The Econometrics of Individual Risk: Credit, Insurance, and Marketing Book

Preface     xi
Introduction     1
Market Risk and Individual Risk     1
Risk Variable     2
Scores     3
Organization of the Book     4
References     5
Dichotomous Risk     7
Risk Prediction and Segmentation     7
Risk Prediction     8
Segmentation     11
Econometric Models     14
Discriminant Analysis     14
Dichotomous Qualitative Models     15
Comparison of Discriminant and Logit Models     18
Risk Heterogeneity     19
Concluding Remarks     20
Appendix: The Logistic Distribution     20
References     21
Estimation     23
Estimation Methods     23
The Maximum Likelihood Approach     23
Maximum Likelihood Estimation of a Logit Model     25
Maximum Likelihood Estimation in Linear Discriminant Analysis     27
Test of the Linear Discriminant Hypothesis     28
Significance Tests     29
Likelihood-Based Testing Procedures     30
Application of the LM Test to the Logit Model     31
Implementation     32
Development of Score Methodology     33
Mortgage Score     35
Concluding Remarks     39
References     40
Score Performance     43
Performance and Selection Curves     43
Definitions     43
Desirable Properties of a Score     46
Comparison of Scores     47
Discriminant Curves     49
Definitions     50
Linear Discriminant Analysis     52
Demand Monitoring, Credit Granting, and Scores     52
Time-Varying Quality of Credit Applicants     53
Analysis of Credit-Granting Decision     55
Performance Curves     58
Concluding Remarks     58
Appendix: Positive Dependence     59
References     60
Count Data Models     61
Poisson Regression     62
The Model     62
Maximum Likelihood Estimator     63
Relationship with the Dichotomous Qualitative Model     64
The Negative-Binomial Regression     64
Model with Gamma Heterogeneity     64
The Bonus-Malus Scheme     66
Semi-Parametric Analysis     69
Mean and Variance Estimators      70
Estimation of the Heterogeneity Distribution     71
Determination of the Premium     72
Applications     73
Car Insurance     73
Presentation of Results     77
Concluding Remarks     82
References     83
Durations     85
Duration Distributions     86
Characterizations of a Duration Distribution     86
Duration Dependence     88
Basic Duration Distributions     89
Duration Models     92
The Exponential Regression Model     93
The Exponential Model with Gamma Heterogeneity     94
Heterogeneity and Negative Duration Dependence     95
Semi-Parametric Models     98
Accelerated Hazard Model     98
Proportional Hazard Model     99
Applications     100
Pension Fund     100
Interest Rate Spreads     101
Prepayment Analysis     103
Concluding Remarks     107
Appendix     109
Expected Residual Lifetime     109
Computation of the Premium Rate for the Pension Contract     110
References     111
Endogenous Selection and Partial Observability     113
Analysis of Dichotomous Risks from a Stratified Sample     113
Description of the Population and the Sample     113
Exogenous Stratification     115
Endogenous Stratification     115
The Role of Stratified Samples     117
Truncation and Censoring in Duration Models     117
Censoring     117
Truncation     118
Competing Risks     119
Bias Correction Using Rejected Credit Applications     120
Selectivity Bias     120
Boundaries for Risk Prediction     121
A Bivariate Model for Bias Correction     122
Concluding Remarks     126
Appendix: First-Order Expansion of the C.D.F. of a Bivariate Normal Distribution     126
References     126
Transition Models     129
Homogeneous Markov Chains     130
Distribution of the Markov Chain     130
Alternative Parametrizations of a Markov Chain     132
Two-State Space     134
Qualitative Representation of the Process     135
Estimation     136
Explanatory Variables     137
Specification of the Transition Probabilities      138
Specification of the Adjustment and Long-Run Parameters     138
Time-Dependent Markov Chain     139
Transitions between Score Categories     140
Revolving Consumer Credit     140
Corporate Rating Dynamics     143
Concluding Remarks     146
References     146
Multiple Scores     149
Examples     150
Default Risk and Preselection     150
Term Structure of Default     151
Differentiated Incident Severity     152
Default and Prepayment     154
Default and Credit Promotion     156
Polytomous Logit Model     157
The Hypothesis of Irrelevant Alternatives     158
Profit- (Utility-) Optimizing Decisions     159
Promotional Mailing Decisions     159
Time-to-Default     161
Utility-Maximizing Behavior     162
Multi-Score Reduction Technique     163
Basic Notions     163
Singular Value Decomposition (SVD)     164
Statistical Inference     165
Household Portfolio Allocation     166
Description of the Data Set     166
Model Estimation     169
Reduction of the Number of Scores     176
Concluding Remarks     178
References     179
Serial Dependence in Longitudinal Data     181
Poisson and Compound Poisson Processes     182
Poisson Process     182
Compound Poisson Process     184
From Discrete Time to Continuous Time     185
Models with Serial Dependence     186
Autoregressive Models     188
Time-Dependent Heterogeneity     192
Applications     195
Cost Sensitivity with Respect to Transitory Shocks     195
Learning in Revolving Credit     197
Concluding Remarks     205
Appendix: Distributions of the Duration and Count Variables     205
Distribution of the First Duration     205
Independence of Durations     206
Distribution of the Count Variable     206
References     206
Management of Credit Risk     209
Measures of Risk and Capital Requirement     209
Value-at-Risk     210
Properties of a Risk Measure     212
Credit Portfolio     213
The P&L Distribution for a Credit Portfolio When the Horizon Is Equal To the Maturity     214
The P&L Distribution for a Credit Portfolio When the Horizon Is Shorter Than the Maturity     216
Corporate Bond Portfolio     223
Informational Content of Bond Prices     223
Default Correlation     224
Stochastic Transition Model     230
Concluding Remarks     235
References     235
Index     239