Expected Credit Loss (ECL) Computation

This example show how to perform ECL computations using simulated loan data, macro scenario data, and an existing lifetime probability of default (PD) model.

Load Data and Model

Load loan data ready for prediction, macro scenario data, and corresponding scenario probabilities.

load DataPredictLifetime.mat
disp(LoanData)

     ID      ScoreGroup      YOB    Year
    ____    _____________    ___    ____

    1304    "Medium Risk"     4     2020
    1304    "Medium Risk"     5     2021
    1304    "Medium Risk"     6     2022
    1304    "Medium Risk"     7     2023
    1304    "Medium Risk"     8     2024
    1304    "Medium Risk"     9     2025
    1304    "Medium Risk"    10     2026
    2067    "Low Risk"        7     2020
    2067    "Low Risk"        8     2021
    2067    "Low Risk"        9     2022
    2067    "Low Risk"       10     2023

disp(head(MultipleScenarios,10))

    ScenarioID    Year    GDP     Market
    __________    ____    ____    ______

    "Severe"      2020    -0.9     -5.5 
    "Severe"      2021    -0.5     -6.5 
    "Severe"      2022     0.2       -1 
    "Severe"      2023     0.8      1.5 
    "Severe"      2024     1.4        4 
    "Severe"      2025     1.8      6.5 
    "Severe"      2026     1.8      6.5 
    "Severe"      2027     1.8      6.5 
    "Adverse"     2020     0.1     -0.5 
    "Adverse"     2021     0.2     -2.5 

disp(ScenarioProbabilities)

                 Probability
                 ___________

    Severe           0.1    
    Adverse          0.2    
    Baseline         0.3    
    Favorable        0.2    
    Excellent        0.2    

load LifetimeChampionModel.mat
disp(pdModel)

  Probit with properties:

        ModelID: "Champion"
    Description: "A sample model used as champion model for illustration purposes."
          Model: [1x1 classreg.regr.CompactGeneralizedLinearModel]
          IDVar: "ID"
         AgeVar: "YOB"
       LoanVars: "ScoreGroup"
      MacroVars: ["GDP"    "Market"]
    ResponseVar: "Default"

Visualize Lifetime PDs

For ECL computations, only the marginal PDs are required. However, first you can visualize the lifetime PDs.

CompanyIDChoice = "1304";
CompanyID = str2double(CompanyIDChoice);
IndCompany = LoanData.ID == CompanyID;
Years = LoanData.Year(IndCompany);
NumYears = length(Years);

ScenarioID = unique(MultipleScenarios.ScenarioID,'stable');
NumScenarios = length(ScenarioID);

LifetimePD = zeros(NumYears,NumScenarios);
for ii=1:NumScenarios
   IndScenario = MultipleScenarios.ScenarioID==ScenarioID(ii);
   data = join(LoanData(IndCompany,:),MultipleScenarios(IndScenario,:));
   LifetimePD(:,ii) = predictLifetime(pdModel,data);
end

plot(Years,LifetimePD)
xticks(Years)
grid on
xlabel('Year')
ylabel('Lifetime PD')
title('Lifetime PD By Scenario')
legend(ScenarioID,'Location','best')

Compute ECL

Strictly speaking, the computation of ECL requires a lifetime PD model, a lifetime LGD model, and a lifetime EAD model, plus the scenarios, scenario probabilities, and an effective interest rate.

For simplicity, this example assumes constant LGD and EAD models and a given interest rate.

LGD = 0.55;
EAD = 100000;
EffRate = 0.045;

CompanyIDChoice = "1304";
CompanyID = str2double(CompanyIDChoice);
IndCompany = LoanData.ID == CompanyID;
Years = LoanData.Year(IndCompany);
NumYears = length(Years);

ScenarioID = unique(MultipleScenarios.ScenarioID,'stable');
NumScenarios = length(ScenarioID);

MarginalPD = zeros(NumYears,NumScenarios);
for ii=1:NumScenarios
   IndScenario = MultipleScenarios.ScenarioID==ScenarioID(ii);
   data = join(LoanData(IndCompany,:),MultipleScenarios(IndScenario,:));
   MarginalPD(:,ii) = predictLifetime(pdModel,data,'ProbabilityType','marginal');
end

DiscTimes = Years-Years(1)+1;
DiscFactors = 1./(1+EffRate).^DiscTimes;

ProbScenario = ScenarioProbabilities.Probability;
ECL_t_s = (MarginalPD*LGD*EAD).*DiscFactors; % ECL by year and scenario
ECL_s = sum(ECL_t_s); % ECL total by scenario
ECL = ECL_s*ProbScenario; % ECL weighted average over all scenarios

% Arrange ECL data for display in table format
% Append ECL total per scenario and scenario probabilities
ECL_Disp = array2table([ECL_t_s; ECL_s; ProbScenario']);
ECL_Disp.Properties.VariableNames = ScenarioID;
ECL_Disp.Properties.RowNames = [strcat("ECL ",string(Years)); "ECL total"; "Probability"];
disp(ECL_Disp)

                   Severe    Adverse    Baseline    Favorable    Excellent
                   ______    _______    ________    _________    _________

    ECL 2020       595.58    507.16      430.44      364.11       306.97  
    ECL 2021       394.24    349.95      310.02      274.11        241.9  
    ECL 2022       235.53     215.4      196.75       179.5       163.57  
    ECL 2023       143.05    135.23      127.75      120.59       113.77  
    ECL 2024       85.219    83.517      81.816      80.118       78.429  
    ECL 2025       51.346    51.514      51.665      51.798       51.917  
    ECL 2026       33.162    33.271      33.368      33.454       33.531  
    ECL total      1538.1      1376      1231.8      1103.7       990.08  
    Probability       0.1       0.2         0.3         0.2          0.2  

fprintf('Lifetime ECL for company %s is: %g\n',CompanyIDChoice,ECL)

Lifetime ECL for company 1304 is: 1217.32