Rating Models and Validation - Oesterreichische Nationalbank

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Rating Models and Validation However, changes to the master scale are still permissible. Such changes might be necessary in cases where new rating procedures are to be integrated or finer/rougher classifications are required for default probabilities in certain value ranges. However, it is also necessary to ensure that data history records always include a rating classÕs default probability, the rating result itself, and the accompanying default probability in addition to the rating class. Chart 68 shows the forecast and realized default rates in our example with ten rating classes. The average realized default rate for the overall sample is 1.3%, whereas the forecast — based on the frequency with which the individual rating classes were assigned as well as their respective default probabilities — was 1.0%. Therefore, this rating model underestimated the overall default risk. Chart 68: Comparison of Forecast and Realized Default Rates in the Data Example Brier Score The average quadratic deviation of the default rate forecast for each case of the sample examined from the rate realized in that case (1 for default, 0 for no default) is known as the Brier Score: 95 BS ¼ 1 X N N ðp n¼1 forecast n ynÞ 2 where yn 1 for default in n 0 for no default in n In the case examined here, which is divided into C rating classes, the Brier Score can also be represented as the total for all rating classes c: BS ¼ 1 X N K Nk p c¼1 observed c ð1 p forecast c Þ 2 þð1 p observed c Þðp forecast c Þ 2 In the equation above, Nc denotes the number of cases rated in rating class c, while pobserved and pforecast refer to the realized default rate and the forecast default rate (both for rating class c). The first term in the sum reflects the defaults in class c, and the second term shows the non-defaulted cases. This Brier Score equation can be rewritten as follows: BS ¼ 1 X N K Nc p c¼1 observed 95 Cf. BRIER, G. W., Brier-Score. c ð1 p observed c Þþðp forecast c p observed c Þ 2 116 Guidelines on Credit Risk Management
The lower the Brier Score is, the better the calibration of the rating model is. However, it is also possible to divide the Brier Score into three components, only one of which is directly linked to the deviations of real default rates from the corresponding forecasts. 96 The advantage of this division is that the essential properties of the Brier Score can be separated. BS ¼ p observed ð1 p observed Þ þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Uncertainty=variation 1 Nc ðp N c¼1 forecast c p observed c Þ 2 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 1 N X K Calibration=reliability XK Nc p c¼1 observed p observed h i 2 c |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Resolution The first term BSref ¼ p observed ð1 p observed Þ describes the variance of the default rate observed over the entire sample ðp observed Þ. This value is independent of the rating procedureÕs calibration and depends only on the observed sample itself. It represents the minimum Brier Score attainable for this sample with a perfectly calibrated but also trivial rating model which forecasts the observed default rate precisely for each case but only comprises one rating class. However, the trivial rating model does not differentiate between more or less good cases and is therefore unsuitable as a rating model under the requirements of the IRB approach. The second term 1 N X K c¼1 h i Nc p forecast c p observed c represents the average quadratic deviation of forecast and realized default rates in the C rating classes. A well-calibrated rating model will show lower values for this term than a poorly calibrated rating model. The value itself is thus also referred to as the Òcalibration.Ó The third term 1 N X K ck¼1 h i Nc p forecast p observed c describes the average quadratic deviation of observed default rates in individual rating classes from the default rate observed in the overall sample. This value is referred to as Òresolution.Ó While the resolution of the trivial rating model is zero, it is not equal to zero in discriminating rating systems. In general, the resolution of a rating model rises as rating classes with clearly differentiated observed default probabilities are added. Resolution is thus linked to the discriminatory power of a rating model. The different signs preceding the calibration and resolution terms make it more difficult to interpret the Brier Score as an individual value for the purpose of assessing the classification accuracy of a rating modelÕs calibration. In addition, the numerical values of the calibration and resolution terms are generally far lower than the variance. The table below (chart 69) shows the values of the Brier Score and its components for the example used here. 96 Cf. MURPHY, A. H., Journal of Applied Meteorology. 2 2 Rating Models and Validation Guidelines on Credit Risk Management 117
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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
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Chart 24: Vertical Linking of Ratin
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e necessary in this case if the def
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4.1.5 Consistency Heuristic models
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Compared to heuristic models, stati
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the data set and statistical testin
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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 and 104: Chart 54: Depiction of a and b erro
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: The table below (chart 67) shows a
Page 119 and 120: Chart 70 shows the reliability diag
Page 121 and 122: Chart 71: Identification of Signifi
Page 123 and 124: estimates, which means that it is e
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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Page 157 and 158: during the realization period. The
Page 159 and 160: Chart 91: Example of Segmentation f
Page 161 and 162: ity of the realization market and t
Page 163 and 164: The level of utilization for off-ba
Page 165 and 166: 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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