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Confidence interval bands


cbTable = confidenceBands(cdc)
cbTable = confidenceBands(cdc,Name,Value)



cbTable = confidenceBands(cdc) returns a table of the requested risk measure and its associated confidence bands. confidenceBands is used to investigate how the values of a risk measure and its associated confidence interval converge as the number of scenarios increases. The simulate function must be run before confidenceBands is used. For more information on using a creditDefaultCopula object, see creditDefaultCopula.


cbTable = confidenceBands(cdc,Name,Value) adds optional name-value pair arguments.


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Load saved portfolio data.

load CreditPortfolioData.mat;

Create a creditDefaultCopula object with a two-factor model.

cdc = creditDefaultCopula(EAD,PD,LGD,Weights2F,'FactorCorrelation',FactorCorr2F)
cdc = 

  creditDefaultCopula with properties:

            Portfolio: [100x5 table]
    FactorCorrelation: [2x2 double]
             VaRLevel: 0.9500
      PortfolioLosses: []

Set the VaRLevel to 99%.

cdc.VaRLevel = 0.99;

Use the simulate function before running confidenceBands. Use confidenceBands with the creditDefaultCopula object to generate the cbTable.

cdc = simulate(cdc,1e5);
cbTable = confidenceBands(cdc,'RiskMeasure','Std','ConfidenceIntervalLevel',0.9);
ans =

  10x4 table

    NumScenarios    Lower      Std      Upper 
    ____________    ______    ______    ______

     1000           22.796    23.633    24.538
     2000            22.62    23.207    23.828
     3000           23.082    23.572    24.084
     4000           23.125    23.549    23.991
     5000           23.228     23.61    24.005
     6000           23.372    23.723    24.085
     7000           23.378    23.702    24.037
     8000           23.268     23.57    23.881
     9000           23.419    23.706    24.001
    10000           23.467    23.739    24.019

Input Arguments

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creditDefaultCopula object obtained after running the simulate function.

For more information on creditDefaultCopula objects, see creditDefaultCopula.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: cbTable = confidenceBands(cdc,'RiskMeasure','Std','ConfidenceIntervalLevel',0.9,'NumPoints',50)

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Risk measure to investigate, specified as the comma-separated pair consisting of 'RiskMeasure' and a character vector or string. Possible values are:

  • 'EL' — Expected loss, the mean of portfolio losses

  • 'Std' — Standard deviation of the losses

  • 'VaR' — Value at risk at the threshold specified by the VaRLevel property of the creditDefaultCopula object

  • 'CVaR' — Conditional VaR at the threshold specified by the VaRLevel property of the creditDefaultCopula object

Data Types: char | string

Confidence interval level, specified as the comma-separated pair consisting of 'ConfidenceIntervalLevel' and a numeric between 0 and 1. For example, if you specify 0.95, a 95% confidence interval is reported in the output table (cbTable).

Data Types: double

Number of scenario samples to report, specified as the comma-separated pair consisting of 'NumPoints' and a nonnegative integer. The default is 100, meaning confidence bands are reported at 100 evenly spaced points of increasing sample size ranging from 0 to the total number of simulated scenarios.


NumPoints must be a numeric scalar greater than 1, and is typically much smaller than total number of scenarios simulated. confidenceBands can be used to obtain a qualitative idea of how fast a risk measure and its confidence interval are converging. Specifying a large value for NumPoints is not recommended and could cause performance issues with confidenceBands.

Data Types: double

Output Arguments

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Requested risk measure and associated confidence bands at each of the NumPoints scenario sample sizes, returned as a table containing the following columns:

  • NumScenarios — Number of scenarios at the sample point

  • Lower — Lower confidence band

  • RiskMeasure — Requested risk measure where the column takes its name from whatever risk measure is requested with the optional input RiskMeasure

  • Upper — Upper confidence band


[1] Crouhy, M., Galai, D., and Mark, R. “A Comparative Analysis of Current Credit Risk Models.” Journal of Banking and Finance. Vol. 24, 2000, pp. 59–117.

[2] Gordy, M. “A Comparative Anatomy of Credit Risk Models.” Journal of Banking and Finance. Vol. 24, 2000, pp. 119–149.

[3] Gupton, G., Finger, C., and Bhatia, M. “CreditMetrics – Technical Document.” J. P. Morgan, New York, 1997.

[4] Jorion, P. Financial Risk Manager Handbook. 6th Edition. Wiley Finance, 2011.

[5] Löffler, G., and Posch, P. Credit Risk Modeling Using Excel and VBA. Wiley Finance, 2007.

[6] McNeil, A., Frey, R., and Embrechts, P. Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, 2005.

Introduced in R2017a

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