Threshold Accepting for Credit Risk Assessment and Validation M. - PowerPoint PPT Presentation

Threshold Accepting for Credit Risk Assessment and Validation M. Lyra 1 A. Onwunta P . Winker COMPSTAT 2010 August 24, 2010 1 Financial support from the EU Commission through COMISEF is logo gratefully acknowledged

Introduction Ex-post validation Optimal buckets Conclusion Appendix Introduction 1 Basel II and credit risk clustering Optimal size and number of clusters 2 Ex-post validation Actual number of defaults 3 Optimal buckets Conclusion 4 Summary - Outlook For further reading logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Introduction 1 Basel II and credit risk clustering Optimal size and number of clusters 2 Ex-post validation Actual number of defaults 3 Optimal buckets Conclusion 4 Summary - Outlook For further reading logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Basel II and credit risk clustering logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Basel II and credit risk clustering Regulatory Capital Accurate regulatory capital calculation. Credit Risk Bucketing Step 1: Compute borrowers’ probability of default ( p k ) logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Basel II and credit risk clustering Regulatory Capital Accurate regulatory capital calculation. Credit Risk Bucketing Step 1: Compute borrowers’ probability of default ( p k ) logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Basel II and credit risk clustering Regulatory Capital Accurate regulatory capital calculation. Credit Risk Bucketing Step 2: Assign borrowers to groups (grades) logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Basel II and credit risk clustering Regulatory Capital Accurate regulatory capital calculation. Credit Risk Bucketing Step 3: Compute MCR for each grade (based on its p g ) logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Basel II and credit risk clustering Regulatory Capital Accurate regulatory capital calculation. Credit Risk Bucketing Step 1: Compute borrowers’ probability of default ( p k ) Step 2: Assign borrowers to groups (grades) Step 3: Compute MCR for each grade (based on its p g ) Approximation Error logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Basel II and credit risk clustering Approximation Error Using p g instead of individual p k causes a loss in precision. Meaningful assignment of borrowers to clusters Choose appropriate size and number of clusters to minimize over/understatement of MCR and allow statistical ex-post validation logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Optimal size and number of clusters Optimal Credit Risk Rating System Choose appropriate size and number of grades (ex post ) Predicts defaults correctly logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Optimal size and number of clusters Optimal Credit Risk Rating System Choose appropriate size and number of grades (ex post ) Predicts defaults correctly logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Optimal size and number of clusters Optimal Credit Risk Rating System Choose appropriate size and number of grades (ex post ) Predicts defaults correctly logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Introduction 1 Basel II and credit risk clustering Optimal size and number of clusters 2 Ex-post validation Actual number of defaults 3 Optimal buckets Conclusion 4 Summary - Outlook For further reading logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Actual number of defaults Validate Actual Number of Defaults Predicted correctly if D a g ∈ [ D f g , l ; D f g , u ] with confidence 1- α D f g , l = n g · max ( p g − ε, 0 ) D f g , u = n g · min ( p g + ε, 1 ) logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Actual number of defaults Validate Actual Number of Defaults Predicted correctly if D a g ∈ [ D f g , l ; D f g , u ] with confidence 1- α D f g , l = n g · max ( p g − ε, 0 ) D f g , u = n g · min ( p g + ε, 1 ) Model actual defaults as binary variable � � D f g , l ≤ D a g ≤ D f P int = P g , u logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Actual number of defaults Validate Actual Number of Defaults Predicted correctly if D a g ∈ [ D f g , l ; D f g , u ] with confidence 1- α D f g , l = n g · max ( p g − ε, 0 ) D f g , u = n g · min ( p g + ε, 1 ) Binomial distribution � n g − k P int = � D f � � n g p k g , u � 1 − p g ≥ 1 − α . g k = D f k g , l logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Introduction 1 Basel II and credit risk clustering Optimal size and number of clusters 2 Ex-post validation Actual number of defaults 3 Optimal buckets Conclusion 4 Summary - Outlook For further reading logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Objective functions Objective function for minimizing within grades variance � 2 � � � min p c , g − p c , k (1) g k ∈ g Objective function for minimizing regulatory capital � � � � � � min 1 . 06 · � UL p g − UL ( p k ) (2) � � � g k ∈ g logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Feasible region Feasible region Minimizing regulatory capital using the validation technique ( α = 1 . 5 % , ε = 1 % ) g = 7 g = 11 0.03 g = 13 0.025 0.02 ǫ 0.015 0.01 0.005 0 0.05 0.1 0.15 α logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Empirical Findings Optimum backet setting Within grades variace (left), Regulatory capital (right) 6 7 x 10 50 Mean objective value Mean objective value 6 48 5 4 46 3 44 2 0 20 40 0 20 40 60 g g logo Figure:

Introduction Ex-post validation Optimal buckets Conclusion Appendix Introduction 1 Basel II and credit risk clustering Optimal size and number of clusters 2 Ex-post validation Actual number of defaults 3 Optimal buckets Conclusion 4 Summary - Outlook For further reading logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix Summary - Outlook Summary Minimum capital requirements to cover unexpected losses Threshold Accepting to cluster loans with real-world constraints Optimal size and number of buckets based on ex-post validation Outlook Relax default risk independence constraint Alternative assumptions for actual default distributions logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix For further reading P . Winker. Onptimization Heuristics in Econometrics: Applications of Threshold Accepting . Wiley, New York, 2001. Basel Committee on Banking Supervision. Capital Standards a Revised Framework. Bank for International Settlements , 2006. M. Lyra and J. Paha and S. Paterlini and P . Winker. Optimization Heuristics for Determining Internal Rating Grading Scales. Computational Statistics & Data Analysis , Article in Press. M. Kalkbrener and A. Onwunta. Validation Structural Credit Portfolio Models. In:Model Risk in Finance , forthcoming. logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix For further reading P . Winker. Onptimization Heuristics in Econometrics: Applications of Threshold Accepting . Wiley, New York, 2001. Basel Committee on Banking Supervision. Capital Standards a Revised Framework. Bank for International Settlements , 2006. M. Lyra and J. Paha and S. Paterlini and P . Winker. Optimization Heuristics for Determining Internal Rating Grading Scales. Computational Statistics & Data Analysis , Article in Press. M. Kalkbrener and A. Onwunta. Validation Structural Credit Portfolio Models. In:Model Risk in Finance , forthcoming. logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix For further reading P . Winker. Onptimization Heuristics in Econometrics: Applications of Threshold Accepting . Wiley, New York, 2001. Basel Committee on Banking Supervision. Capital Standards a Revised Framework. Bank for International Settlements , 2006. M. Lyra and J. Paha and S. Paterlini and P . Winker. Optimization Heuristics for Determining Internal Rating Grading Scales. Computational Statistics & Data Analysis , Article in Press. M. Kalkbrener and A. Onwunta. Validation Structural Credit Portfolio Models. In:Model Risk in Finance , forthcoming. logo

Introduction Ex-post validation Optimal buckets Conclusion Appendix For further reading P . Winker. Onptimization Heuristics in Econometrics: Applications of Threshold Accepting . Wiley, New York, 2001. Basel Committee on Banking Supervision. Capital Standards a Revised Framework. Bank for International Settlements , 2006. M. Lyra and J. Paha and S. Paterlini and P . Winker. Optimization Heuristics for Determining Internal Rating Grading Scales. Computational Statistics & Data Analysis , Article in Press. M. Kalkbrener and A. Onwunta. Validation Structural Credit Portfolio Models. In:Model Risk in Finance , forthcoming. logo