings to probabilities of default 2295 Validating rating models 2375.1 Validation profiles 2375.2 Roles of internal validation units 2395.3 Qualitative and quantitative validation 2415.3.1 Qualitative validation 2425.3.2 Quantitative validation 2496 Case study: Validating PanAlp Bank’s statistical-based rating system for financial institutions 2576.1 Case study objectives and context 2576.2 The ‘Development report’ for the validation unit 2586.2.1 Shadow rating approach for financial institutions 2586.2.2 Missing value analysis 2596.2.3 Interpreting financial ratios for financial institutions and setting working hypotheses 2606.2.4 Monotonicity 2636.2.5 Analysis of means 2636.2.6 Assessing normality of distributions: histograms and normal Q–Q plots 2636.2.7 Box plots analysis 2666.2.8 Normality tests 2676.2.9 Homogeneity of variance tests 2696.2.10 F-ratio and F-Test 2706.2.11 ROC curves 2706.2.12 Correlations 2706.2.13 Outliers 2706.2.14 Short listing and linear discriminant analysis 2726.3 The ‘Validation report’ by the validation unit 2747 Ratings usage opportunities and warnings 2857.1 Internal ratings: critical to credit risk management 2857.2 Internal ratings assignment trends 2897.3 Statistical-based ratings and regulation: conflicting objectives? 2917.4 Statistical-based ratings and customers: needs and fears 2957.5 Limits of statistical-based ratings 2987.6 Statistical-based ratings and the theory of financial intermediation 3057.7 Statistical-based ratings usage: guidelines 310Bibliography 315Index 321