creditDefaultCopula Simulation Workflow

This example shows a common workflow for using a creditDefaultCopula object for a portfolio of credit instruments.

For an example of an advanced workflow using the creditDefaultCopula object, see Modeling Correlated Defaults with Copulas.

Step 1. Create a creditDefaultCopula object with a two-factor model.

Load the saved portfolio data. Create a creditDefaultCopula object with a two-factor model using with the values EAD, PD, LGD, and Weights2F.

load CreditPortfolioData.mat;
cdc = creditDefaultCopula(EAD, PD, LGD,Weights2F,'FactorCorrelation',FactorCorr2F);
disp(cdc)

  creditDefaultCopula with properties:

            Portfolio: [100×5 table]
    FactorCorrelation: [2×2 double]
             VaRLevel: 0.9500
          UseParallel: 0
      PortfolioLosses: []

disp(cdc.Portfolio(1:10:100,:))

    ID     EAD          PD        LGD              Weights          
    __    ______    __________    ____    __________________________

     1    21.627     0.0050092    0.35      0.35         0      0.65
    11    29.338     0.0050092    0.55      0.35         0      0.65
    21    3.8275     0.0020125    0.25    0.1125    0.3375      0.55
    31    26.286     0.0020125    0.55    0.1125    0.0375      0.85
    41    42.868     0.0050092    0.55      0.25         0      0.75
    51    7.1259    0.00099791    0.25         0      0.25      0.75
    61    10.678     0.0020125    0.35         0      0.15      0.85
    71     2.395    0.00099791    0.55         0      0.15      0.85
    81    26.445      0.060185    0.55         0      0.45      0.55
    91    7.1637       0.11015    0.25      0.35         0      0.65

Step 2. Set the VaRLevel to 99%.

Set the VarLevel property for the creditDefaultCopula object to 99% (the default is 95%).

cdc.VaRLevel = 0.99;

Step 3. Run a simulation.

Use the simulate function to run a simulation on the creditDefaultCopula object for 100,000 scenarios.

 cdc = simulate(cdc,1e5)

cdc = 
  creditDefaultCopula with properties:

            Portfolio: [100×5 table]
    FactorCorrelation: [2×2 double]
             VaRLevel: 0.9900
          UseParallel: 0
      PortfolioLosses: [30.1008 3.6910 3.2895 19.2151 7.5761 44.5088 19.5419 1.7909 72.1443 12.6933 36.0228 1.7909 4.8512 23.0230 54.0877 35.9298 35.3757 26.1678 36.8868 24.6242 2.9770 15.3030 0 0 10.5546 61.2268 32.5802 42.5504 … ] (1×100000 double)

Step 4. Generate a report for the portfolio risk.

Use the portfolioRisk function to obtain a report for risk measures and confidence intervals for EL, Std, VaR, and CVaR.

[portRisk,RiskConfidenceInterval] = portfolioRisk(cdc)

portRisk=1×4 table
      EL       Std       VaR      CVaR 
    ______    ______    _____    ______

    24.876    23.778    102.4    121.28

RiskConfidenceInterval=1×4 table
           EL                 Std                 VaR                 CVaR      
    ________________    ________________    ________________    ________________

    24.729    25.023    23.674    23.883    101.19     103.5    120.13    122.42

Step 5. Visualize the distribution.

Use the histogram function to display the distribution for EL, VaR, and CVaR.

histogram(cdc.PortfolioLosses);
title('Distribution of Portfolio Losses');

Step 6. Generate a risk contributions report.

Use the riskContribution function to display the risk contribution. The risk contributions, EL and CVaR, are additive. If you sum each of these two metrics over all the counterparties, you get the values reported for the entire portfolio in the portfolioRisk table.

rc = riskContribution(cdc);

disp(rc(1:10,:))

    ID        EL           Std           VaR          CVaR   
    __    __________    __________    _________    __________

     1      0.036031      0.022762     0.083828       0.13625
     2      0.068357      0.039295      0.23373       0.24984
     3        1.2228       0.60699       2.3184        2.3775
     4      0.002877    0.00079014    0.0024248     0.0013137
     5       0.12127      0.037144      0.18474       0.24622
     6       0.12638      0.078506      0.39779       0.48334
     7       0.84284        0.3541       1.6221        1.8183
     8    0.00090088    0.00011379    0.0016463    0.00089197
     9       0.93117       0.87638       3.3868        3.9936
    10       0.26054       0.37918       1.7399        2.3042

Step 7. Simulate the risk exposure with a t copula.

Use the simulate function with optional input arguments for Copula and t. Save the results to a new creditDefaultCopula object (cct).

cdct = simulate(cdc,1e5,'Copula','t','DegreesOfFreedom',10)

cdct = 
  creditDefaultCopula with properties:

            Portfolio: [100×5 table]
    FactorCorrelation: [2×2 double]
             VaRLevel: 0.9900
          UseParallel: 0
      PortfolioLosses: [3.6910 1.9775 128.4550 2.1852 4.8512 0 26.2682 0 54.8980 24.3618 16.8483 1.9775 26.5877 40.3189 13.0581 26.2682 2.0924 15.4193 25.1406 32.6275 34.6938 1.4985 24.0275 4.8512 228.3562 4.1248 1.4985 34.6339 … ] (1×100000 double)

Step 8. Compare confidence bands for different copulas.

Use the confidenceBands function to compare confidence bands for the two different copulas.

confidenceBands(cdc,'RiskMeasure','Std','ConfidenceIntervalLevel',0.90,'NumPoints',10) 

ans=10×4 table
    NumScenarios    Lower      Std      Upper 
    ____________    ______    ______    ______

       10000        23.525    23.799    24.079
       20000        23.564    23.758    23.955
       30000        23.543    23.701    23.861
       40000        23.621    23.758    23.897
       50000        23.565    23.687    23.811
       60000        23.604    23.716    23.829
       70000        23.688    23.792    23.897
       80000        23.663     23.76    23.858
       90000        23.639     23.73    23.823
       1e+05        23.691    23.778    23.866

confidenceBands(cdct,'RiskMeasure','Std','ConfidenceIntervalLevel',0.90,'NumPoints',10)

ans=10×4 table
    NumScenarios    Lower      Std      Upper 
    ____________    ______    ______    ______

       10000        31.923    32.294    32.675
       20000        31.775    32.036    32.302
       30000        31.759    31.972    32.188
       40000        31.922    32.107    32.295
       50000        32.012    32.179    32.347
       60000        31.911    32.062    32.216
       70000        31.879    32.019    32.161
       80000        31.909     32.04    32.173
       90000        31.866     31.99    32.114
       1e+05        31.933     32.05    32.169