Example analysis of credit rating model (taking consumer finance as an example)

Example analysis of credit rating model (taking consumer finance as an example)original 2016-10-13 Canlanya General Assembly data Click "Asia-General data" to follow us!

the fifth chapter analysis and treatment of self-variable

There are two types of model variables, namely, continuous type variables. A continuous variable refers to the actual value of the variable as observed data, and is not processed by a group. discontinuous variables are referred to as qualitative or categorical variables.

Both types of variables are applicable to scoring models, but it is recommended that variables develop scoring models using discontinuous patterns, mainly for the following reasons:

1. Discontinuous variables help to deal with extreme values or variables with a small number of samples.

2. Nonlinear dependent variables (dependencies) can be applied to linear models (linear model).

3. Discontinuous variables help model developers to understand the trend relationship between variables and target events.

4. The development unit may have prior knowledge of the development sample of the target event, its rough behavior characteristics.

1 Detailed classification (Fine classing)

• After the long variable list is completed, it will be followed by a detailed classification (Fine classing), the continuous type variable is divided into several intervals, in order to facilitate the single-variable analysis;

• The detailed classification method divides the variables into 10 to 20 intervals according to the sample ratio (equal population).

• The observed variable and the corresponding trend of the target event (logical trend) are consistent with the actual business experience, if the trend and cognition do not match, that is to say that the variable is not suitable for the development model, and then, with the results of univariate analysis to filter variables.

Example  

Example one: Quota usage for nearly 1 months

According to the general credit card business experience, when the customer's quota utilization rate is greater, the probability of future default is higher, compared with the trend chart of the quota usage rate clustering and default rate of nearly 1 months can be found.

Example two: Periods with bank transactions

General credit card business experience tells us that the longer the customer and bank transactions, the probability of future default will be lower, the comparison with the bank during the period of grouping and default rate of the trend map found that the development of the sample "with the bank", and the default rate does not have any significant trend, and business experience is inconsistent, said " During the transaction with the bank "is not suitable for the development of credit rating models.

2 univariate Analyses (single Factor analysis)

• The long variable list lists all kinds of variables, the development unit to be the variable to be carefully grouped, compare business experience and trend, eliminate inconsistent variables, followed by a single variable analysis of variables;

• Using the analysis data to observe the stability of variables in different periods, and the ability to predict the target events;

• The most commonly used indicators are the maternal stability indicator (Population stability index;psi) and the message value (value of Information;voi).

3 Maternal stability Index (Population stability index;psi)

The main purpose of the maternal stability index is to understand whether the sample morphology at different time points has changed, which can be used to evaluate the overall model scoring profile, or the variation formula of individual variables:

In general, when the PSI is less than 0.1 means the point is not at the same time, the percentage of the grouping sample of the variable has no significant change, the stability is very well, can be used to develop the model;

As can be seen through table 5-3, the usage rate of the last 1 months has gradually decreased with time, but the PSI is only 0.0327, the change amplitude is not big, can be used to build the scoring model after the development Unit.

4 message Value (value of Information;voi)

Message value helps model developers understand that each variable has a single predictive capability for the target event, which is developed by selecting a variable with high predictive capacity. Formula:

Criteria for determining the value of a message:

20 grouped message value plus the total found that "the last 1 months of quota utilization" of the voi is 2.09, indicating that the variable for the next 12 months of the sample is a default has a strong predictive ability, model developers can be used to develop models.

5 correlation coefficient (Correlation coefficient)

When the correlation between the scoring model variables is too high, the problem of collinearity (collinearity) can be produced, resulting in a decrease in the predictive ability of the model, and even an unexplained phenomenon contrary to the predicted results. To avoid high correlation between variables to weaken the predictive ability of the model, the developer calculates the correlation coefficients between the variables:

Correlation coefficient and degree of correlation:

General correlation coefficient and the corresponding degree of correlation standards are arranged in table 5-6, for the development of scoring model, if the correlation coefficient of more than 0.7, indicating that the correlation between variables is too high, you must filter to avoid reducing the model's predictive ability.

6 variable filtering (Variables Selection)

• The long list collects all the variables that can be produced in the database before the model is developed, and not every variable can be used to develop the model.

• Through the PSI, voi and correlation coefficients of each variable, the variables are screened by considering the stability, prediction ability, correlation degree between variables and business cognition.

• In general, when the PSI of a variable is less than 0.1 and voi is greater than 0.1, it means that the variable is fairly stable over different periods and has significant predictive power over the target event, so the variable is retained to the short list of variables first.

• When the correlation coefficient between the reserved variables is greater than 0.7, the subsequent development steps are selected based on the business experience for the variables that are more suitable for predicting the target event.

7 Rough Classification (coarse classing)

A rough classification has the following principles:

1. The trend of variable rise or fall should be consistent with practical experience

2, a single variable should be maintained up to 8 intervals

3, each grouping good or bad contrast value (g/b Index) need at least 15 more than the gap

4, each grouping needs to cover more than 2% model development samples

5. Each cluster must have at least 30 development samples of the target event or 1% of the group sample

6. Combine blanks, missing values, or other special variable values into the same interval, which is called the empty set (Null Group)

7, generally null group clustering is better than the overall low (good or bad ratio is close to 100B or more).

The sample uses a detailed classification table of "Nearly 1 months ' quota usage" to further illustrate how to make a rough classification of variables:

Step One:

Because the quota utilization of nearly 1 months is less than or equal to 4.78% of 11 clusters, its default rate is less than 0.3%, good or bad than 400 and good or bad contrast value is greater than 400G, so will be the 11 clusters into a single grouping.

Steps Two:

Nearly 1 months quota utilization is greater than 4.78%, less than or equal to 10.21% of three clusters, because the default rate is between 0.3% to 0.38%, good or bad ratio is more similar to the ratio, so the three clusters into a new grouping.

Step Three:

The use rate of the last 1 months is greater than 10.21%, less than or equal to 20.51% of the two clusters, because the default rate, good or bad ratio and the ratio and before and after the clustering has a significant gap, so the two grouping into a new grouping.

Step Four:

A rough classification of the quota usage for nearly 1 months and examine the principles described above:

1. The trend of rising or falling variables should be consistent with practical cognition

2, a single variable should be maintained up to 8 intervals

3, each grouping good or bad ratio needs at least 15 or more

4, each grouping needs to cover more than 2% model development samples

5. Each cluster must have at least 30 development samples of the target event or 1% of the group sample

The sixth Chapter model establishment method

The example uses "nearly 1 Monthly quota usage rate " Detailed classification table that further explains how to perform a rough classification of the variable steps:

• There are many ways to build models, such as differential analysis (discriminant analyses), linear regression (Linear regression), Rogers regression (logistic regression), and classification trees (classification Trees), or non-statistical methods such as neural networks (neural Networks), genetic algorithms (genetic algorithms), and expert systems.

• In practice, the choice of linear regression or Rogers regression to construct the scoring model, the cost is relatively fast in the implementation of the model, is the model developers most often choose the way.

1 linear regression (Linear Regression)

Linear regression is the study of the relationship between a single strain and one or more independent variables. Linear regression is suitable for model pairing of continuous attributes, when there is only one independent variable, its regression model is:

General Line the following basic assumptions must be met for sexual regression:

1. Linear relationship between self-variable and strain amount

2. The expected value of residual items is 0

3, the variance of the residual term is a constant

4. Observation values are independent of each other

5. Residual items are subject to normal distribution

1. (a) Variable selection

When selected from variables, the most commonly used method is stepwise regression (stepwise multiple regression), which is divided into three options:

• Forward Selection method (Forward selection)

First, from all variables, select the most contributors to the model to enter the regression equation, and then select the second, third ... A variable with a higher predictive force enters the model and enters a standard that has a minimum F-probability value, usually set at 0.50, and if the F-value of the argument is less than this, it is selected to enter.

• Reverse elimination method (backward elimination)

This method, in contrast to the forward selection method, starts by selecting all the variables, then deleting each one to minimize the contribution to the pattern, and then selecting the other variables to enter the model, and the criteria for culling is the maximum f probability value, usually set at 0.10, and if the F value of the self variable is greater than this, it will be selected for culling.

• Stepwise Analytical Method (stepwise analysis)

This is a synthesis of the above two technologies. First, no predictor variables are included in the pattern, and then a forward selection method is adopted to select the self variables that contribute the most to the pattern into the regression mode. In each step, the self-variable that has been incorporated into the pattern must be tested by the reverse elimination method to determine whether the variant is to be eliminated or left behind. The entry criteria for the F-probability value of stepwise regression method are usually 0.15, and the rejection standard is also 0.15.

(ii) Model performance

In the use of linear regression analysis to make inferences, the most commonly used to T-Test, F-Test and R2 to determine whether the important statistics produced statistically significant level, judge whether this regression is meaningful:

• T-Test (T-test):

The verification of the regression coefficient is statistically significant, T-Test statistics are used to determine whether each coefficient is 0, if through the verification found that a factor is not significant, that is, with 0 no significant difference, it is necessary to inspect whether there is the problem of the data itself (such as insufficient number of samples), or non-linear correlation, If this variable does not contribute to the performance of the model, consider removing it.

• F Verification:

In regression analysis, the F-value is used to determine whether there is a significant relationship between the set of self-variables and the strain amount, in which the whole regression formula is measured by the f statistic, that is, whether all coefficients of the regression formula are 0, if all are 0, the estimated regression formula cannot properly describe the behavior of the strain amount, and it is necessary to

• Complex correlation coefficients R2 and adjusted R2:

The complex correlation coefficient is used to illustrate the extent of the estimated regression formula to explain the actual situation, usually determining the relationship between the strain amount and the whole self-variable by determining the coefficient R2, that is, the ability to interpret the regression model is sufficient.

2 Rogers Regression (Logistic Regression)

(i) Model Settings

The strain amount of the Rogers regression model is two, which is a qualitative change, and its variable value is only two possible events of good and bad (including default/non-default event, failure/success, etc.). This method has the advantages of easy-to-understand, non-black-box work, and probability combination, so it is the most commonly used method for developing scorecard. The assumption is that the Y,y value is 0 or 1, and the self variable is x= (x1,x2,..., Xk).

Make

(ii) Parameter estimation

The parameter estimation of the Rogers regression model is estimated by using the most approximate likelihood method. Each observation value is a numeric value of 0 or 1, so (this is Bernoulli allocation, n is the number of samples), and its approximate function is represented as follows:

(c) The self-variable processing

Common methods are the woe values that are grouped by each variable, or the virtual variables (dummy ariable), which are grouped by the variables.

1) Woe value:

Using the woe value of each variable in the previous stage to replace the original variable value as the input of the regression model training, in addition to avoid the extreme value (Outliers) in the variable value of the case, can also reduce the model over-adaptation (Overfitting) phenomenon.

The woe is calculated as follows:

which

I: Group of characteristic variable sub-bins

Distr good: The proportion of good pieces in each group.

Distr bad: The proportion of all bad pieces in each group.

2) virtual variables (dummy variable):

Set up virtual variables with each variable grouping (dummy variable) in Rogers regression, discrete or nominal scale variables, such as gender, education, marital status, etc. are not appropriate, take the interval scale as an example, each number represents a different level, at this time the number does not represent any significant, in this case, You can use virtual variables as a method.

Taking "education level" as an example, this explanatory variable is divided into 5 groups, including primary, middle, high school, tertiary and research institutes, the virtual variable design left.

In general, if the nominal scale of the variable is divided into n groups, it is necessary to n-1 a different form of the virtual variable is designed, which is set as the basis of the grouping, that is, the value is all 0 of the decision, usually using bad% closest to the whole group.

(iv) Model performance

It is necessary to verify whether the parameters have significant effect by using the estimation of the parameters obtained by the algorithm.

Under the condition of large sample, the verification, at the significant level, when the Wald statistic value is greater than, indicates that the coefficient is significantly nonzero.

In the Model Fit degree Verification section, the verification of the suitability degree of the model after the whole model is established, that is, the verification statistic of -2log (L) is based on the approximate function. When -2log (L) is greater than, it indicates that the model is improperly adapted.

3 two stage-style building method

• When commenting on a card in general, the Rogers regression will always be 0 or 1, and cannot use continuous variables, so consider using linear regression to make the residual value from the regression analysis of the previous phase Rogers as the second phase of the response variable.

• With the two-stage regression, it is possible to choose the variable with strong predictive force into the post-stage linear regression model, so that the scoring model is less susceptible and biased than the variable with high predictive force. For example: When building credit card scorecard, in order to avoid the model over-reliance on the variables, the first phase of the Rogers regression is only included in-row variables for analysis, the associated variables are added in the second phase.

Perform a two-phase regression build step as follows:

1. Model Establishment: in order to make the model have better accuracy and stability, the model sample is usually differentiated into "training-test" two sets of Datasets (Development & Hold-out sample), accounting for the overall sample of "70% to 30%", using 70 % of the training sample to perform stepwise regression.

2. First-phase regression-Rogers regression model: If there is a contradiction between the interval of the variable and its corresponding good or bad contrast value (GB Index), or with the practice cognition repulsion, you need to redesign the variable interval or choose to exclude the variable, and then re-execute the regression action.

3. Correlation Analysis: Check the correlation of the selected variables, the correlation coefficient analysis of all variables, the correlation coefficient is higher than 0.85 of the variables to take voi, in order to avoid the problem of the model has collinearity.

4. Repeat the 2 to 3 action to find the best model.

5. Second phase regression: Step 4 can obtain the residual value of the first stage Rogers regression, as the strain amount of the second-stage linear regression. Similar regression analysis processes are performed in the second phase, with 2 to 5 steps being repeated to ensure that the selected variable combination conforms to the statistical and practical experience, culminating in the final scoring model.

6. Model test: use 30% of the test (hold-out) samples and time-out (out-of-time) samples for the validity of the test, to ensure the accuracy and stability of the model, if the specified criteria can not be met, repeat steps 1 to 5. Usually the Gini value and K-s value as the specified standard, generally speaking, the Gini value of 40%, k-s value of 30%, indicating that the model of good or bad case discrimination strong

7. Multiply the variable coefficients from the final scoring model by 1,000 to get the scorecard score.

(i) initial model discussion

For the scoring card build process, PA meeting (preliminary analyses meeting) focuses on the previous stages of the process, and focuses on the discussion of the initial model inclusion variables, which relies on the practical experience and model of all units to combine Therefore, the scorecard product upstream to downstream related units should be sent to participate in the discussion, such as business units, marketing units, the unit and policy units and so on.

The agenda for PA meeting focuses on the following:

1. Brief description of scorecard purpose and process structure

2. Sample Interval Description

3. Introduction of Information

4, the quality of the score card definition Introduction

5. Introduction to the development process of scorecard

6. The discussion of the points and weights of each interval of the rating card variables

7. Correction of rating Card

Subsequently, the development model staff according to the questions and suggestions presented in the implementation of model correction analysis, such as variable replacement and interval redesign, and then put forward the final model scoring results.

(ii) examples

To build the model for the sample, the steps are as follows:

Step One: Variable conversion

Convert variables to virtual variables to ensure the stability of the data and the model.

Step Two: Rogers regression

The first stage model can be obtained by using the virtual variables to Rogers the variables of the regression model.

Step Three: Linear regression

Using the residual error of the Rogers regression in the former stage as the variable, the associated variable is an independent variable, and the linear regression analysis

Step four: Rogers regression and linear regression model merging

After repeated variable group resets and incorporating practical experience, the initial model can be generated. Next, a discussion session should be held by the model staff and the user for the initial model.

Seventh chapter declined inference (Reject inference)

Application Scorecard is the use of historical data from the auditor to establish the model, this model will ignore the original declined the influence of the customer, so that the model is slightly optimistic, it is necessary to pass the deduction of the model to modify the models to make the model more accurate and stable.

1 reasons for refusal of inference

The reason for the refusal of the deduction, the most important is to prevent the application of a sample of the possible bias, and then restore the actual distribution of the mother at the time of the application, as for the other reasons for the decline of the reason still:

1. Increase the number of modeling samples: This statement is similar to the reason for preventing sample errors. In general, modeling samples only consider the approval, the proportion of the whole sample is too small, the deduction can increase the modeling sample to the proportion of the whole sample, the model is more representative.

2. Changes in the company's internal policies may result in past applicants being unable to represent prospective applicants; Similarly, the past refusal to represent the future will be declined, so if only the approval of the building model can lead to miscalculation.

3, from the point of view of making decisions, the refusal of inference can be applied to all customers to make more accurate and realistic speculation. For example, a bank that has traditionally approved scorecard scores greater than or equal to more than 500 points, but is too conservative in its current policy and wants to be approved by more than 450 customers, will not be able to know how much the risk will increase if the bank has never approved a customer under 500? The refusal of inference allows estimates of the bad debt rate of cases not approved and can help make decisions.

4. The use of declined inference may also identify good customers who have been rejected in the past, explore these customers, and then improve internal processes and identify the benefits that can be added.

The opportunity to use the deduction is not appropriate:

1, high approval rate, and confidence in judgment is very strong, not applicable: At this time because of the approval rate is too high, and a high degree of confidence in decision-making, it can be assumed to be declined by the average person is bad.

2, high approval rate, regardless of bad debt rate, not applicable: High bad debt rate, because the high approval rate of the mother has been close to all the applications, representing the majority of the parent group is not bad debt, whether or not do not make the deduction effect is not big. Low bad debt rate, the same as above, at this time can be "declined is the bad guys" inference.

3, medium and low approval rate applies: With appropriate risk strategy, declined inference can help to find more suitable customers.

After adding the declined inference, the application model of the building flowchart:

2 The method of rejecting inference

One, all the declined pieces are bad pieces

This approach is less appropriate because some part of the data is likely to be a good customer, which may reduce the accuracy of the model. Of course, if a high approval rate, such as more than 95%, and the high level of judgment, then, to the degree of reliability, it can be assumed that all the rejected items are bad pieces.

Second, the assignment of declined customers according to the current and approved pieces of the ratio to make inferences

This method assumes that the current judgment system is very impartial and not biased. But assuming that such proportions do not help, it needs to be complemented by relevant calculations and simulations.

Third, ignore all declined customers

This method is to pretend that there is no such denial of the existence of customers, and by the way, customers below the segmentation point declined, the steps are:

1. Establish a scoring model using all approved components.

2. Once again scored, the people below the segmentation point are all considered to be declined.

However, this approach is only an afterthought to the current system, which has no confidence in the current system or the procedure, and is generally not used frequently.

Iv. approval of all application items

This approach is to find out what the customer's real performance is, and this will be linked to a specific time-approved customer, which shows that the sample is truly approved by the customer, and this method is the most practical and scientific approach, and there will be no too conservative or overvalued bad debt rate.

V. Methods based on internal or off-line data

(i) two scorecard interactive application

This approach is for customers who have been rejected in one product but approved for another similar product, using internal data to analyze their behavior.

(ii) Use of out-of-line data

Customers who are declined by us but approved by other companies may use their external data to track the performance of the customer. This method approximates real performance, but its drawbacks are as follows:

1, can only improve the performance of a card, but the actual bad debt still occurs for the asset quality within the line has not improved.

2, in the management of the obstacles are not able to get the credit rating of customers declined to record, in addition to the authority or time limit, there is a factor in the law, so that banks may not be able to collect or buy the relevant information of the customer.

Assuming that the data needs to be used for cross-use within the line, the following points need to be noted:

1, must be at the same time from the point, in order to avoid the difference in time caused by the season errors.

2, the definition of good or bad to close.

3, the sample number will not be too much: because the bad customer applies for the same bank product, may be declined in the second scorecard.

VI. Allocation Act (parceling)

This method distributes the good and bad parts according to the ratio of each interval, and assigns the rejected pieces to each of the fraction intervals, which contains the following steps:

1. Use a known good/bad sample to build an initial scorecard model.

2. Use the first stage model to score all the rejections and estimate their expected default probability.

3, the known good/bad pieces of samples according to the score score of the high and low group, calculate the actual default rate within each group.

4, in the same way, the rejected pieces according to the points of the previous steps to group. The actual default rate of each subgroup is taken as the sampling proportion, and the declined parts under the subgroup are randomly selected, and the remainder is a bad part, and the rest is a good piece.

5. A sample of these rejected samples, which have been inferred as good/bad pieces, was added to the original sample of approved samples, and the scorecard model was re-commented.

Approval and the rejection of the score card in the allocation of scores, in which the block is the use of the approval of the scorecard to determine the score distribution, as for the good or bad distribution of the rejected pieces, is the use of bad% and good% to distribute the approved pieces, for example, in 753 to 850 of this interval, 605 declined, in the approval of the bad%=10.6 %, so there will be 64 rejected pieces assigned to the bad Pieces (605x10.6%=64), while the good pieces are 541 pieces (605x89.4%=541).

Vii. Rigid truncation method (hard Cutoff)

Also known as the Simple expansion method (augmentation), the method is similar to the Parceling method, but the hard cutoff is to assign all the rejected pieces to the bad or good pieces according to the given score, and the Parceling law is in different fractions, according to different proportions, Allocate the declined pieces to each of the sub-scale intervals. The hard cutoff steps are as follows:

1. A sample of known good/bad pieces was used to comment on the card model.

2, use scoring model to score all the rejected pieces, and establish the expected bad debt rate p (poor).

3, set a bad account level to distinguish good or bad pieces, in this bad debt level above as bad pieces, the following is considered a nice piece.

4, the merits of the deduction of the good or bad re-placed in the model and commented on the sub-card model.

When simulating the application, the percentage of rejection is approved to moderately weighted the rejected part of the sample. Take the left-hand image as an example, the proportion of the application for the approval of the parent and the distribution of the rejected pieces is 70% and 30%, the model sample approval and the proportion of the distribution of rejected parts is 66.6% and 33.3%, you can speculate that the model sample declined slightly higher, you need to use the proportion of the parent weight adjustment, so you can adjust the proportion 33.3%)/(70%/30%) = 0.8574.

Eight, fuzzy method (vague)

This method is not to assign samples as good/bad pieces, but to split each sample of rejected pieces into parts of the bad pieces and good pieces. The steps of the fuzzy method are as follows:

1. Use the model of the known approved sample to score the rejected parts and estimate the probability of default.

2, according to the estimated default rate of each declined to calculate the P (good) and P (bad).

3, will be declined samples of the sample to distinguish between good pieces and bad pieces of two samples. The bad part is weighted to the probability of default, and a good piece is weighted against the probability of non-default.

4. A combination of rejected and approved samples was re-established to comment on the model of the card.

Ix. iterative re-classification (iterative reclassification)

This method is similar to hard Cutoff, but this method repeats the grouping until a certain threshold is reached. The steps for this method are as follows:

1, according to the approval of the case to establish scoring cards;

2, the use of existing models to the customers to be declined to score. After scoring the use of each interval is better or worse than to do a poor customer's good or bad, and randomly given pieces or pieces;

3, after a given merger of the approved pieces, re-establish the model until the specified statistics converge, such as the use of ln (odds) vs. score scatter map, or use the model parameters to reach a certain convergence range, etc.

4, if the use of good or bad than the model of the icon method, you need to pay attention to all the lines in the known better than the line, or there will be declined customers than the approval of customers better quality of doubts.

Eighth chapter final model selection and risk calibration (calibration)

The model regression, which is derived from the characteristic variable analysis and the two-stage regression model, is the most important architecture of the scorecard and default probability (probability of DEFAULT;PD) model, from which the architecture can be developed separately:

1. Application or Behavioral scorecard

2. PD Model for Capital accrual

1 Final model output

• The final model output is a regression formula, its model is not easy to explain in the application of scorecard, so it is necessary to convert the variables into fractions to facilitate the application of the business;

• The conversion of a variable can be replaced by a virtual variable (dummy variable) or woe value, where the virtual variable can simply multiply each variable group by 1,000 to express the weight of the group of variables, whereas the woe value needs to apply a more complex conversion.

Using the scoring card scale technology to convert the scorecard coefficient into a convenient way to read the weights:

1. Ratio of (Good/bad):

The average score is 200 points, every 20 points odds ratio (ODDS) doubled, Odds refers to the ratio of good and bad (Good/bad), that is, every 20 points, the proportion of bad pieces will be doubled, so we can plan a reasonable risk area according to this fractional interval for the differential management.

2. Fractional scale:

(1) Basically we built the scorecard rules for the additive rules, therefore, the adjusted score according to the above hypothesis must be a simple linear equation: SCORE=A+BXLN (odds) (Formula 1)

Since the assumption is that the average score is 200, the 20 odds of each cell doubles, so we can put this assumption into equation 1 to get the following equations: Score+pdo=a+bxln (2ODDS) (Formula 2)

(where PDO is point of double Odds, indicating how many points Odds doubled) the Formula 2 reduction 1,score offset each other, you can get the following program:

PDO=BXLN (2odds)-BXLN (odds) =bxln (2) (Formula 3.1)

B=PDO/LN (2) (Formula 3.2)

At this point, we can calculate the B value according to the assumption of PDO, and then bring the B value into the equation to calculate A value: A=SCORE-BXLN (odds) (Formula 4)

(where score is the average fraction, odds is brought in at the average level when the model is built)

(2) According to the Rogers regression equation, the odds equals the variables and the regression equation coefficients and the constant term combination, according to the equation calculation, the following fractional scale formula can be obtained: SCORE=A+BXLN (odds)

Where the value of the variable is in the woe value of the grouping, n is the number of variables in the model regression formula.

In this way, the final model can be produced as a table:

The purpose of this approach is as follows:

1. Easy to compare each version of the scoring card during the build process.

2. User-friendly interpretation.

3. Facilitate the information disclosure of supervision agencies and the probability of default integration.

2 Set up risk calibration (Risk calibration)

Score Adjustment for different scorecard

• If the same product due to different characteristics cut into a number of scorecard, such as credit card score Cache for the full clearance of the card and the cycle of the user scorecard, so that the two scorecard model base may stand at different levels, so you must set up a risk calibration (Risk calibration) to convert the score of each grouping;

• In terms of good or bad performance defined in different clusters between the same premise, the risk of calibration is to use the same good or bad ratio to convert each grouping score score, so that the same good or bad than to achieve the same score results, and the score and bad ratio should be positive correlation.

The scoring model risk calibration process is as follows:

1. Calculate the final model score of all the samples in each grouping.

2, each grouping sample score from low to high order.

3, the sorted samples are cut into n equal, may be 20, 30 and 50, and so on, and then calculate the number of good pieces of each sub-divided, bad pieces, better or worse, Ln (Odds) and the average score.

4, establish the average score of each cut and the regression between ln (ODDS), observe in which kind of cut, the regression formula will have the best interpretation ability, that is, the highest r-square, and observe the ratio of expected good or bad vs. whether the actual ratio is close.

5, by the above regression type into SCORE=A+BXLN (ODDS), you can get the final calibration function, such as base score for 400,PDO 40, then final SCORE=400+40/LN (2) xln (Odds)

The logarithm ratio of "ln (ODDS)" is the best regression model which is established by the average fraction and logarithmic good/bad ratio, which can be obtained by using various statistical software packages.

6, the calibration score is the variable, the final scoring model of the variables for the self-variable regression analysis, you can get the coefficients of the last variable attributes, which is the risk calibration score card (calibrated scorecard) scores. In future, the use of scorecard variables and regular monitoring are mainly calibrated scorecard.

In table 8-2 and table 8-3, for example, you can get the best interpretation of grouping 30 (R2 is 0.993 highest), then its calibration function is listed as follows: Last score =400+40/ln (2) x ( -190.7+0.002-0.25 +0.01)

3 isolation of risk levels

For the benefit of practical application, the score card should be based on the risk of the partition, generally not more than 20 equal parts mainly, commonly used in the way of segmentation:

(a) good or bad than law:

Cut the risk level from similar to the same level, mainly to the same risk level of the group management, its upward gap is about double good or bad ratio (double odds).

(ii) The matrix sharing method:

Each risk level is assigned a similar number of people, and there should be more than one modeling sample per interval. Levels with too few samples can be combined with other neighboring levels, which generally occur in low-clustering and high-clustering hierarchies. The risk level for each slice is completed, and its sample count is at least 3% to 5% of the total model sample, which is enough sample quantity.

3 example of an interval of risk levels

4 Model Validation

In order to effectively evaluate the predictive ability of credit scorecard and whether the diagnosis needs further correction during the establishment of Credit scorecard, the scorecard effectiveness must be examined through the following model verification.

• Gini (Gini) coefficient

• Kolmogrov-smirnov Value (hereinafter referred to as K-s value)

• Area on the ROC curve (areas under ROC CURVE;AUC)

One, the Gini (Gini) coefficient:

The mid-downward bend curve, known as Lorenz's Curve, is a standard chart used to evaluate the scorecard's identification effect, which is based on a high-to-low score, with a cumulative normal customer ratio of the total normal customer, while the vertical axis is the fraction from high to low, and the cumulative default client accounts for the total default client.

Because the score is low-risk customers, the cumulative default rate will grow lower than the cumulative normal customer, therefore, Lorenz's curve will present a downward curved curve, in the Lorenz's curve graph, the right-projecting half-moon area is divided by the ratio of the triangular area below the 45-degree line, Called the Gini coefficient (Gini coefficient).

The larger the coefficient, the higher the discriminating force, and the smaller the coefficient, the lower the discriminating power. The meaning of the 45-degree line means that the model has no distinguishing ability (i.e., stochastic model).

Second, Kolmogrov-smirnov value (k-s value):

The ROC curve is calculated at all possible truncation points, the error rate of the scoring model (type one error rate, false rate indicating that the model will default customer mistakenly rated as good customer, the ratio of credit service) and 1-false rejection rate (type two error rate, false rejection rate of the model will normal customer mistakenly rated bad customer, The proportion of the refusal of its credit service), is drawn.

The AUC value is the total area below the curve.

The area on the ROC curve (areas under ROC CURVE;AUC)

The K-s test chart is used to assess what scoring range in the scorecard can separate normal customers from default clients, the higher the K-s value, the greater the distance between them, so the maximum value of the k-s curve is the best point to identify the normal and defaulting households.

Model Distinguishing Force Judging index

Model Validation In addition to the identification of the Development Group sample (development sample), it is also necessary to verify the test group (holdout sample) and the sample (out sample).

The test group, as the name implies, is a validation sample as well as a part of the modeling sample, randomly extracting part of the modeling sample, as a validation sample for in-sample validation.

Out-of-sample validation is the validation data from non-modeling samples, which can be divided into sample (out of sample) validation samples and sample time (out of date) validation samples, depending on the sampling period. The sample verification sample is a sample of samples at the sampling point and the sample time, while the samples out-of-date verification sample does not contain sample samples at the same sampling point as the modeling sample.

Training Group and test group (development & Hold-out Sample) validation

The training group accounted for 70% of the modeling sample, the test group accounted for 30% of the modeling sample, the following table for example, the Training Group and test group through the Gini value and K-s value identification, with good or bad district ability.

Validation of outside time samples (out-of-tIME sample)

This is to ensure that the model is not adaptive due to external factors, but also to ensure that the model is not disturbed by time. This dataset differs from the original dataset only at a point in time, and the other data fields and definitions are still the same as the original data.

Gini value and K-s value decrease slightly, but all are in the range of good or bad, which indicates that the model is not disturbed by the time factor, and the model can still maintain its original discriminating ability.

According to the result of risk grading, the model identification force is verified according to the training Group, test group and sample data, in order to ensure that the classification method is discriminating.

As shown, Gini values and k-s values in this classification are very good.

This topic will also continue to launch, please pay attention!

Next section:

Nineth Chapter Decision point (cut-off) setting

The tenth chapter of credit rating Model monitoring report

The 11th chapter of credit Evaluation model Strategy application

The 12th chapter of credit rating model case

Example analysis of credit rating model (taking consumer finance as an example)