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Confidence interval bands



cbTable = confidenceBands(cmc) returns a table of the requested risk measure and its associated confidence bands. Use confidenceBands to investigate how the values of a risk measure and its associated confidence interval converge as the number of scenarios increases. Before you run the confidenceBands function, you must run the simulate function. For more information on using a creditMigrationCopula object, see creditMigrationCopula.


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


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Load the saved portfolio data.

load CreditMigrationData.mat;

Scale the bond prices for portfolio positions for each bond.

migrationValues = migrationPrices .* numBonds;

Create a creditMigrationCopula object with a four-factor model using creditMigrationCopula.

cmc = creditMigrationCopula(migrationValues,ratings,transMat,...
cmc = 
  creditMigrationCopula with properties:

            Portfolio: [250x5 table]
    FactorCorrelation: [4x4 double]
         RatingLabels: [8x1 string]
     TransitionMatrix: [8x8 double]
             VaRLevel: 0.9500
          UseParallel: 0
      PortfolioValues: []

Set the VaRLevel to 99%.

cmc.VaRLevel = 0.99;

Use the simulate function to simulate 100,000 scenarios, and then use the confidenceBands function to generate the cbTable.

cmc = simulate(cmc,1e5);
cbTable = confidenceBands(cmc,'RiskMeasure','Std','ConfidenceIntervalLevel',0.9,'NumPoints',50);
ans=10×4 table
    NumScenarios    Lower     Std     Upper
    ____________    _____    _____    _____

        2000        11996    12308    12637
        4000        12871    13108    13354
        6000        12556    12744    12939
        8000        12830    12997    13168
       10000        12702    12850    13001
       12000        12784    12920    13059
       14000        12895    13022    13151
       16000        12747    12864    12983
       18000        12948    13060    13174
       20000        12971    13077    13186

Input Arguments

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creditMigrationCopula object obtained after running the simulate function.

For more information on creditMigrationCopula objects, see creditMigrationCopula.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

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

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 creditMigrationCopula object

  • 'CVaR' — Conditional VaR at the threshold specified by the VaRLevel property of the creditMigrationCopula 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 that 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. NumPoints is typically much smaller than total number of scenarios simulated. You can use confidenceBands 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 can potentially 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.

Version History

Introduced in R2017a