Lunch at the Lab Book Review Chapter 11 – Credit Risk Greg Orosi March

Outline Credit Risk –Definition and properties Bond Market –Default risk and Credit rating Modeling Credit Risk –CreditRisk+ –CreditMetrics

Credit risk Credit risk is the uncertainty in the value of a portfolio due to the fact that the counterparties to the contracts may be unable to meet their financial obligations. Lot of contracts are OTC in the energy market

Credit risk -Properties Difficult to model because rare events contribute to large losses A good model should have 2 qualities: Capture default risk and credit quality risk

Credit risk modeling Default risk: –The risk that an institution may actually default on its obligations Credit quality risk: –Changes in credit rating of the counterparty

Bond Market The bond's credit rating is indication of the bond's quality. Rating agencies such as Standard and Poor's (S&P), Moody's and Fitch assign ratings to bonds, which reflect their evaluation of the creditworthiness of an issuer. Investment grade bonds are less likely to have their ratings downgraded or to default than non- investment grade bonds.

Ratings examples:

Transition Matrix

Other important terms Credit spread: –Difference between yield of risky bond and risk-free bond Recovery rate: –In the event of a default, the fraction of the exposure may be recovered through bankruptcy proceedings or some other form of settlement

Measurement of Credit Risk 2 models: –CreditRisk+ (Credit Suisse) –CreditMetrics (JP Morgan)

CreditRisk+ An approach focused only on default event; it ignores migration and market risk. For a large number of obligors, the number of defaults during a given period has a Poisson distribution. Belongs to the class of reduced-form models. Default risk is not linked to the capital structure of the firm.

CreditRisk+ Given the number of credit defaults X within a fixed period and average number of defaults µ in the j-th sector: Moment generating function is given by:

CreditRisk+

CreditMetrics It takes into account credit quality rating migration, credit defaults, recovery rates. Unlike CreditRisk+, CreditMetrics is capable of modeling changes in credit ratings, recovery rates.

CreditMetrics Due to this additional modeling it is no longer possible to present the loss distribution of the portfolio in an analytically closed form. Instead, Monte Carlo simulations are used to approximate the loss distribution. The downside of this approach is that a broad data basis is necessary to parameterize this model: in particular, credit default probabilities, credit quality migration likelihoods, credit spreads, recovery rates, stock prices and industry indices.

CreditMetrics Credit quality is assumed to be tied to values of the companies in the portfolio. The portfolio has to be simulated. GBM model with j=1,…,N independent risk factors Correlated values can be computed by Cholesky (Eigenvalue decompositions)

Mapping between Asset Returns and Credit Ratings Rating changes depend on final value of asset Example - starting value = BBB bond

CreditMetrics – Recovery Rate Assumed that distribution of recovery rate follows beta distribution, pdf given by:

Recovery Rate Pdf Plot

Conclusion Credit risk can be incorporated into energy portfolio using models developed for fixed income products