Lunch at the Lab Book Review Chapter 11 Credit Risk

1. Lunch at the LabBook ReviewChapter 11 � Credit Risk Greg Orosi March 20 2006

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

3. 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

4. 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

5. 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

6. 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.

7. Ratings examples:

8. Transition Matrix

9. 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

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

11. 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.

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

13. CreditRisk+

14. 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. Outcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classesOutcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classes

15. 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. Outcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classesOutcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classes

16. 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) Outcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classesOutcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classes

17. Mapping between Asset Returns and Credit Ratings Rating changes depend on final value of asset Example - starting value = 107.5 BBB bond  Outcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classesOutcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classes

18. CreditMetrics � Recovery Rate Assumed that distribution of recovery rate follows beta distribution, pdf given by: Outcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classesOutcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classes

19. Recovery Rate Pdf Plot

20. Conclusion Credit risk can be incorporated into energy portfolio using models developed for fixed income products Outcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classesOutcome of Credit Risk Difference between current bond value and expected value of bond at t=1. Expected Value at t=1 is based migration Probability and discount curve of different rating classes