CREDITRISK + By: A V Vedpuriswar. October 2, 2016

Transcription

1 CREDITRISK + By: A V Vedpuriswar October 2, 2016

2 Introduction (1) CREDITRISK ++ is a statistical credit risk model launched by Credit Suisse First Boston (CSFB) in CREDITRISK + can be applied to loans, bonds, financial letters of credit and derivatives. CREDITRISK + allows only two outcomes: default and no default. The probability of default depends on: credit rating, risk factors the sensitivity of the obligor to the risk factors. 1

3 Introduction (2) CREDITRISK + uses analytical techniques, as opposed to simulations, to estimate credit risk. The techniques used are similar to those applied in the insurance industry. No assumptions are made about the cause of default. Default event is considered sudden. Default rates are treated as continuous random variables. A mapping from credit ratings to a set of default rates provides a convenient approach to setting the level of the default rate. 2

4 Taking into account correlations The model takes into account the influence of background factors by using default rate volatilities that result in increased defaults. Default correlations are not used as a direct input. The model takes into account that default correlations are inherently unstable. Moreover, there is little empirical data on default correlations. Defaults themselves are rare. Thus the model specifies a default rate and a default rate volatility. 3

5 Data requirements Exposure Default rates Default rate volatilities Recovery rates 4

6 Methodology Model the frequency of default events. Model the severity of default losses. Model the distribution of default losses. Do sector analysis. Carry out Stress testing. 5

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. 6

8 Poisson Distribution The timing of default events cannot be predicted. The probability of default by any debtor is relatively small. CREDITRISK + concerns itself with sudden default. The Poisson distribution is used to model the frequency of default. The Poisson 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. 7

9 Understanding 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) = 8

10 Modelling 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. Recovery rates depend on factors such as seniority, collateral, etc and are provided by companies such as Moody s. In the model, the exposures net of recovery are divided into bands. The level of exposure in each band is approximated by a common average. From this, we can calculate the severity of default losses. 9

11 Modelling the Distribution of Default Losses After estimating the number of default events and the severity of losses, the distribution of losses is arrived at. As mentioned earlier, CREDITRISK + first groups the loss given default into bands of exposures. The exposure level for each band is approximated by a common average.. 10

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. 11

13 Stress Testing Stress tests can be carried out within CREDITRISK + or outside CREDITRISK +. Within the model, 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 outside the model. 12

14 Applications of CREDITRISK + Calculating credit risk provisions CreditRisk+ can be used to set provisions for credit losses in a portfolio. This in turn can help arrive at economic capital. Enforcing credit limits Credit limits can be used to cap exposure to different debtors, maturities, credit ratings and sectors. Managing credit portfolios CreditRisk+ incorporates all the factors that determine credit risk into a single measure. This is known as a portfolio-based approach. 13

15 Illustration Ref: CREDITRISK + Technical document 14

16 Inputting the data Ref: CREDITRISK + Technical document 15

17 Input data check Ref: CREDITRISK + Technical document 16

18 Portfolio Loss Distribution Summary statistics Ref: CREDITRISK + Technical document 17

19 Summary statistical data Ref: CREDITRISK + Technical document 18

20 Loss Distribution Ref: CREDITRISK + Technical document 19