improving pd and lgd models following the changes in the ... · improving pd and lgd models...

Improving PD and LGD modelsfollowing the changes in the market

Wemke.vanderWeij@SNSREAAL.nlMarcel.denHollander@SNSREAAL.nl

Credit Scoring Conference 2009 - Edinburgh

Wemke van der Weij Marcel den Hollander

- 2 -

Agenda

• Introduction

• Basel II

• Modelling: Rating

• Modelling: Level

• Conclusion

- 3 -

Introduction

- 4 -

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

- 5 -

Credit Risk is real...

- 6 -

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

- 7 -

But… not always accurate

Realisation versus estimate

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%20

0611

2006

12

2007

01

2007

02

2007

03

2007

04

2007

05

2007

06

2007

07

2007

08

2007

09

2007

10

2007

11

2007

12

Month

Per

cent

age

Realisation

Estimate

Note that the figures in the presentation do not correspond to actual data

- 8 -

Basel II

- 9 -- 9 -

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

- 10 -

Conceptual example of default

Default End of defaultPeriod t

EAD

recovery

NPV(Loss)

RLR =NPVd(Loss)

EAD

write-off

- 11 -- 11 -

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

- 12 -

Modelling: Rating

- 13 -

Profile

Credit risk

Client Loan

Payment behaviour

Product

Securities

Risk Factors

- 14 -

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

- 15 -

Modelling: Level

- 16 -

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

- 17 -

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?

- 18 -

Calibration of the estimated valueLayers– Client (1)– Risk buckets (2)– Portfolio (3)

Frequency– monthly– quarterly– yearly

Average Value Estimated

(1)

(2)

(3)

- 19 -

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

- 20 -

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

- 21 -

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

- 22 -

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

- 23 -

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

- 24 -

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

- 25 -

Results for moving average (LGD)

- 26 -

Results for moving average (LGD)

- 27 -

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