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# FRADE_STA5168_paper - Credit Risk Modeling Default...

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Unformatted text preview: Credit Risk Modeling: Default Probabilities Jaime Frade December 28, 2008 Contents 1 Introduction 1 1.1 Credit Risk Methodology . . . . . . . . . . . . . . . . . . . . . . 1 2 Preliminaries 2 2.1 Financial Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 Methods of Modeling Credit Risk 3 3.1 Existing Methods of Quantitatively Scoring . . . . . . . . . . . . 3 3.2 Two Classes of Quantitative Models . . . . . . . . . . . . . . . . 4 3.2.1 Statistical Models . . . . . . . . . . . . . . . . . . . . . . 4 3.2.2 Structural Models . . . . . . . . . . . . . . . . . . . . . . 4 4 Methodology 7 4.1 A Statistical Model: Logistic Regression . . . . . . . . . . . . . . 7 4.2 Choosing a Significant Model . . . . . . . . . . . . . . . . . . . . 8 5 Data Description 9 5.1 Defaulted Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.3 Predictors for Logistic Regression Model . . . . . . . . . . . . . . 10 6 Results 12 6.1 Saturated Logistic Regression Model 1 . . . . . . . . . . . . . . . 12 6.1.1 Saturated Logistic Regression Model 1: Output and Di- agnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.1.2 Saturated Logistic Regression Model 1 Interpretation . . 13 6.2 Logistic Regression Reduced Model 2 . . . . . . . . . . . . . . . . 14 6.2.1 Logistic Regression Model 2: Output and Diagnostics . . 14 6.2.2 Logistic Regression Model 2: Interpretation . . . . . . . . 14 6.3 Logistic Regression Reduced Model 3 . . . . . . . . . . . . . . . . 16 6.3.1 Logistic Regression Model 3: Output and Diagnostics . . 16 6.3.2 Logistic Regression Model 3: Interpretation . . . . . . . . 16 6.3.3 Logistic Regression Model: Excel Output . . . . . . . . . 17 7 Validation Techniques 18 7.1 Bootstrapping Confidence Intervals for Accuracy Ratios . . . . . 18 7.1.1 Bootstrapping Confidence Intervals: Output . . . . . . . . 19 7.1.2 Accuracy Ratios Confidence Intervals: Interpretation . . . 19 i 8 Comparison and Predications 20 8.1 Comparison of Results . . . . . . . . . . . . . . . . . . . . . . . . 20 9 Conclusion 26 ii List of Figures 6.1 Correlation Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6.2 SAS Output: Saturated Logistic Model . . . . . . . . . . . . . . 13 6.3 SAS Output: Reduced Logistic Model 2 . . . . . . . . . . . . . . 14 6.4 SAS Output: Reduced Logistic Model 3 . . . . . . . . . . . . . . 16 6.5 Excel Output: Logistic Models . . . . . . . . . . . . . . . . . . . 17 7.1 Confidence Intervals for Accuracy Ratios of Model. . . . . . . . . 19 8.1 Sorted Comparison of Prediction Results: By Reduced Logistic Model 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8.2 Sorted Comparison of Prediction Results: By Reduced CRE Model 23 8.3 Sorted Comparison of Prediction Results: By Reduced CDP Model 24 8.4 Sorted Comparison of Prediction Results: By Reduced Altman’s Z-Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 iii Acknowledgments...
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FRADE_STA5168_paper - Credit Risk Modeling Default...

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