JJ Mois Année

SMILOVICE

Jan NeckařDana Chromíková

Scoring Unit (SCOR)2 April 2008

Basel II concept differs two types of loss:

0%

1%

2%

3%

4%

5%

6%

7%

8%

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Years

los

s

Unexpected loss

Expected loss

Frequency

UNEXPECTED LOSS

EXPECTED LOSS

B2 - CONCEPT

LOSSES IN TIME

Scoring Unit (SCOR)3 April 2008

Probability 0,1%

Probability 99,9%

Creation of Provisions

-Covered by

SRC

CAPITAL RESERVESMAINTENANCE

STRESS TESTING

BASEL II CONCEPT – distribution of the losses

VALUE AT RISK

LOSS

FR

EQ

UE

NC

YB2 - CONCEPT

Scoring Unit (SCOR)4 April 2008

B2 - CONCEPT

EXPECTED LOSS

EL = PD * LGD * EAD

PD – probability of default- estimation of probability then client is longer than 90 days delayed with payments, insolvency, …

LGD – loss given default- estimation of the resulting economic loss after the recovery process- conditional estimation in case of client is in default

EAD – exposure at default- conditional estimation of exposures in case of client is in default- average drawing at default is higher than outside default

EL = PD*E(loss|default) + (1-PD)*E(loss|nedefault) = PD * LGD * EAD

Scoring Unit (SCOR)5 April 2008

N(x) – distribution function of normalized normal distribution of random quantityG(x) – inversion function to distribution function of normalized normal distributionScaling factor – according to direction of ČNB is equal to 1,06Maturity (M) – Average maturity of the expected cash-flows (repayments)Factor of maturity

Correlation factor R for retail exposures (excl. Mortgages = 0,15, qualifying revolving = 0,04):

Correlation factor for non-retail exposures:

S – Annual sales for the consolidated group (million EUR)

B2 - CONCEPT

UNEXPECTED LOSS – CAPITAL REQUIREMENT

Factor Scaling12,50PDb1,51

PDb2,5M1PD0,999G

R1

RPDG

R1

1NLGDRW

2ln 0,05478 - 0,11852 b(PD) PD

45

5)5),50,max(min(10,04-

e1

e110,24

e1

e10,12R

50

PD50

50

PD50

S

Tier1 + Tier2 ≥ 8% * Σ RW * EAD Tier1 ≥ Tier2 &

53

PD53

53

PD53

e1

e1116,0

e1

e10,03R

Scoring Unit (SCOR)6 April 2008

B2 - CONCEPT

UNEXPECTED LOSS – CAPITAL REQUIREMENT

Scoring Unit (SCOR)7 April 2008

Behavior under stress is not easy to predict

STRESS-TESTING

Scoring Unit (SCOR)8 April 2008

Frequency0%

2%

4%

6%

8%

10%

12%

14%

16%

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Years

loss

BASELINE

DEPRESSION

LOSSES IN TIME

STRESS-TESTING

Scoring Unit (SCOR)9 April 2008

STRESS-TESTING

ECONOMETRICMODEL

STRESSSCENARIOS

STRESS-TESTINGMODELS

STRESSED CHARACTERISTICS

Scoring Unit (SCOR)10 April 2008

Econometric model predicts the macroeconomic characteristic as:

These models have usually 50 – 100 formulas and above 200 parametersThere are several various of predictions, called as scenarios:

The most probable scenario is selected for development of the model.

STRESS-TESTING

GDP unemployment interest rates inflation / deflation price of oil …

baseline depression deep depression high inflation …

ECONOMETRICMODEL

STRESS-TESTINGSCENARIOS&

Scoring Unit (SCOR)11 April 2008

STRESS-TESTING

STRESS-TESTINGMODELS

Stress testing= a way how to measure risk of

Modeled via scenarios for macroeconomics characteristics

extreme but realistic events

Two type of models:Logistic regression

Factor model based on Merton’s model

We assume that portfolio depends on macroeconomic situation and we need to find relation between stressed variable (PD, LGD, CCF) and macroeconomic characteristics:

PDt = f (Mt1)t ≥ t1, f (Mt1) function of macroeconomic characteristics

Example for stressing PD:

Scoring Unit (SCOR)12 April 2008

STRESS-TESTING

STRESS-TESTINGMODELS

Y is explained variable (indicator of default), EY is probability of default

is vector of explanatory variables (macro-economic indicators).

k

iiiXexp

YE

0

)(1

1

Main advantages of this model:

Basic statistical model used for modelling 0-1 variable with good mathematical properties

),...,( 1 kXXX

Logistic regression

Scoring Unit (SCOR)13 April 2008

STRESS-TESTING

STRESS-TESTINGMODELS

Factor model based on Merton’s model

ittit UFR 1

Where

is logarithmic change of client’s asset

is systematic factor

is specific factor

itR

tF

itU

)1(

log

ti

itit A

AR

)1,0(NFt

)1,0(NU it

),( jtit RRcor),( tit FRcor

Scoring Unit (SCOR)14 April 2008

STRESS-TESTING

STRESS-TESTINGMODELS

Factor model based on Merton’s model

)()1( CRPYP itit

itY

J

jjtjxC

10

1 in case of default

0 in case of non-default

J

jjtj

J

jjtjitt

ititit

xxUFP

CRPYPPD

1100 )()1(

)()1(

Probability of default

Scoring Unit (SCOR)15 April 2008

STRESS-TESTING

STRESS-TESTINGMODELS

1)|1()( 1

0 t

J

jjtj

itttittit

fx

UPfFYPfPD

T

ttt

dnJ

jtjtj

dJ

jtjtj

t

tJ dff

fxfx

d

nl

ttt

1

10

10

0 )(1

11

log),,...,(

Conditional probability of default:

Factor model based on Merton’s model

Likelihood function derivated from binomial distribution of default rate: