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

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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. 1

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22 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. 3

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Data requirements Exposure Default rates Default rate volatilities Recovery rates 4

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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 5

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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. 6

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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. 7

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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. 8

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99 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)=

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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. 10

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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.. 11

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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. 12

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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. 13

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Applications of CreditRisk+ Calculating credit risk provisions Enforcing credit limits Managing credit portfolios 14

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Calculating Credit Risk Provisions CreditRisk+ can be used to set provisions for credit losses in a portfolio. 15

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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. 16

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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. 17

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Illustration 18 Ref: Credit Risk Plus Technical document

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Inputting the data 19 Ref: Credit Risk Plus Technical document

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Input data check 20 Ref: Credit Risk Plus Technical document

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Portfolio Loss Distribution Summary statistics 21 Ref: Credit Risk Plus Technical document

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Summary statistical data 22 Ref: Credit Risk Plus Technical document

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Loss Distribution 23 Ref: Credit Risk Plus Technical document

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