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
.
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
| nearcorr
| portfolioRisk
| riskContribution
| simulate
| table