Credit Risk Plus November 15, 2010 By: A V Vedpuriswar.
-
Upload
kourtney-mapel -
Category
Documents
-
view
223 -
download
2
Transcript of Credit Risk Plus November 15, 2010 By: A V Vedpuriswar.
Credit Risk Plus
November 15, 2010
By: A V Vedpuriswar
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.
2
33
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.
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.
4
Data requirements
¨ Exposure
¨ Default rates
¨ Default rate volatilities
¨ Recovery rates
5
Methodology
¨ Model the frequency of default events
¨ Model the severity of default losses
¨ Model the distribution of default losses
¨ Sector analysis
¨ Stress testing
6
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.
7
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.
8
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.
9
1010
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) = !
e
n
n
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.
11
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.
.
12
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.
13
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.
14
Applications of CreditRisk+
¨ Calculating credit risk provisions
¨ Enforcing credit limits
¨ Managing credit portfolios
15
Calculating Credit Risk Provisions
¨ CreditRisk+ can be used to set provisions for credit losses in a portfolio.
16
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.
17
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.
18
Illustration
19Ref: Credit Risk Plus Technical document
Inputting the data
20Ref: Credit Risk Plus Technical document
Input data check
21Ref: Credit Risk Plus Technical document
Portfolio Loss Distribution Summary statistics
22Ref: Credit Risk Plus Technical document
Summary statistical data
23Ref: Credit Risk Plus Technical document
Loss Distribution
24Ref: Credit Risk Plus Technical document