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.

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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.

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

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

19Ref: Credit Risk Plus Technical document

Inputting the data


Input data check


Portfolio Loss Distribution Summary statistics


Summary statistical data


Loss Distribution


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

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