Rating Models and Validation - Oesterreichische Nationalbank

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Rating Models and Validation An ideal rating procedure would classify all actual defaults in the worst rating class. Accordingly, the ROC curve of the ideal procedure would run vertically from the lower left point (0%, 0%) upwards to point (0%, 100%) and from there to the right to point (100%, 100%). The x and y values of the ROC curve are always equal if the frequency distributions of good and bad cases are identical. The ROC curve for a rating procedure which cannot distinguish between good and bad cases will run along the diagonal. If the objective is to review rating classes (as in the given example), the ROC curve always consists of linear sections. The slope of the ROC curve in each section reflects the ratio of bad cases to good cases in the respective rating class. On this basis, we can conclude that the ROC curve for rating procedures should be concave (i.e. curved to the right) over the entire range. A violation of this condition will occur when the expected default probabilities do not differ sufficiently, meaning that (due to statistical fluctuations) an inferior class will show a lower default probability than a rating class which is actually superior. This may point to a problem with classification accuracy in the rating procedure and should be examined with regard to its significance and possible causes. In this case, one possible cause could be an excessively fine differentiation of rating classes. Chart 56: Non-Concave ROC Curve a—b error curve The depiction of the a—b error curve is equivalent to that of the ROC curve. This curve is generated by plotting the a error against the b error. The a—b error curve is equivalent to the ROC curve with the axes exchanged and then tilted around the horizontal axis. Due to this property, the discriminatory power measures derived from the a—b error curve are equivalent to those derived from the ROC curve; both representations contain exactly the same information on the rating procedure examined. 104 Guidelines on Credit Risk Management
Chart 57: Shape of the a—b Error Curve for the Data Example Area under Curve (AUC) as a Measure of Discriminatory Power AUC (area under curve) is a graphic measure of a rating procedureÕs discriminatory power derived from the ROC curve and refers to the area under the ROC curve (expressed in units where 100% ¼ 1 for both axes). 81 In ideal rating models, AUC ¼1, for models which cannot differentiate between good and bad cases, AUC ¼1/2. Values where AUC
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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
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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 and 102: numbers of cases per class observed
Page 103: Chart 54: Depiction of a and b erro
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
Page 153 and 154: 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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