Development and risk quantification of internal credit rating systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
2005
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 180 S. graph. Darst. |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804135470039302144 |
|---|---|
| adam_text | Contents
List of Figures vii
List of Tables ix
Glossary xi
1 Introduction 1
1.1 Uses of internal ratings 1
1.2 Outline of analysis 3
2 2 group classification versus rating of firms 7
2.1 Introduction 7
2.2 Architecture of internal rating systems 9
2.2.1 Risk factors 12
2.2.2 Value functions 19
2.2.3 Risk factor weights 21
2.2.4 Rating assignment rule 22
2.3 Statistical credit scoring 24
2.3.1 Linear discriminant analysis 24
2.3.2 The linear probability model 27
2.3.3 Logistic regression 29
2.3.4 The logistic perceptron 31
2.4 Comparison of estimation methods 33
2.4.1 Comparison of CML and LS BP 33
2.4.2 Comparison of CML and LDA 34
2.5 A location model for combinations of risk factors 36
2.6 Monte Carlo setup 39
2.6.1 Specification of the qualitative risk factors 39
2.6.2 Specification of the quantitative risk factors 40
2.6.3 Measures of classification and rating assignment accuracy 44
iii
iv CONTENTS
2.7 Results 48
2.7.1 Accuracy of 2 group classifications 50
2.7.2 Accuracy of rating assignments 53
2.8 Concluding remarks 57
3 Estimation of transition probabilities 61
3.1 Introduction 61
3.2 Literature review 63
3.3 Methods for estimating transition intensities 64
3.3.1 The continuous time case 65
3.3.2 The discrete time case 67
3.3.3 Comparison of estimation methods 69
3.4 External versus internal rating data 69
3.4.1 The temporal difference 71
3.4.2 The monitoring intensity based difference 72
3.4.3 The internal incentive based difference 74
3.5 Implications for transition probability estimation 75
3.5.1 Implications from the temporal difference 75
3.5.2 Implications from the monitoring intensity based difference 78
3.6 A Maximum Likelihood estimation method 79
3.7 Empirical application 81
3.7.1 The data 81
3.7.2 Results 84
3.8 Concluding remarks 103
4 Missing ratings 105
4.1 Introduction 105
4.2 Inference under missing rating data 107
4.2.1 Agency problems as driving forces for missing ratings . . 108
4.2.2 Inference without assumptions concerning the missingness
mechanism 113
4.2.3 Inference when internal ratings are missing completely at
random 114
4.2.4 Inference when internal ratings are missing at random . . 116
4.2.5 Inference when internal ratings are non ignorable missing 119
4.3 Empirical application 124
4.3.1 The data and variables 124
4.3.2 Results 130
4.4 Estimation of non default transition probabilities 140
4.5 Concluding remarks 144
CONTENTS v
5 Conclusion 147
A The EM algorithm 151
A.I The case of non ignorable missingness 151
A.2 The case of data missing at random 156
B Additional tables 159
References 165
List of Figures
2.1 A possible transformation curve 22
2.2 The logistic perceptron 31
2.3 2 group classification versus assignment of ordinal rating grades . 35
2.4 Course of the difference {dif) between the estimated unconditional
error rate £(0.632) and the optimal error rate eiu for the logistic
regression (CML) and the discriminant analysis (LDA) approach
of estimating scoring model A 51
2.5 Course of the difference (dif) between the estimated unconditional
error rate S(o.632) and me optimal error rate emi for the logistic
regression (CML) and the discriminant analysis (LDA) approach
of estimating scoring model B 52
2.6 Course of the difference (dif) between the estimated unconditional
error rate S(o.632) and the optimal error rate e/,A/ for the two dis¬
criminant analysis approaches (LDA and FL/LDA) of estimating
scoring model A 53
2.7 Course of the difference (dif) between the estimated unconditional
error rate ?(o.632) and tne optimal error rate e^m for the two dis¬
criminant analysis approaches (LDA and FL/LDA) of estimating
scoring model B 54
2.8 Course of the average proportion of firms with correspondence
between true and estimated rating assignments for the three ap¬
proaches (CML, LDA and FL/LDA) of estimating scoring model
A 55
2.9 Course of the average proportion of firms with correspondence
between true and estimated rating assignments for the three ap¬
proaches (CML, LDA and FL/LDA) of estimating scoring model
B 56
vii
viii LIST OF FIGURES
2.10 Course of the average proportion of firms with a small ( 0.005)
absolute difference among true and estimated capital requirements
for the three approaches (CML, LDA and FL/LDA) of estimating
scoring model A 58
2.11 Course of the average proportion of firms with a small ( 0.005)
absolute difference among true and estimated capital requirements
for the three approaches (CML, LDA and FL/LDA) of estimating
scoring model B 59
3.1 Evolution of credit quality for a fictitious borrower over 66 months 73
4.1 Tables with complete and incomplete data 117
4.2 Estimated cumulative hazard functions 131
List of Tables
2.1 Criteria catalogues of major rating agencies and a representative bank 13
2.2 International survey of financial ratios used in credit scoring models 14
2.3 Group distance 41
2.4 Features of data samples used by Moody s 42
2.5 Parameter constellation for the 27 distinct simulation situations . . 43
2.6 Theoretical error rates 49
3.1 Different data situations and corresponding ML procedures for es¬
timating the generator of a homogeneous continuous time Markov
process 70
3.2 Risk/size distribution (1996 2002) 82
3.3 Rating distribution over time 83
3.4 Definitions of variables and hypotheses 86
3.5 Determinants of interexamination time 88
3.6 The ML estimator of the generator Q based upon discrete time ob¬
servations for the two periods 1996 2000 and 1996 2002 92
3.7 Transition probabilities: comparing estimation methods 93
3.8 Internal rating prediction model 95
3.9 Bootstrap results for the distance metric AMsvd(Pml, Pc) be¬
tween ML and cohort method 97
3.10 Characteristics of sample portfolios and calibration of portfolio
model 98
3.11 Credit risk capital: comparing estimation methods 100
3.12 Results for the test of business cycle effects and non Markov be¬
havior of transition intensities to a neighboring rating class .... 102
4.1 Different default probability estimators 125
4.2 Size distribution (all data) 126
4.3 Risk distribution (1996 2002, completely observed data) 127
ix
x LIST OF TABLES
4.4 Distribution of default events (1996 2002) 128
4.5 Rating class default probability estimates 133
4.6 The default model 134
4.7 Bootstrap results for the difference in estimates 136
4.8 The missingness model 137
4.9 The rating distribution 138
B. 1 Mean and standard deviation of area under the ROC curve (AUC)
for scoring model A and n= 1,000 160
B.2 Mean and standard deviation of area under the ROC curve (AUC)
for scoring model A and n= 10,000 161
B.3 Mean and standard deviation of area under the ROC curve (AUC)
for scoring model B and n= 1,000 162
B.4 Mean and standard deviation of area under the ROC curve (AUC)
for scoring model B and n= 10,000 163
B.5 Transition probabilities: comparing estimation methods 164
|
| adam_txt |
Contents
List of Figures vii
List of Tables ix
Glossary xi
1 Introduction 1
1.1 Uses of internal ratings 1
1.2 Outline of analysis 3
2 2 group classification versus rating of firms 7
2.1 Introduction 7
2.2 Architecture of internal rating systems 9
2.2.1 Risk factors 12
2.2.2 Value functions 19
2.2.3 Risk factor weights 21
2.2.4 Rating assignment rule 22
2.3 Statistical credit scoring 24
2.3.1 Linear discriminant analysis 24
2.3.2 The linear probability model 27
2.3.3 Logistic regression 29
2.3.4 The logistic perceptron 31
2.4 Comparison of estimation methods 33
2.4.1 Comparison of CML and LS BP 33
2.4.2 Comparison of CML and LDA 34
2.5 A location model for combinations of risk factors 36
2.6 Monte Carlo setup 39
2.6.1 Specification of the qualitative risk factors 39
2.6.2 Specification of the quantitative risk factors 40
2.6.3 Measures of classification and rating assignment accuracy 44
iii
iv CONTENTS
2.7 Results 48
2.7.1 Accuracy of 2 group classifications 50
2.7.2 Accuracy of rating assignments 53
2.8 Concluding remarks 57
3 Estimation of transition probabilities 61
3.1 Introduction 61
3.2 Literature review 63
3.3 Methods for estimating transition intensities 64
3.3.1 The continuous time case 65
3.3.2 The discrete time case 67
3.3.3 Comparison of estimation methods 69
3.4 External versus internal rating data 69
3.4.1 The temporal difference 71
3.4.2 The monitoring intensity based difference 72
3.4.3 The internal incentive based difference 74
3.5 Implications for transition probability estimation 75
3.5.1 Implications from the temporal difference 75
3.5.2 Implications from the monitoring intensity based difference 78
3.6 A Maximum Likelihood estimation method 79
3.7 Empirical application 81
3.7.1 The data 81
3.7.2 Results 84
3.8 Concluding remarks 103
4 Missing ratings 105
4.1 Introduction 105
4.2 Inference under missing rating data 107
4.2.1 Agency problems as driving forces for missing ratings . . 108
4.2.2 Inference without assumptions concerning the missingness
mechanism 113
4.2.3 Inference when internal ratings are missing completely at
random 114
4.2.4 Inference when internal ratings are missing at random . . 116
4.2.5 Inference when internal ratings are non ignorable missing 119
4.3 Empirical application 124
4.3.1 The data and variables 124
4.3.2 Results 130
4.4 Estimation of non default transition probabilities 140
4.5 Concluding remarks 144
CONTENTS v
5 Conclusion 147
A The EM algorithm 151
A.I The case of non ignorable missingness 151
A.2 The case of data missing at random 156
B Additional tables 159
References 165
List of Figures
2.1 A possible transformation curve 22
2.2 The logistic perceptron 31
2.3 2 group classification versus assignment of ordinal rating grades . 35
2.4 Course of the difference {dif) between the estimated unconditional
error rate £(0.632) and the optimal error rate eiu for the logistic
regression (CML) and the discriminant analysis (LDA) approach
of estimating scoring model A 51
2.5 Course of the difference (dif) between the estimated unconditional
error rate S(o.632) and me optimal error rate emi for the logistic
regression (CML) and the discriminant analysis (LDA) approach
of estimating scoring model B 52
2.6 Course of the difference (dif) between the estimated unconditional
error rate S(o.632) and the optimal error rate e/,A/ for the two dis¬
criminant analysis approaches (LDA and FL/LDA) of estimating
scoring model A 53
2.7 Course of the difference (dif) between the estimated unconditional
error rate ?(o.632) and tne optimal error rate e^m for the two dis¬
criminant analysis approaches (LDA and FL/LDA) of estimating
scoring model B 54
2.8 Course of the average proportion of firms with correspondence
between true and estimated rating assignments for the three ap¬
proaches (CML, LDA and FL/LDA) of estimating scoring model
A 55
2.9 Course of the average proportion of firms with correspondence
between true and estimated rating assignments for the three ap¬
proaches (CML, LDA and FL/LDA) of estimating scoring model
B 56
vii
viii LIST OF FIGURES
2.10 Course of the average proportion of firms with a small ( 0.005)
absolute difference among true and estimated capital requirements
for the three approaches (CML, LDA and FL/LDA) of estimating
scoring model A 58
2.11 Course of the average proportion of firms with a small ( 0.005)
absolute difference among true and estimated capital requirements
for the three approaches (CML, LDA and FL/LDA) of estimating
scoring model B 59
3.1 Evolution of credit quality for a fictitious borrower over 66 months 73
4.1 Tables with complete and incomplete data 117
4.2 Estimated cumulative hazard functions 131
List of Tables
2.1 Criteria catalogues of major rating agencies and a representative bank 13
2.2 International survey of financial ratios used in credit scoring models 14
2.3 Group distance 41
2.4 Features of data samples used by Moody's 42
2.5 Parameter constellation for the 27 distinct simulation situations . . 43
2.6 Theoretical error rates 49
3.1 Different data situations and corresponding ML procedures for es¬
timating the generator of a homogeneous continuous time Markov
process 70
3.2 Risk/size distribution (1996 2002) 82
3.3 Rating distribution over time 83
3.4 Definitions of variables and hypotheses 86
3.5 Determinants of interexamination time 88
3.6 The ML estimator of the generator Q based upon discrete time ob¬
servations for the two periods 1996 2000 and 1996 2002 92
3.7 Transition probabilities: comparing estimation methods 93
3.8 Internal rating prediction model 95
3.9 Bootstrap results for the distance metric AMsvd(Pml, Pc) be¬
tween ML and cohort method 97
3.10 Characteristics of sample portfolios and calibration of portfolio
model 98
3.11 Credit risk capital: comparing estimation methods 100
3.12 Results for the test of business cycle effects and non Markov be¬
havior of transition intensities to a neighboring rating class . 102
4.1 Different default probability estimators 125
4.2 Size distribution (all data) 126
4.3 Risk distribution (1996 2002, completely observed data) 127
ix
x LIST OF TABLES
4.4 Distribution of default events (1996 2002) 128
4.5 Rating class default probability estimates 133
4.6 The default model 134
4.7 Bootstrap results for the difference in estimates 136
4.8 The missingness model 137
4.9 The rating distribution 138
B. 1 Mean and standard deviation of area under the ROC curve (AUC)
for scoring model A and n= 1,000 160
B.2 Mean and standard deviation of area under the ROC curve (AUC)
for scoring model A and n= 10,000 161
B.3 Mean and standard deviation of area under the ROC curve (AUC)
for scoring model B and n= 1,000 162
B.4 Mean and standard deviation of area under the ROC curve (AUC)
for scoring model B and n= 10,000 163
B.5 Transition probabilities: comparing estimation methods 164 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Mählmann, Thomas |
| author_facet | Mählmann, Thomas |
| author_role | aut |
| author_sort | Mählmann, Thomas |
| author_variant | t m tm |
| building | Verbundindex |
| bvnumber | BV021659602 |
| classification_rvk | QK 320 |
| ctrlnum | (OCoLC)255704674 (DE-599)BVBBV021659602 |
| dewey-full | 332.1753 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.1753 |
| dewey-search | 332.1753 |
| dewey-sort | 3332.1753 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| format | Thesis Book |
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| index_date | 2024-07-02T15:05:33Z |
| indexdate | 2024-07-09T20:41:01Z |
| institution | BVB |
| language | English |
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| publishDateSort | 2005 |
| record_format | marc |
| spelling | Mählmann, Thomas Verfasser aut Development and risk quantification of internal credit rating systems von Thomas Mählmann 2005 XIV, 180 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Köln, Univ., Diss., 2005 Rating (DE-588)4255219-9 gnd rswk-swf Risikoanalyse (DE-588)4137042-9 gnd rswk-swf Kreditrisiko (DE-588)4114309-7 gnd rswk-swf Bank (DE-588)4004436-1 gnd rswk-swf Kreditgewährung (DE-588)4132159-5 gnd rswk-swf Kreditwürdigkeitsprüfung (DE-588)4123575-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kreditrisiko (DE-588)4114309-7 s Risikoanalyse (DE-588)4137042-9 s DE-604 Bank (DE-588)4004436-1 s Kreditgewährung (DE-588)4132159-5 s DE-188 Kreditwürdigkeitsprüfung (DE-588)4123575-7 s Rating (DE-588)4255219-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014874114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mählmann, Thomas Development and risk quantification of internal credit rating systems Rating (DE-588)4255219-9 gnd Risikoanalyse (DE-588)4137042-9 gnd Kreditrisiko (DE-588)4114309-7 gnd Bank (DE-588)4004436-1 gnd Kreditgewährung (DE-588)4132159-5 gnd Kreditwürdigkeitsprüfung (DE-588)4123575-7 gnd |
| subject_GND | (DE-588)4255219-9 (DE-588)4137042-9 (DE-588)4114309-7 (DE-588)4004436-1 (DE-588)4132159-5 (DE-588)4123575-7 (DE-588)4113937-9 |
| title | Development and risk quantification of internal credit rating systems |
| title_auth | Development and risk quantification of internal credit rating systems |
| title_exact_search | Development and risk quantification of internal credit rating systems |
| title_exact_search_txtP | Development and risk quantification of internal credit rating systems |
| title_full | Development and risk quantification of internal credit rating systems von Thomas Mählmann |
| title_fullStr | Development and risk quantification of internal credit rating systems von Thomas Mählmann |
| title_full_unstemmed | Development and risk quantification of internal credit rating systems von Thomas Mählmann |
| title_short | Development and risk quantification of internal credit rating systems |
| title_sort | development and risk quantification of internal credit rating systems |
| topic | Rating (DE-588)4255219-9 gnd Risikoanalyse (DE-588)4137042-9 gnd Kreditrisiko (DE-588)4114309-7 gnd Bank (DE-588)4004436-1 gnd Kreditgewährung (DE-588)4132159-5 gnd Kreditwürdigkeitsprüfung (DE-588)4123575-7 gnd |
| topic_facet | Rating Risikoanalyse Kreditrisiko Bank Kreditgewährung Kreditwürdigkeitsprüfung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014874114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mahlmannthomas developmentandriskquantificationofinternalcreditratingsystems |