Confidence interval bands
returns a table of the requested risk measure and its associated confidence
cbTable = confidenceBands(
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
confidenceBands is used. For more information on using
creditDefaultCopula object, see
Load saved portfolio data.
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 UseParallel: 0 PortfolioLosses: 
VaRLevel to 99%.
cdc.VaRLevel = 0.99;
simulate function before running
confidenceBands with the
creditDefaultCopula object to generate the
cdc = simulate(cdc,1e5); cbTable = confidenceBands(cdc,'RiskMeasure','Std','ConfidenceIntervalLevel',0.9); cbTable(1:10,:)
ans=10×4 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
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
cbTable = confidenceBands(cdc,'RiskMeasure','Std','ConfidenceIntervalLevel',0.9,'NumPoints',50)
'RiskMeasure'— Risk measure to investigate
'CVaR'(default) | character vector or string with values
Risk measure to investigate, specified as the comma-separated pair
'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
property of the
'CVaR' — Conditional VaR at
the threshold specified by the
VaRLevel property of the
'ConfidenceIntervalLevel'— Confidence interval level
0.95(default) | numeric between
Confidence interval level, specified as the comma-separated pair
'ConfidenceIntervalLevel' and a
example, if you specify
0.95, a 95% confidence
interval is reported in the output table
'NumPoints'— Number of scenario samples to report
100(default) | nonnegative integer
Number of scenario samples to report, specified as the
comma-separated pair consisting of
and a nonnegative integer. The default is
meaning confidence bands are reported at 100 evenly spaced points of
increasing sample size ranging from 0 to the total number of
NumPoints must be a numeric scalar
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
NumPoints is not recommended and
could cause performance issues with
cbTable— Requested risk measure and associated confidence bands
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
RiskMeasure — Requested
risk measure where the column takes its name from whatever
risk measure is requested with the optional input
Upper — Upper confidence
 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.
 Gordy, M. “A Comparative Anatomy of Credit Risk Models.” Journal of Banking and Finance. Vol. 24, 2000, pp. 119–149.
 Gupton, G., Finger, C., and Bhatia, M. “CreditMetrics – Technical Document.” J. P. Morgan, New York, 1997.
 Jorion, P. Financial Risk Manager Handbook. 6th Edition. Wiley Finance, 2011.
 Löffler, G., and Posch, P. Credit Risk Modeling Using Excel and VBA. Wiley Finance, 2007.
 McNeil, A., Frey, R., and Embrechts, P. Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, 2005.