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Create `creditDefaultCopula`

object to simulate and analyze
multifactor credit default model

The `creditDefaultCopula`

class simulates portfolio
losses due to counterparty defaults using a multifactor model.
`creditDefaultCopula`

associates each counterparty with a
random variable, called a latent variable, which is mapped to default/non-default
outcomes for each scenario such that defaults occur with probability
`PD`

. In the event of default, a loss for that scenario is
recorded equal to `EAD`

* `LGD`

for the
counterparty. These latent variables are simulated using a multi-factor model, where
systemic credit fluctuations are modeled with a series of risk factors. These
factors can be based on industry sectors (such as financial, aerospace),
geographical regions (such as USA, Eurozone), or any other underlying driver of
credit risk. Each counterparty is assigned a series of weights which determine their
sensitivity to each underlying credit factors.

The inputs to the model describe the credit-sensitive portfolio of exposures:

`EAD`

— Exposure at default`PD`

— Probability of default`LGD`

— Loss given default (1 −*Recovery*)`Weights`

— Factor and idiosyncratic model weights

After the `creditDefaultCopula`

object is created (see Create creditDefaultCopula and Properties), use the `simulate`

function to simulate credit defaults using the multifactor
model. The results are stored in the form of a distribution of losses at the
portfolio and counterparty level. Several risk measures at the portfolio level are
calculated, and the risk contributions from individual obligors. The model calculates:

Full simulated distribution of portfolio losses across scenarios

Losses on each counterparty across scenarios

Several risk measures (

`VaR`

,`CVaR`

,`EL`

,`Std`

) with confidence intervalsRisk contributions per counterparty (for

`EL`

and`CVaR`

)

`cdc = creditDefaultCopula(EAD,PD,LGD,Weights)`

`cdc = creditDefaultCopula(___,Name,Value)`

creates a `cdc`

= creditDefaultCopula(`EAD`

,`PD`

,`LGD`

,`Weights`

)`creditDefaultCopula`

object. The
`creditDefaultCopula`

object has the following properties:

A table with the following variables (each row of the table represents one counterparty):

`ID`

— ID to identify each counterparty`EAD`

— Exposure at default`PD`

— Probability of default`LGD`

— Loss given default`Weights`

— Factor and idiosyncratic weights for counterparties

Factor correlation matrix, a

`NumFactors`

-by-`NumFactors`

matrix that defines the correlation between the risk factors.The value-at-risk level, used when reporting VaR and CVaR.

Portfolio losses, a

`NumScenarios`

-by-`1`

vector of portfolio losses. This property is empty until the`simulate`

function is used.

sets Properties using
name-value pairs and any of the arguments in the previous syntax. For
example, `cdc`

= creditDefaultCopula(___,`Name,Value`

)```
cdc =
creditDefaultCopula(EAD,PD,LGD,Weights,'VaRLevel',0.99)
```

. You
can specify multiple name-value pairs.adds optional name-value pair
arguments.

`simulate` | Simulate credit defaults using a creditDefaultCopula object |

`portfolioRisk` | Generate portfolio-level risk measurements |

`riskContribution` | Generate risk contributions for each counterparty in portfolio |

`confidenceBands` | Confidence interval bands |

`getScenarios` | Counterparty scenarios |

[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.

`confidenceBands`

| `getscenarios`

| `portfolioRisk`

| `riskContribution`

| `simulate`

| `table`

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