Rating Models and Validation - Oesterreichische Nationalbank

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Rating Models and Validation Chart 17: Functional Forms for Logit and Probit Models In this formula, n refers to the number of financial indicators included in the scoring function, Ki refers to the specific value of the creditworthiness criterion, and bi stands for each indicatorÕs coefficient within the scoring function (for i ¼ 1; :::n). The constant b0 has a decisive impact on the value of p (i.e. the probability of membership). Selecting an S-shaped logistic function curve ensures that the p values fall between 0 and 1 and can thus be interpreted as actual probabilities. The typical curve of a logit function is shown again in relation to the result of the exponential function (score) in chart 18. Chart 18: Logit Function Curve The maximum likelihood method is used to estimate the coefficients. The maximum likelihood function describes how frequently the actual defaults observed match the model forecasts in the development sample. 27 27 Cf. KALTOFEN, D./MO‹LLENBECK, M./STEIN, S., Risikofru‹herkennung im Kreditgescha‹ft mit kleinen und mittleren Unternehmen, p. 14. 44 Guidelines on Credit Risk Management
Logistic regression has a number of advantages over MDA. First, logistic regression does not require normal distribution in input indicators. This allows logistic regression models to process qualitative creditworthiness characteristics without previous transformation. Second, the result of logistic regression can be interpreted directly as the probability of group membership. This makes it possible to assign a one-year default rate to each result, for example by rescaling the value p. Logistic regression models are often characterized by more robust 28 and more accurate results than those generated by discriminant analysis. In recent years, logistic regression has seen more widespread use both in academic research and in practice. This can be attributed to the lower demands it makes on data material as well as its more robust results compared to discriminant analysis. One example of the practical use of logistic regression in banks is the BVR-II rating model used by the Federal Association of German Cooperative Banks to rate small and medium-sized enterprises. 29 3.2.3 Artificial Neural Networks Structure of Artificial Neural Networks Artificial neural networks use information technology in an attempt to simulate the way in which the human brain processes information. In simplified terms, the human brain consists of a large number of nerve cells (neurons) connected to one another by a network of synapses. Neurons receive signals through these synapses, process the information, and pass new signals on through other neurons. The significance of a particular piece of information is determined by the type and strength of the links between neurons. In this way, information can be distributed and processed in parallel across the entire network of neurons. The human brain is able to learn due to its capacity to adjust the weighting of links between neurons. Artificial neural networks attempt to model this biological process. An artificial neural network consists of an input layer, the inner layers and an output layer (see chart 19). The input layer serves the purpose of taking in information (e.g. specific indicator values) and passing it on to the downstream neurons via the connections shown in the diagram below. These links are assigned weights in an artificial neural network and thus control the flow of information. In the neurons, all incoming information ij is first linked with a value v. This is done by means of a simple sum function. Each piece of information is then assigned a connection weight w. The compressed value v is transformed into value o by a nonlinear function. The function used for this purpose depends on the specific model. One example is the following logistic function: o ¼ 1 1 þ e 28 Cf. KALTOFEN, D./MO‹LLENBECK, M./STEIN, S., Risikofru‹herkennung im Kreditgescha‹ft mit kleinen und mittleren Unternehmen, p. 14. 29 Cf. STUHLINGER, MATTHIAS, Rolle von Ratings in der Firmenkundenbeziehung von Kreditgenossenschaften, p. 72. v : Rating Models and Validation Guidelines on Credit Risk Management 45
Page 1 and 2: ≈√ Guidelines on Credit Risk Ma
Page 3 and 4: The ongoing development of contempo
Page 5 and 6: 5 Developing a Rating Model 60 5.1
Page 7 and 8: Rating Models and Validation I INTR
Page 9 and 10: This segmentation from the business
Page 11 and 12: The best-practice segmentation pres
Page 13 and 14: Chart 2: Data Requirements for Gove
Page 15 and 16: 2.2 Financial Service Providers In
Page 17 and 18: Insurance Companies Due to their di
Page 19 and 20: Capital Market-Oriented/Internation
Page 21 and 22: — Market prospects are not assess
Page 23 and 24: Chart 5: Data Requirements for Corp
Page 25 and 26: elationships in the project, these
Page 27 and 28: Before the Project As the repayment
Page 29 and 30: Chart 6: Data Requirements for Reta
Page 31 and 32: During the Credit Term Instead of o
Page 33 and 34: 3.1 Heuristic Models Heuristic mode
Page 35 and 36: Chart 9: Information Categories for
Page 37 and 38: Explanatory Component The explanato
Page 39 and 40: This example defines linguistic ter
Page 41 and 42: ments as to whether higher or lower
Page 43: Chart 16: Indicators in the ÒCrebo
Page 47 and 48: adapts the network according to any
Page 49 and 50: 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
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Chart 46: Aspects of Rating Model V
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— Model development procedure Mod
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and bad refer to whether a credit d
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numbers of cases per class observed
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Chart 54: Depiction of a and b erro
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Chart 57: Shape of the a—b Error
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Interpretation of the Pietra Index
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The following relation applies to t
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Chart 62: ROC Curve with Simultaneo
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Chart 65: Interpretation of the Bay
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The table below (chart 67) shows a
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The lower the Brier Score is, the b
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Chart 70 shows the reliability diag
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Chart 71: Identification of Signifi
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estimates, which means that it is e
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transition matrix, the data require
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tency of the cumulative and conditi
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to internal back-testing results in
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Changes in correlations One of the
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6.4.3 Developing Stress Tests This
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Counterparty-based and credit facil
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tify decisive factors influencing i
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III ESTIMATING AND VALIDATING LGD/E
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Chart 81: Loss Components in LGD to
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assets, as the danger exists that m
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— Collateral: Collateral value, c
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Chart 87: Overview of Customer Type
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transaction, however, it is also ne
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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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Rating Models and Validation - Oesterreichische Nationalbank

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