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Simulate and analyze multifactor credit migration rating model

The `creditMigrationCopula`

takes as input a portfolio of
credit-sensitive positions with a set of counterparties and performs a copula-based,
multifactor simulation of credit rating migrations. Counterparty credit rating
migrations and subsequent changes in portfolio value are calculated for each
scenario and several risk measurements are reported.

`creditMigrationCopula`

associates each counterparty with a
random variable, called a latent variable, which is mapped to credit ratings based
on a rating transition matrix. For each scenario, the value of the position with
each counterparty is recomputed based on the realized credit rating of the
counterparty. These latent variables are simulated by using a multifactor model,
where systemic credit fluctuations are modeled with a series of risk factors. These
factors can be based on industry sectors (such as financial or aerospace),
geographical regions (such as USA or 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 are:

`migrationValues`

— Values of the counterparty positions for each credit rating.`ratings`

— Current credit rating for each counterparty.`transitionMatrix`

— Matrix of credit rating transition probabilities.`LGD`

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

— Factor and idiosyncratic model weights

After you create `creditMigrationCopula`

object (see Create creditMigrationCopula and Properties), use the `simulate`

function to simulate credit migration by using the
multifactor model. Then, for detailed reports, use the following functions:
`portfolioRisk`

, `riskContribution`

, `confidenceBands`

, and `getScenarios`

.

`cmc = creditMigrationCopula(migrationValues,ratings,transitionMatrix,LGD,Weights)`

`cmc = creditMigrationCopula(___,Name,Value)`

creates a `cmc`

= creditMigrationCopula(`migrationValues`

,`ratings`

,`transitionMatrix`

,`LGD`

,`Weights`

)`creditMigrationCopula`

object. The
`creditMigrationCopula`

object has the following properties:

A table with the following variables:

`ID`

— ID to identify each counterparty`migrationValues`

— Values of counterparty positions for each credit rating`ratings`

— Current credit rating for each counterparty`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 set of all possible credit ratings.

The matrix of probabilities that a counterparty transitions from a starting credit rating to a final credit rating. The rows represent the starting credit ratings and the columns represent the final ratings. The top row holds the probabilities for a counterparty that starts at the highest rating (for example

`AAA`

) and the bottom row holds those for a counterparty starting in the default state. The bottom row may be omitted, indicating that a counterparty in default remains in default. Each row must sum to`1`

. The order of rows and columns must match the order of credit ratings defined in the`RatingLabels`

parameter. The last column holds the probability of default for each of the ratings. If unspecified, the default rating labels are:`"AAA","AA","A","BBB","BB","B","CCC","D"`

.The value-at-risk level, used when reporting VaR and CVaR.

A

`NumScenarios`

-by-`1`

vector of portfolio values. This property is empty until you use the`simulate`

function.

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

= creditMigrationCopula(___,`Name,Value`

)```
cmc =
creditMigrationCopula(migrationValues,ratings,transitionMatrix,LGD,Weights,'VaRLevel',0.99)
```

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

`simulate` | Simulate credit migrations using creditMigrationCopula 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`

| `creditDefaultCopula`

| `getScenarios`

| `portfolioRisk`

| `riskContribution`

| `simulate`

| `table`