Credit Risk Plus

1. Credit Risk Plus By: A V Vedpuriswar November 15, 2010

2. Introduction • CreditRisk+ is a statistical credit risk model launched by Credit Suisse First Boston (CSFB) in 1997. • CreditRisk+ can be applied to loans, bonds, financial letters of credit and derivatives.

3. Credit Risk Plus • Credit Risk + allows only two outcomes – default and no default. • In case of default, the loss is of a fixed size. • The probability of default depends on • credit rating, • risk factors and • the sensitivity of the obligor to the risk factors. 2

4. Analytical techniques • CreditRisk+ uses analytical techniques, as opposed to simulations, to estimate credit risk. • The techniques used are similar to those applied in the insurance industry. • CreditRisk+ makes no assumptions about the cause of default. • Default event is considered sudden. • Default rates are treated as continuous random variables.

5. Data requirements • Exposure • Default rates • Default rate volatilities • Recovery rates

6. Methodology • Model the frequency of default events • Model the severity of default losses • Model the distribution of default losses • Sector analysis • Stress testing

7. Factors for Estimating Credit Risk • When estimating credit risk, CreditRisk+ considers : • credit quality and systematic risk of the debtor • size and maturity of each exposure • concentrations of exposures within a portfolio • CreditRisk+ accounts for the correlation between different default events by analyzing default volatilities across different sectors, such as different industries or countries. • Defaults in different sectors are often related to the same background factors, such as an economic downturn. • To estimate credit risk due to extreme/ low probability events such as earthquakes, CreditRisk+ uses stress testing or a scenario-based approach.

8. Frequency of default events • The timing of default events cannot be predicted. • The probability of default by any debtor is relatively small. • CreditRisk+ concerns itself with sudden default  when estimating credit risk.

9. Poisson Distribution • CreditRisk+ uses the Poisson distribution to model the frequency of default events. • Poisson distribution is used to calculate probability of a given number of events happening during a specific period of time. • This distribution is useful when the probability of an event occurring is low and there are a large number of events. • For this reason, it is more appropriate than the normal distribution for estimating the frequency of default events.

10. Using the Poisson distribution • Suppose there are N counterparties of a type and the probability of default by each counterparty is p. • The expected number of defaults, , for the whole portfolio is Np. • If p is small, the probability of n defaults is given by the Poisson distribution, i.e, the following equation: • p (n) = 9

11. Modeling the Severity of Default Losses • After calculating the frequency of default events, we need to look at the exposures in the portfolio and model the recovery rate for each exposure. • From this, we can conclude the severity of default losses.

12. Modeling the Distribution of Default Losses • After estimating the number of default events and the severity of losses, CreditRisk+ calculates the distribution of losses for the items in a portfolio. • In order to calculate the distributed losses, CreditRisk+ first groups the loss given default into bands of exposures. • The exposure level for each band is approximated by a common average. .

13. Sector analysis • Each sector is driven by a single underlying factor, which explains the volatility of the mean default rate over time. • Through sector analysis, CreditRisk+ can measure the impact of concentration risk and the benefits of portfolio diversification. • As the number of sectors is increased, the level of concentration risk is reduced.

14. Stress Testing • Stress tests can be carried out in CreditRisk+ and outside CreditRisk+. • Stress testing can be done by increasing default rates and the default rate volatilities and by stressing different sectors to different degrees. • Some stress tests, such as those that model the effect of political risk, can be difficult to carry out in CreditRisk+. • In this case, the effect should be measured without reference to the outputs of the model.

15. Applications of CreditRisk+ • Calculating credit risk provisions • Enforcing credit limits • Managing credit portfolios

16. Calculating Credit Risk Provisions • CreditRisk+ can be used to set provisions for credit losses in a portfolio.

17. Enforcing Credit Limits • Credit limits are an effective way of avoiding concentrations. • They limit exposure to different debtors, maturities, credit ratings and sectors. • The credit limit can be inversely proportional to the default rating associated with a particular debtor's credit rating.

18. Managing Portfolios • CreditRisk+ incorporates all the factors that determine credit risk into a single measure. • This is known as a portfolio-based approach. • The four factors that determine default risk are: • size • maturity • probability of default • concentration risk • CreditRisk+ provides a means of measuring diversification and concentration by sector. • More diverse portfolios with fewer concentrations require less economic capital.

19. Illustration Ref: Credit Risk Plus Technical document

20. Inputting the data Ref: Credit Risk Plus Technical document

21. Input data check Ref: Credit Risk Plus Technical document

22. Portfolio Loss Distribution Summary statistics Ref: Credit Risk Plus Technical document

23. Summary statistical data Ref: Credit Risk Plus Technical document

24. Loss Distribution Ref: Credit Risk Plus Technical document