Rating Models and Validation - Oesterreichische Nationalbank

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Rating Models and Validation Chart 53: Curve of the Cumulative Probabilities Functions of Good/Bad Cases in the Data Example The density functions show a substantial difference between good and bad cases. The cumulative frequencies show that approximately 70% of the bad cases — but only 20% of the good cases — belong to classes 6 to 10. On the other hand, 20% of the good cases — but only 2.3% of the bad cases — can be found in classes 1 to 3. Here it is clear that the cumulative probability of bad cases is greater than that of the good cases for almost all rating classes when the classes are arranged in order from bad to good. If the rating classes are arranged from good to bad, we can simply invert this statement accordingly. a and b errors a and b errors can be explained on the basis of our presentation of density functions for good and bad cases. In this context, a caseÕs rating class is used as the decision criterion for credit approval. If the rating class is lower than a predefined cutoff value, the credit application is rejected; if the rating class is higher than that value, the credit application is approved. In this context, two types of error can arise: — a error (type 1 error): A case which is actually bad is not rejected. — b error (type 2 error): A case which is actually good is rejected. In practice, a errors cause damage due to credit defaults, while b errors cause comparatively less damage in the form of lost business. When the rating class is used as the criterion for the credit decision, therefore, it is important to define the cutoff value with due attention to the costs of each type of error. Usually, a and b errors are not indicated as absolute numbers but as percen- tages. a error refers to the proportion of good cases below the cutoff value, that is, the cumulative frequency F good cum of good cases starting from the worst rating class. a error, on the other hand, corresponds to the proportion of bad cases above the cutoff value, that is, the complement of the cumulative frequency of bad cases F bad cum. 102 Guidelines on Credit Risk Management
Chart 54: Depiction of a and b errors with Cutoff between Rating Classes 6 and 7 ROC Curve One common way of depicting the discriminatory power of rating procedures is the ROC Curve, 80 which is constructed by plotting the cumulative frequencies of bad cases as points on the y axis and the cumulative frequencies of good cases along the x axis. Each section of the ROC curve corresponds to a rating class, beginning at the left with the worst class. 80 Receiver Operating Characteristic. Chart 55: Shape of the ROC Curve for the Data Example Rating Models and Validation Guidelines on Credit Risk Management 103
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≈√ Guidelines on Credit Risk Ma
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The ongoing development of contempo
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5 Developing a Rating Model 60 5.1
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Rating Models and Validation I INTR
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This segmentation from the business
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The best-practice segmentation pres
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Chart 2: Data Requirements for Gove
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2.2 Financial Service Providers In
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Insurance Companies Due to their di
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Capital Market-Oriented/Internation
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— Market prospects are not assess
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Chart 5: Data Requirements for Corp
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elationships in the project, these
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Before the Project As the repayment
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Chart 6: Data Requirements for Reta
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During the Credit Term Instead of o
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3.1 Heuristic Models Heuristic mode
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Chart 9: Information Categories for
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Explanatory Component The explanato
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This example defines linguistic ter
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ments as to whether higher or lower
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Chart 16: Indicators in the ÒCrebo
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Logistic regression has a number of
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adapts the network according to any
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The parameters required to calculat
Page 51 and 52: ture of the borrowerÕs creditworth
Page 53 and 54: Chart 24: Vertical Linking of Ratin
Page 55 and 56: e necessary in this case if the def
Page 57 and 58: 4.1.5 Consistency Heuristic models
Page 59 and 60: Compared to heuristic models, stati
Page 61 and 62: the data set and statistical testin
Page 63 and 64: data collection procedure. This pro
Page 65 and 66: full surveys is often too high, esp
Page 67 and 68: essential structural characteristic
Page 69 and 70: For each block, interim objectives
Page 71 and 72: Chart 34: Creating the Analysis Dat
Page 73 and 74: Chart 35: Creating the Analysis and
Page 75 and 76: Once a quality-assured data set has
Page 77 and 78: an indicator should only be used in
Page 79 and 80: Transformation of Indicators In ord
Page 81 and 82: the scoring functions developed usi
Page 83 and 84: Chart 37: Significance of Quantitat
Page 85 and 86: — For all other statistical and h
Page 87 and 88: of approximately 10 intervals shoul
Page 89 and 90: With regard to the time interval be
Page 91 and 92: around the main diagonal, however,
Page 93 and 94: tial increase in marginal default r
Page 95 and 96: Chart 46: Aspects of Rating Model V
Page 97 and 98: — Model development procedure Mod
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Page 101: numbers of cases per class observed
Page 105 and 106: Chart 57: Shape of the a—b Error
Page 107 and 108: Interpretation of the Pietra Index
Page 109 and 110: The following relation applies to t
Page 111 and 112: Chart 62: ROC Curve with Simultaneo
Page 113 and 114: Chart 65: Interpretation of the Bay
Page 115 and 116: The table below (chart 67) shows a
Page 117 and 118: The lower the Brier Score is, the b
Page 119 and 120: Chart 70 shows the reliability diag
Page 121 and 122: Chart 71: Identification of Signifi
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Page 125 and 126: transition matrix, the data require
Page 127 and 128: tency of the cumulative and conditi
Page 129 and 130: to internal back-testing results in
Page 131 and 132: Changes in correlations One of the
Page 133 and 134: 6.4.3 Developing Stress Tests This
Page 135 and 136: Counterparty-based and credit facil
Page 137 and 138: tify decisive factors influencing i
Page 139 and 140: III ESTIMATING AND VALIDATING LGD/E
Page 141 and 142: Chart 81: Loss Components in LGD to
Page 143 and 144: assets, as the danger exists that m
Page 145 and 146: — Collateral: Collateral value, c
Page 147 and 148: Chart 87: Overview of Customer Type
Page 149 and 150: transaction, however, it is also ne
Page 151 and 152: Implementing an in-house LGD estima
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nents; this is analogous to the use
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those assets which serve as collate
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during the realization period. The
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Chart 91: Example of Segmentation f
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ity of the realization market and t
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The level of utilization for off-ba
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8.3 EAD Estimation Methods As in th
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IV REFERENCES Backhaus, Klaus/Erich
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Stuhlinger, Matthias, Rolle von Rat
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Pytlik, Martin, Diskriminanzanalyse
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