predict

Predict loss given default

Since R2021a

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Syntax

LGD = predict(lgdModel,data)

Description

LGD = predict(lgdModel,data) computes the loss given default (LGD).

When using a Regression model, the predict function operates on the underlying compact statistical model and then transforms the predicted values back to the LGD scale.

When using a Tobit model, the predict function operates on the underlying Tobit regression model and returns the unconditional expected value of the response, given the predictor values.

example

Examples

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Open Live Script

This example shows how to use fitLGDModel to fit data with a Regression model and then predict the loss given default (LGD) values.

Load Data

Load the loss given default data. 

load LGDData.mat
head(data)
      LTV        Age         Type           LGD   
    _______    _______    ___________    _________

    0.89101    0.39716    residential     0.032659
    0.70176     2.0939    residential      0.43564
    0.72078     2.7948    residential    0.0064766
    0.37013      1.237    residential     0.007947
    0.36492     2.5818    residential            0
      0.796     1.5957    residential      0.14572
    0.60203     1.1599    residential     0.025688
    0.92005    0.50253    investment      0.063182

Partition Data

Separate the data into training and test partitions. 

rng('default'); % for reproducibility
NumObs = height(data);

c = cvpartition(NumObs,'HoldOut',0.4);
TrainingInd = training(c);
TestInd = test(c);

Create Regression LGD Model

Use fitLGDModel to create a Regression model using training data.

lgdModel = fitLGDModel(data(TrainingInd,:),'regression');
disp(lgdModel)    
  Regression with properties:

    ResponseTransform: "logit"
    BoundaryTolerance: 1.0000e-05
              ModelID: "Regression"
          Description: ""
      UnderlyingModel: [1×1 classreg.regr.CompactLinearModel]
        PredictorVars: ["LTV"    "Age"    "Type"]
          ResponseVar: "LGD"
           WeightsVar: ""

Display the underlying model.

disp(lgdModel.UnderlyingModel)
Compact linear regression model:
    LGD_logit ~ 1 + LTV + Age + Type

Estimated Coefficients:
                       Estimate       SE        tStat       pValue  
                       ________    ________    _______    __________

    (Intercept)        -4.7549      0.36041    -13.193    3.0997e-38
    LTV                 2.8565      0.41777     6.8377    1.0531e-11
    Age                -1.5397     0.085716    -17.963    3.3172e-67
    Type_investment     1.4358       0.2475     5.8012     7.587e-09


Number of observations: 2093, Error degrees of freedom: 2089
Root Mean Squared Error: 4.24
R-squared: 0.206,  Adjusted R-Squared: 0.205
F-statistic vs. constant model: 181, p-value = 2.42e-104

Predict LGD on Test Data

Use predict to predict the LGD for the test data set. 

predictedLGD = predict(lgdModel,data(TestInd,:))
predictedLGD = 1394×1

    0.0009
    0.0037
    0.1877
    0.0011
    0.0112
    0.0420
    0.0529
    0.0000
    0.0090
    0.0239
    0.0035
    0.0065
    0.0720
    0.0061
    0.0012
      ⋮

You can analyze and validate these predictions using modelDiscrimination and modelCalibration.

Open Live Script

This example shows how to use fitLGDModel to fit data with a Tobit model and then predict the loss given default (LGD) values.

Load Data

Load the loss given default data.

load LGDData.mat
head(data)
      LTV        Age         Type           LGD   
    _______    _______    ___________    _________

    0.89101    0.39716    residential     0.032659
    0.70176     2.0939    residential      0.43564
    0.72078     2.7948    residential    0.0064766
    0.37013      1.237    residential     0.007947
    0.36492     2.5818    residential            0
      0.796     1.5957    residential      0.14572
    0.60203     1.1599    residential     0.025688
    0.92005    0.50253    investment      0.063182

Partition Data

Separate the data into training and test partitions. 

rng('default'); % for reproducibility
NumObs = height(data);

c = cvpartition(NumObs,'HoldOut',0.4);
TrainingInd = training(c);
TestInd = test(c);

Create Tobit LGD Model

Use fitLGDModel to create a Tobit model using training data.

lgdModel = fitLGDModel(data(TrainingInd,:),'tobit');
disp(lgdModel)    
  Tobit with properties:

      CensoringSide: "both"
          LeftLimit: 0
         RightLimit: 1
            Weights: [0×1 double]
            ModelID: "Tobit"
        Description: ""
    UnderlyingModel: [1×1 risk.internal.credit.TobitModel]
      PredictorVars: ["LTV"    "Age"    "Type"]
        ResponseVar: "LGD"
         WeightsVar: ""

Display the underlying model.

disp(lgdModel.UnderlyingModel)
Tobit regression model:
     LGD = max(0,min(Y*,1))
     Y* ~ 1 + LTV + Age + Type

Estimated coefficients:
                       Estimate        SE         tStat       pValue  
                       _________    _________    _______    __________

    (Intercept)         0.058257     0.027279     2.1356       0.03283
    LTV                  0.20126      0.03136     6.4177    1.7064e-10
    Age                -0.095407    0.0072633    -13.135             0
    Type_investment      0.10208     0.018077     5.6471    1.8542e-08
    (Sigma)              0.29288    0.0057084     51.306             0

Number of observations: 2093
Number of left-censored observations: 547
Number of uncensored observations: 1521
Number of right-censored observations: 25
Log-likelihood: -698.383

Predict LGD on Test Data

Use predict to predict the LGD for the test data set. 

predictedLGD = predict(lgdModel,data(TestInd,:))
predictedLGD = 1394×1

    0.0879
    0.1243
    0.3204
    0.0934
    0.1672
    0.2238
    0.2370
    0.0102
    0.1592
    0.1989
    0.1276
    0.1457
    0.2618
    0.1448
    0.0941
      ⋮

You can analyze and validate these predictions using modelDiscrimination and modelCalibration.

Open Live Script

This example shows how to use fitLGDModel to fit data with a Beta model and then predict the loss given default (LGD) values.

Load Data

Load the loss given default data.

load LGDData.mat
head(data)
      LTV        Age         Type           LGD   
    _______    _______    ___________    _________

    0.89101    0.39716    residential     0.032659
    0.70176     2.0939    residential      0.43564
    0.72078     2.7948    residential    0.0064766
    0.37013      1.237    residential     0.007947
    0.36492     2.5818    residential            0
      0.796     1.5957    residential      0.14572
    0.60203     1.1599    residential     0.025688
    0.92005    0.50253    investment      0.063182

Partition Data

Separate the data into training and test partitions. 

rng('default'); % for reproducibility
NumObs = height(data);

c = cvpartition(NumObs,'HoldOut',0.4);
TrainingInd = training(c);
TestInd = test(c);

Create Beta LGD Model

Use fitLGDModel to create a Beta model using training data.

lgdModel = fitLGDModel(data(TrainingInd,:),'Beta');
disp(lgdModel)    
  Beta with properties:

    BoundaryTolerance: 1.0000e-05
              ModelID: "Beta"
          Description: ""
      UnderlyingModel: [1×1 risk.internal.credit.BetaModel]
        PredictorVars: ["LTV"    "Age"    "Type"]
          ResponseVar: "LGD"
           WeightsVar: ""

Display the underlying model.

disp(lgdModel.UnderlyingModel)
Beta regression model:
     logit(LGD) ~ 1_mu + LTV_mu + Age_mu + Type_mu
     log(LGD) ~ 1_phi + LTV_phi + Age_phi + Type_phi

Estimated coefficients:
                           Estimate       SE        tStat       pValue  
                           ________    ________    _______    __________

    (Intercept)_mu          -1.3772     0.13201    -10.433             0
    LTV_mu                  0.60269     0.15087     3.9947    6.7021e-05
    Age_mu                 -0.47464    0.040264    -11.788             0
    Type_investment_mu      0.45372    0.085143     5.3289    1.0941e-07
    (Intercept)_phi        -0.16336     0.12591    -1.2974       0.19465
    LTV_phi                0.055881     0.14719    0.37965       0.70424
    Age_phi                 0.22887    0.040335     5.6742    1.5867e-08
    Type_investment_phi    -0.14102    0.078155    -1.8044      0.071312

Number of observations: 2093
Log-likelihood: -5291.04

Predict LGD on Test Data

Use predict to predict the LGD for the test data set. 

predictedLGD = predict(lgdModel,data(TestInd,:))
predictedLGD = 1394×1

    0.0937
    0.1492
    0.3526
    0.0964
    0.1886
    0.2595
    0.2677
    0.0213
    0.1774
    0.2256
    0.1337
    0.1677
    0.2916
    0.1617
    0.1051
      ⋮

You can analyze and validate these predictions using modelDiscrimination and modelCalibration.

Input Arguments

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Loss given default model, specified as a previously created Regression, Tobit, or Beta object using fitLGDModel.

Data Types: object

Data, specified as a NumRows-by-NumCols table with predictor and response values. The variable names and data types must be consistent with the underlying model.

Data Types: table

Output Arguments

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Loss given default values, returned as a NumRows-by-1 numeric vector.

More About

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References

[1] Baesens, Bart, Daniel Roesch, and Harald Scheule. Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS. Wiley, 2016.

[2] Bellini, Tiziano. IFRS 9 and CECL Credit Risk Modelling and Validation: A Practical Guide with Examples Worked in R and SAS. San Diego, CA: Elsevier, 2019.

Version History

Introduced in R2021a

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See Also

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