Transcript Credit Risk Modelling

Credit Risk Plus
By: A V Vedpuriswar
November 15, 2010
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.
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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.
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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.
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Data requirements
Exposure
Default rates
Default rate volatilities
Recovery rates
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Methodology
Model the frequency of default events
Model the severity of default losses
Model the distribution of default losses
Sector analysis
Stress testing
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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.
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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.
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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.
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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!
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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.
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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.
.
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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.
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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.
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Applications of CreditRisk+
Calculating credit risk provisions
Enforcing credit limits
 Managing credit portfolios
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Calculating Credit Risk Provisions
CreditRisk+ can be used to set provisions for credit losses
in a portfolio.
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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.
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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.
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Illustration
Ref: Credit Risk Plus Technical document
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Inputting the data
Ref: Credit Risk Plus Technical document
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Input data check
Ref: Credit Risk Plus Technical document
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Portfolio Loss Distribution Summary statistics
Ref: Credit Risk Plus Technical document
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Summary statistical data
Ref: Credit Risk Plus Technical document
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Loss Distribution
Ref: Credit Risk Plus Technical document
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