# Documentation

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# confidenceBands

Confidence interval bands

## Syntax

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

## Description

example

````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`.```

example

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

## Examples

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```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); cbTable(1:10,:) ```
```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.

### Note

`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

## References

[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.