improving pd and lgd models following the changes in the ... · improving pd and lgd models...
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![Page 1: Improving PD and LGD models following the changes in the ... · Improving PD and LGD models following the changes in the market Wemke.vanderWeij@SNSREAAL.nl Marcel.denHollander@SNSREAAL.nl](https://reader035.vdocument.in/reader035/viewer/2022062402/5f139c5972f91001a768f859/html5/thumbnails/1.jpg)
Improving PD and LGD modelsfollowing the changes in the market
[email protected]@SNSREAAL.nl
Credit Scoring Conference 2009 - Edinburgh
Wemke van der Weij Marcel den Hollander
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Agenda
• Introduction
• Basel II
• Modelling: Rating
• Modelling: Level
• Conclusion
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Introduction
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Introduction
• SNS Bank– Among the largest banking companies in The Netherlands– Balance sheet total of € 77 billion – 3245 employees (FTEs)
• Corporate staff: Group Risk Management – Credit Risk Management
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Credit Risk is real...
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Managing Credit Risk
Acceptation Scorecard• New prospects• Not required for Basel II• Decision to accept
IN OUT
Behaviour models• Current customers• Required for Basel II• Capital requirements
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But… not always accurate
Realisation versus estimate
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%20
0611
2006
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2007
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2007
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Month
Per
cent
age
Realisation
Estimate
Note that the figures in the presentation do not correspond to actual data
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Basel II
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Key Measures used in Basel II
General Terminology
• Default• PD: Probability of Default• LGD: Loss Given Default• EAD: Exposure at Default• EL: Expected Loss• UL: Unexpected Loss
• ELT: Economic Loss Term• DR: Default Rate• RLR: Realised Loss Rate
SNS Terminology
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Conceptual example of default
Default End of defaultPeriod t
EAD
recovery
NPV(Loss)
RLR =NPVd(Loss)
EAD
write-off
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Framework
Defaults
Probability of Default model
Exposure at Default estimate
PD fixed
100%
Loss Given Default model LGD
Best Estimate model
LGD
X
PD
X
EAD
EL = Non- Defaults
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Modelling: Rating
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Profile
Credit risk
Client Loan
Payment behaviour
Product
Securities
Risk Factors
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Clients are categorised in buckets
0,00%
5,00%
10,00%
15,00%
20,00%
25,00%
30,00%
35,00%
1 2 3 4 5 6
-
5.000
10.000
15.000
20.000
25.000
30.000
35.000
Customers (#) RLR LGD
• Buckets have strictly increasing estimate (LGD or PD)• Sufficient observations needed to create buckets
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Modelling: Level
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Scoring in pools versus estimated value
Score for each client based on the
characteristics
Score are categorized in risk classes (buckets)
Each bucket gets an estimated value for the risk
Client and loan characteristics
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Estimated values
Example
PD pools
1 0.01 %2 0.05 %3 0.20%4 1.00%5 2.00%6 8.00%7 15.00%8 25.00%
LGD pools
1 0.02%2 0.09%3 0.50%4 2.10%5 7.00%6 13.00%7 18.00%8 30.00%
Commonly based on historical data
How can we get these valuesup to date?
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Calibration of the estimated valueLayers– Client (1)– Risk buckets (2)– Portfolio (3)
Frequency– monthly– quarterly– yearly
Average Value Estimated
(1)
(2)
(3)
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Realisation matrix (observed in the x th month)
2009094.4200908
5.53.4200907
2.32.15.42009061.42.14.23.4200905
1.01.12.61.92.32009040.70.81.21.93.21.7200903
0.30.10.42.11.24.23.42009020.10.20.61.20.92.24.53.22009010.30.60.21.03.22.13.43.52008120.00.12.20.81.22.34.32.3200811
0.10.10.00.10.10.41.20.71.21.92.32.32008010.00.20.10.00.60.30.41.11.31.34.26.22007120.00.10.20.00.00.20.50.91.51.23.23.4200711>24242322…87654321Period \ month
PD: clients observed in 200902 and in default in the 3rd month
LGD: clients in default in 200902 and recovered / lost in the 3rd month
Not observable at the period 200909
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Economic Loss Term
2009094.4200908
5.53.42009072.32.15.4200906
1.42.14.23.42009051.01.12.61.92.3200904
0.70.81.21.93.21.72009030.30.10.42.11.24.23.4200902
0.10.20.61.20.92.24.53.22009010.30.60.21.03.22.13.43.52008120.00.12.20.81.22.34.32.3200811
0.10.10.00.10.10.41.20.71.21.92.32.32008010.00.20.10.00.60.30.41.11.31.34.26.22007120.00.10.20.00.00.20.50.91.51.23.23.4200711
>24242322…87654321Period \month
How to deal with a default with a
very long default period
Estimate the loss
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Realisation matrix (observed in the x th month)
2009094.4200908
5.53.4200907
2.32.15.42009061.42.14.23.4200905
1.01.12.61.92.32009040.70.81.21.93.21.7200903
0.30.10.42.11.24.23.42009020.10.20.61.20.92.24.53.22009010.30.60.21.03.22.13.43.52008120.00.12.20.81.22.34.32.3200811
0.10.10.00.10.10.41.20.71.21.92.32.32008010.00.20.10.00.60.30.41.11.31.34.26.22007120.00.10.20.00.00.20.50.91.51.23.23.4200711>24242322…87654321Period \ month
SUM XtSUM Xt+1
SUM Xt+1
Historic data used for calibration
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How to use the realisations• Linear regression
– a x + b = y– a = 1 and x +b =y⇒ linear trend taken
• Moving Average– 1/n Sum (x) =y⇒ average over the last n observations
• Exponential Smoothing– a y(t) = x(t) + (1- a)y(t-1) =>weighted moving average
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Realisation matrix (observed in the x th month)
2009094.4200908
5.53.4200907
2.32.15.42009061.42.14.23.4200905
1.01.12.61.92.32009040.70.81.21.93.21.7200903
0.30.10.42.11.24.23.42009020.10.20.61.20.92.24.53.22009010.30.60.21.03.22.13.43.52008120.00.12.20.81.22.34.32.3200811
0.10.10.00.10.10.41.20.71.21.92.32.32008010.00.20.10.00.60.30.41.11.31.34.26.22007120.00.10.20.00.00.20.50.91.51.23.23.4200711>24242322…87654321Period \ month
Xt Xt+1 Historic data used for calibration
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Which is the best
( )∑=
−n
ttt zy
n 1
21
Root mean square error
∑=
−n
ttt zy
n 1
1Mean square error
∑=
−n
t t
tt
z
zy
n 1
1
Mean absolute percentage error
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Results for moving average (LGD)
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Results for moving average (LGD)
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Conclusion• Basel II
– guidelines → credit risk models• Observed
– Realisations versus estimates• Calibration is needed
– Using historical data avoiding the performance period• Case study
Remarks• ELT• Macro economic variables