Lyn Thomas-Book

8/10/2019 Lyn Thomas-Book

1/85

Credit Scoring-from risk assessment topricing, profits and portfolios

Lyn C.Thomas

Quantitative Financial Risk Management CentreSchool of Management

University of Southampton

Santiago de Chile, June 11 2008


2/85

Structure

Recap of consumer credit and credit scoring

Methodologies for building default risk scorecards Current Pressures

Issues Arising and Future Developments

Changing objectives of risk assessment bring new methodologies

Using survival analysis to build scorecards

Profitability modelling

Variable pricing

New issues in data cleaning and enhancing

Impact of new Basel Accord

Low default portfolios Loss Given Default modelling Need for models of credit risk of portfolios of consumer loans

Conclusions


3/85

History of consumer credit

Babylonians lent for seed to be repaid at harvest

The commerce of consumer lending around for 750 years sinceMedieval pawnbrokers

1920s saw Ford/Sloan not only mass produce cars but ways of

financing them for the masses

1960s saw the arrival of credit cards and the start of the explosion inconsumer credit. Same time saw the growth in home ownership in most

Western countries

Now consumer credit is ubiquitous it is argued as a human right.


4/85

Current consumer credit levels

Chile; (main information from Cox, Parrado, Ruiz-Tagle 2006)

Household debt 60% of average annual income (US is 130%, UK,Canada , etc>100%)

75% own home: 64% of consumer debt is mortgage but held byonly 16% households ( US 76%, Canada 69%, UK 73%)

3 million + Mastercard Credit cards

Private label credit/store cards 5 million +


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6/85


7/85

figure 1.1.1 Comparison of US household and business debt

0

2000

4000

6000

8000

10000

12000

14000

1970 1975 1980 1985 1990 1995 2000 2005 2010

$Billions

Total household mortgage consumer credit total business corporate

Comparison of US household and

corporate debt 1974-2006


8/85

Countries with largestMastercard/Visa circulation 2003

Top 10 Represent 72% of Global VISA/MC Cards

2,362,042TOTALGLOBAL

1,699,902TOTALTOP 10

51,100Canada10

56,239Spain9

60,330Taiwan8

94,632S. Korea7

109,482Germany6

121,281Japan5

125,744UK4

148,435Brazil3

177,359China2

755,300USA1

CardsCountryRank

VISA/MC (Credit + Debit) (Cards in Circulation) 000's


9/85

Recap of default based credit scoring-

application scoring Two types of credit scoring

application scoring and behavioural scoring

Application Scoring:

Grant credit to new applicant?

Information available applicants application form details

credit reference agency check

application details/credit histories previous applicants

No information available on credit histories of previous applicantswho were rejected. Leads to bias.


10/85

Application scoring Shaped by original application : whether to accept a new customer

pragmatic philosophy, predict not explain, no causal modelling

assumes credit worthiness time independent over 2-3 years

redo scorecard rather than put in dynamics

Objective to rank applicants correctly; default level forecast is secondary

reflected in performance measures Gini coefficient, swap sets

specific risk: prob. of missing 3 consecutive months in next year.

50 years since first commerical application scoring introduced

Credit bureau data greatly improved decision making accuracy

different information levels available in different countries

Legal considerations

what cannot be used (race/gender/age?);

what must be used (affordability in Australia)

Can there be a world wide consumer credit risk system?


11/85

Behavioural models arrived in 1960s the revolution thatwasnt.

uses performance data as well as application data (but dominates

latter in strength of characteristics)

what is behavioural scoring used for?

different decisions to application scoring (credit limit, cross selling).

Same risk PD in next 12 months

use classification (static) models rather than model dynamics ofconsumer credit risk behaviour

application scoring: snapshot to snapshot behavioural scoring: video clip to snapshot

profit scoring; video clip to video clip

History of consumer credit

modelling- Behavioural scoring


12/85

Classification methods used incredit granting Take sample of previous applicants;

classify into good payers or defaulters one year later.Classification methods find characteristics identifying two groups.

In future accept those with good characteristics; reject bad.

Existing credit scoring classification methods

discriminant analysis/ linear regression logistic regression

Classification trees, random forests linear programming

Developmental credit scoring approaches

neural networks Support vector machines

expert systems genetic algorithms nearest neighbour methods Bayesian learning networks


13/85

xx

xx

x

x

x

x

xx

xx

x

x

xx

x

x

x

x x

xx

x

xx

x x

x

xx

x

x

x

x

x

x

x

age

income

x - bads

x-goods

Graph of simple scorecard on age and income

Not perfectBut only two parametersAge+a(income)=b

Better classifier

But lots moreparameters


14/85

Linear regression and Logistic regression

Discriminant analysis(LDF) is equivalent to linear

regression if only two classification groups so can useleast squares

pi = Exp{Yi}= w1X1+....+wpXpwhere Y

i

= 1 if ith applicant good; 0 if bad

Logistic regression (LR) assumes

. log(pi/(1-pi)) = w1X1+....+wpXp

LR holds for much wider class of models than LDF

In both cases need to coarse classify variables to deal withnon-monotonicity in relationship with defaulting


15/85

Default risk with age

0

5

10

15

20

25

30

18 24 30 36 42 48 54 60 66 72 78

default risk


16/85

All variables are categorical

Since risk is not linear in the

continuous variables, make thesevariables categorical as well

So age splits into are you 18-21;

22-28; 29-36; 37-59;60+ So coarse classify all variables-

categorical and continuous0

510

15

20

25

18-21

22-28

29-36

37-59

6

0+

default risk


17/85

Linear Programming approach

Assume nG goods labelled i = 1, 2, nGnB bads labelled i = nG+1, .nG+nB

Require weights wj j= 1, 2, . . . . p and a cut off value, c such that

For goods: w1 xi1 + w2 xi2 + + wp xip > cFor bads: w1 xi1 + w2 xi2 + + wp xip


18/85

Classification treesgrouping rather than scoring

Methods like classification trees, expert systems neural nets classifyapplicants into groups rather than giving a scorecard.

Classification tree developed both in statistics and computer science sois also called Recursive partitioning algorithm

Splits sample A into two subsets, using attributes of one characteristicso two subsets have maximum difference in bad rate

Take each subset and repeat the process until one decides to stop

Each terminal node is classified as Good or Bad

Classification tree depends on

Splitting rule how to choose best daughter subsets

Stopping rule- when one decides this is a terminal node

Assigning rule- which categories for terminal nodes


19/85

Classification tree:credit risk example

wholesample

residential status

owner not owner

years at bank age

years > 2 years < 2 age < 26 age >26

numberchildren

0 child 1+

employment

prof not prof

age

21

res. status

parents otherwith

Extend to random forests:lots of such trees each onsubset of sample data and subset of characteristicsMajority voting to classify


20/85

Yrs ataddress

Income

Age

(X1)

(X2)

(Xp)

NET OUT

ARTIFICIAL NEURON

ACTIVATIONFUNCTION

Neural Network

W1

W2

Wp

1 1( ) ( ) ( ... )p pOUT f NET f f wx w x= = = + +w.x

Neural network; computer system consisting on number of processing unitsProcessors connected together in layersFor credit scoring, characteristics nput layer, prediction of Bads output layer


21/85

TWO LAYER NEURAL NETWORK

X1

X2..

.

.Xp

ZGood/Bad

W11

W12

W1qK1

K3

If only input and output layer then can be no better than linear regression

Train by pattern discrimination or backward propogation

Age

Yrs at bank

Income

w11 x1 + w21 x2 + .... = s1

o1 = 1 / ( 1 + es

1 )

K2


22/85

Problems when using Neural networks

in Credit ScoringCan take too long to run Do not meet legal requirements that one can give reasons for rejecting Local Minima

A

B

C

Error

Time

How many hidden layers? - often only three*How many nodes in each layer?How to interpret weights or restrict connections?

ornn11.ppt


23/85

Is there a best classification method ?

Logistic regression industry norm

often used in conjunction with other approaches

classification trees, linear regression, linear programming

Segmented population: different scorecard each segment

system reasons ( e,g. new accounts)

Statistical reasons ( way of dealing with interactions in variables) Strategic reasons ( want to be able to deal differently with some groups)

Newer classification methods have been piloted

dont have transparency or robustness

Flat maximum effect lots of almost equally good scorecards


24/85

Relative ranking of 17 methods on 8 consumer credit data sets(Baesens JORS 2003)

9512211012181310Number times statisticinsignificant difference

with best

022634411Number time method

best out of 17 tried

NearestNeighbour

Otherversionsof

classificationtrees

Bestversionof

classi

ficationtrees

NeuralNets

other

versionsof

SVM

BestversionofSVM

Linea

rProgram

Logis

ticReg

Linea

rReg

Methods applied to 8 datasets using 3 measures (

24 tests)


25/85

Differences are in other features Regression approach allows statistical tests to say how

important each characteristic is to classification

gives lean/mean scorecards

helps devise new application forms

Linear programming allows firms to set requirements on scores

score (age score (age >60) deals more easily with large numbers of application characteristics

Classification trees, neural nets, Support vector machines pickup relationships between variables which may not be obvious


26/85

Measuring scorecards in credit scoring

Three aspects of scorecard performance

Discriminatory power ( only scorecard needed) How good is the system at separating the two classes of goods and bads

Divergence statistic

Mahalanobis distance

Somers D-concordance statistic

Kolmogorov Smirnov statistic

ROC curve

Gini coefficient

Calibration of forecast ( scorecard plus population odds) Not used much until Basel requirements and so few tests

Chi-square ( Hosmer-Lemeshow ) test

Binomial and normal tests

Prediction error( scorecard + population odds + cut-off) how many erroneous classifications

Error rates

Confusion matrix, swap sets, specificity, sensitivity


27/85

ROC curves and Gini Coefficient

Gini coefficient,G, =2x(ratio of area between curve and diagonal )=2(ABC)

G =1 then perfect discrimination; G =0 no discrimination.

K-S is greatest vertical distance from diagonal to curve.

A

C

F(s | G)

F(s|B)

B

F(s|B)


28/85

Current pressures

Lenders want to maximise profit not minimise default rates

want to optimise all decisions in customer relationship

not just whether to accept customer for vanilla loan.

Consumers

market near saturation in some countries

so take rates dropping, attrition rates rising

want customized products will they buy into risk-based pricing ?

Industry

Basel New capital Accord begun in 2007 means IRB systems ofconsumer credit de rigeur

need models of credit risk of portfolio of consumer loans

Basel II uses corporate model , need models for Basel III securitization: bundling and pricing models are primitive

Ch i bj i f i k


29/85

Changing objectives of riskassessment bring new methodologies

Changes in objectives are more likely than a need forimproved accuracy to force changes in methodology

Move to assessing profitability not just default risk

Need to estimate several events- default, cross selling,churn and also when these events will occur

survival analysis approaches

Markov chain models

need for dynamic models which incorporate economic/market effects


30/85

Traditional approach to credit scoring

Take Fixed time horizon T

If default occurs within that time Bad; if no default within that time - Good/Indeterminate

Arbitrary: if time horizon is T, default at T-1 is bad, default at T+1 isgood ( or at least indeterminate).

Lose information: indeterminates left out.

Those who fail at 3 months classified same as those who fail at T-1 months.

Competing risks ignored: those who leave/pay off early duringoutcome period left out of default scorecard building and vice versa.


31/85

Survival analysis: ask when

Ask when events happen- default, early repayment,

purchase

deals with censored data easily

gives a handle on profit as profit depends on time until

certain event occur (default,switch lenders)

does not require any choice of time horizon so noarbitrariness or loss of information

uses the data on everyone so no loss of information

allows competing risks models so can build default ,purchase and attrition models on same data.


32/85

Censoring Mechanism

Months on Books

0 6 12 24 47

A

B

C

Default

Censored (Closed Account)

Censored (Truncated)

XX

End of

sample date

End ofEnd of

sample datesample date

Censored (Truncated and

started after start of sample)


33/85

Using Survival Analysis

How long customers survivebefore they default?

How long customers staybefore they change companies?

How long until customer makes next purchase? =

How long deteriorating systems survivebefore failure?

Survival analysis analysis of lifetime data when censoring

Lifetime T lime before loan defaults ( repays early,purchase made).

Standard ways of describing the randomness of T are

distribution function, F(t), where F(t) = Prob{ T t}

( S(t)=1-F(t) is the survivor function)

density function, f(t) where Prob{ t T t+t)= f(t)t

hazard function h(t) =f(t)/(1-F(t)) so h(t)t = Prob{t T t+t |T t)


34/85

Hazard Function

T- r.v. representing failure time (time to default/early pay-off)

Hazard function

If discrete time , probability default in period t given not defaulated before.

( )

( )

+


35/85

Proportional hazards (PH) and

accelerated life (AL) models Explanatory variables allows for heterogeneity of the population.

Proportional hazard models and accelerated life models connect

explanatory variables to failure times in survival analysis

Let x = ( x1, x2, ...., xN)be explanatory variables.

Accelerated life models assume

S0 ,h0 are baseline survivor /hazard rate function and x's speedup or slow down 'ageing'

Proportional hazard models

Explanatory variables have

multiplier effect on base hazard rate.

0 0( , ) ( ) or ( , ) ( )S t S e t h t e h e t = =b.x b.x b.xx x

h(t)

0( , ) ( )h t e h t =b.xx


36/85

Cox Proportional Hazards Model

( Non-parametric approach)

:

Cox showed can estimatebwithout knowledge of h0(t) by using rankof failure and censored times.

If times are discrete so 'lots of ties' need approximation in MaximumLikelihood estimator.So if T- r.v. representing failure time (time to default/early pay-off)and x -vector of covariates

h(t,x) is hazard for individual with characteristics x

acts like a scorecard ( minus to ensure higher score better loan)

( )

0

1 1 2 2

( , ) ( )

( ) . . . .

hs

h n n

h t e h t

s b x b x b x

=

= + + +

xx

x


37/85

Comparison of logistic regression

and survival analysis For a borrower with characteristics x

Logistic regression

Performance horizon of t*; if p=PG(t*,x), score sdefined by

Proportional hazards

Can estimate P G (t,x) for any t and x. Consider p=PG(t*,x)

-

- - log (-log( ))she

h

p c s p= = =w.x

1

ln .1 1 sp

s pp e

= = = + w.x


38/85

Building a credit scorecard for estimating whencustomers default using proportional hazards

Take sample of past customers with their applicationand bureau characteristics ( as usual)

For each, give time of default or the time history was

censored (no further info in sample/ time left lender)

Coarse classify variables without using time horizon

Check need for time dependent variables

Build proportional hazards model

Statistical tests for validating model


39/85

Coarse-classifying using

PH approach Split variable into n binary variables, (each covering a category or in continuousvariable case range of (1/n)th of population).

Apply PH model with these binary variables as characteristics

Chart parameter estimates

choose splits based on similarity of parameter estimates

Note: It is important to do splits separately for every type of failure. Here areestimates for default( left), early repayment(right)

Comparing Logistic Regression and


40/85

Comparing Logistic Regression andProportional Hazards for estimating default risk

Two definitions of bad

1. Defaulted on loan in first 12 months

2. still repaying after 12 months but defaulted in the nexttwelve months.

Two separate LR models for each definition.

One PH model predicting time to early pay-off.

So LRs should be best as they are designed for each specific

definition of bad

Compare models performance using ROC curves


41/85

ROC curves for PH and LR predicting default

PH vs LR 1

(1st 12 mths)

PH vs LR 2

(2nd 12 mths)

li i i l


42/85

pplication in Basel II

Basel II is new regulations concerning how much banksneed to set aside to cover credit losses

Use credit scoring to identify PD,probability of default innext 12 months which feeds into Basel formulae of howmuch to set aside

Low default Portfolios ( like mortgages) do not have enoughbads over 12 months to build good models

Use longer time intervals go bad at any time

How to recover 12 month PD

Answer survival analysis


43/85

Profitability Modelling

Emphasis moving away from minimising default to maximising profit

Acceptance decisions ( no longer yes/n0) Several variants of the product

Customized product

price appropriate for profit

Customize non price features on line

Operational decisions

Credit limit adjustments

Cross sell or up sell Counter attrition measures

optimise collections process for defaulters

Behavioural score on its own not enough

Current Profit Approach


44/85

ppRisk/Reward Matrix

$5000$ 1000No overdraftBehav score500

Balance >$5000Balance $1000-$5000

Balance < $1000Overdraft limit

Use behavioural score (risk) and average balance ( return)No recognition of dynamics of customer behaviourSubjective decision in each cell. No optimization model within each cellOvercome this by using dynamic models-

survival analysis and markov chains

PH model to calculate


45/85

PH model to calculateprofit on fixed term loan

L - loan amount; T- term of the loan a- repayment per period

r - interbank lending rate ;

he(i) hazard function that early repayment in period i

Can generalise and allow r to be time dependent (yield curve) or stochastic

Build PH model to estimate time to default and henceS( i) no default probability before month i

Similarly build PH model for time until early repayment and henceE(i) no early repayment probability before monthI

1

1

Profit(no consideration of default/early repayment)= (1 )

( ) ( , )True Profit ( ) ( 1)

(1 ) (1 )

T

ii

Te

i ii

a

Lr

h i R r LaS i E i L

r r

=

=

+

= +

+ +


46/85

Plots of profits at for loans

of different durations

Default score: Increasing default probability

M k Ch i M d l


47/85

Markov Chain Models Already used for roll rate analysis

Extend to more general states

0 1 2 3

0.95 0.05 0 0

.4 .2 .4 0

.3 .1 .1 .5

months month month month+

1000000Default

0100000Overlimit

0010000Closed

.1.05.05.3.3.20Beh Score Band 4

.05.1.05.2.3.3.1Beh Score Band 3

0.05.05.05.05.4.4Beh Score Band 2

00.10.02.03.85Beh Score Band 1

DefaultOverlimi

t

ClosedBS4BS3BS2BS1

Overdue by

0 months

1 month

2 months

Credit Limits set by


48/85

Markov chain profitability model

(Capital One; Interfaces 2003)

State: s, Credit limit L

Estimate monthly profit r(s,L),- transition probability p(s|s,L)

Markov decision process Vn(s,L) optimal profit over n periods startingin state s with limit L

Can improve model by

Second Order Markov chain ( s(t) = ( BS(t), BS(t-1)) Include economic variables in transition matrix

Include age of loan in transition matrix

Segment population

Mover/stayer Revolver/transactor

1( , ) ( , ) ( | , ) ( , )n nL L

s

V s L m ax r s L p s s L V s L

= +


49/85

Pricing Surprising for 40 years

consumer lending has had only

one price

Decision was is riskacceptable/non acceptable

Now beginning to price for risk

177.0%Provident

23.1%Citi Finance

16.7%Autocredit

11.4%Lloyds TSB

9.9%Tesco

9.7%Intelligent Finance

8.9%Nationwide Building Society

8.7%Halifax

8.0%Nat West Bank

7.8%Royal Bank of Scotland

7.4%Northern Rock

7.1%Sainsbury

6.9%GE Money

6.7%Bradford and Bingley

6.3%Yourpersonalloan.co.uk

APR rate advertisedCompany

Key points in developing


50/85

y p p gpricing models

Lost quote data is valuable

Find out who did not take offer ( and if possible why)

Regulations will set constraints on minimum and maximum prices

Could say take everyone but the price for some is so high no one willaccept but there are always idiots ( who the regulations will protect).

Market changes much faster than economic changes

response scorecards need to be rebuilt faster than risk ones Utilization of product is important for profitability

Pre payment and re financing need modelling

Prices are always will be negotiable once they are variable.

Adverse selection

Offer at interest rate 6% does not get normal population mix , butmore of those who could not get better offer than 6%


51/85

Take Probability q(p,r)

Profitability depends vitally on take probability

Take probability is function of

risk probability p, ( prob of being good) of borrower

Rate offered r

Take probability can also depend on other features

Need to estimate this probability Cannot estimate without considering adverse

selection ( i.e. does depend on p and more so thanyou may estimate)


52/85

Pr { Take} as function of Pr{Good}

Common risk free


53/85

Common risk free

take functions q(r) q(r) fraction who will take loan at rate r

dq/dr 0 w(r)- density function of maximum willingness to pay

Linear response function

Logistic response function

)q(moreorrpaytowillingpopulationofFraction)( 111

rdrrwr

( ) max{0,1 ( )} for 0L Lq r b r r r r = >

( )( ) ln

1 1 ( )

a br

responsea br

e q rq r a br s

e q r

= =

+

Optimal price for risk free


54/85

Optimal price for risk free

response function

( )( )[ ( )] ( ) ( ) ( ((1 )r A F D F ax E P r q r r r p l r p= +

( )( ) ( ) ( ((1 ) ( ) 0

( )(1 )( )

( )

( )( )

( )

F D F

D FF

s

F D F

q r r r p l r p q r p

l r pq rr r

q r p

q rr r l r e

q r

+ + =

+ = +

= + +

Example with logistic response


55/85

a p e w t og st c espo se

a=4, b=32, rF =0.05, lD =0.5

54.711.91.00

52.712.20.99

50.512.40.98

45.713.00.96

40.213.70.94

28.015.50.9

4.522.00.8

0.231.70.7

0.00344.80.6

0.00000963.10.5

Take probability q(r ) as %Optimal interest rate r as %Probability of being Good, p

Risky response rates q(r p)


56/85

Risky response rates q(r,p)

Same principle but now have to worry about

Adverse selection

Affordability is probability of borrower being Good if interest

rate charged is r, if p is probability of being Good atbenchmark interest rate

( , )p r p%

[ ( , )] ( , )(( ( ) ) ( , ) ( )(1 ( , )))A F D FE P r p q r p r p r p r p l r p r p= + % %

( )

( )

( , )

( , ) ( , )( ( ) ) ( , ) ( )(1 ( , ) ( , ) ( , ) ( ( ) ) 0

( ) ( , ) ( , ) ( )

( , ) ( , )

F D F D

q r p

D F rD

r

q r p p r pr p r p r p l r p r p q r p p r p r p l

r r

l r p r p q r pr p l

p r p q r p

+ + + + =

+

= +

%% % %

%

%

Example with logistic response


57/85

p g p

a=4, b=32, rF =0.05, lD =0.5 and c=50

54.754.711.91.00

52.758.213.00.9950.561.314.20.98

45.766.516.60.96

40.270.619.10.94

28.076.524.40.94.584.238.50.8

0.287.453.30.7

0.00388.468.60.6

0.00000987.384.60.5

Take probability from

equivalent risk free logit

response rate function

Take probability

q(r ) as %

Optimal interest

rate r as %

Probability of being

Good, p

( )( ) ln

1 1 ( )

a br cp

responsea br cp

e q rq r a br cp s

e q r

= =

+ Risky Response rate


58/85


59/85


60/85

Profit scoring and pricing


61/85

g p g

Profit scoring involves much more of organisationthan default based scoring

Risk based pricing needs much more carefulmodelling and parameter estimation

Adverse selection

Cannibalisation

Other features might affect response rate not justprice ( interest rate charged)

Dynamic Price modelling will come

.proved successful in airlines, hotels, car rentals

Has arrived in consumer credit

HBOS claim benefits of 7 million per year already

Storing up trouble: Data cleaningand parameter estimation


62/85

and parameter estimation

Reject inference :

sample biased because of those rejected in the past

Well established problem with controversial but standard techniques

used by industry resurgence of interest, new ideas suggested and old approaches

revisited. Some ideas coming from economics literature

Surely 1 in n(s) must be satisfactory compromise

Drop/withdrawal(churn) inference

this group can be 2 to 5 times larger than reject group

should they be in the sample /Could make product attractive to them

Policy inference

Customer scores used in more operating decisions, will affectsubsequent performance of customer, including default risk

Can one ( How to ) construct what would performance/risk have beenunder vanilla operating policy

New Basel Capital Accord(started parallel implementation Jan 1 2007


63/85

started for real 1 January 2008) Basel committee of banking regulators ( Fed etc) required banks to set aside

8% of loans ( capital requirement) to cover risks on losses.

New system based on using banks internal risk rating systems.

Risks split into market, credit and operational. Capital set aside to cover each

For credit risk, minimum capital requirement can be set using internal ratingsbased (IRB) model as well as standard ( fixed %) model

In IRB models, segment portfolio of loans and for each segment give

PD ( long run average probability of default in next 12 months)

LGD (downturn loss given default)

EAD ( expected exposure at default)

Used in Basel formulae to calculate capital needed to cover UL (unexpected lossdue to credit risk).

EL ( expected loss due to credit risk) should be covered by provisions

For customer lending IRB is credit scoring

Basel forces scores to forecast accurately not just rank accurately.

Credit risk weighted assetsfor corporate and retail exposures


64/85

for corporate and retail exposures

Capital needed is

where N is Cumulative Normal Distribution, N-1 is inverse distributionand R is correlation

Only covers unexpected risk; so if R=0, K=0 ; if R=1, K=LGD(1-PD)

+

=

35

35

35

35

1

1116.0

1

10.03R

e

e

e

e PDPD-

+

+

=

b5.11

2.5)b-(M1)999.0(1

2/1

1

)(12/1

R-1

1NLGD.KCapital PDN

R

RPDN

Retail exposuresM=1 ( maturity term disappears)For Mortgages R=0.15

For Revolving R=0.04For other retail

Corporate exposures b=(.11852-.05478ln(PD))2

+

=

50

50

50

50

1

1124.0

1

10.12R

e

e

e

e PDPD-


65/85

Updated Basel capital requirements for K to cover UL ( LGD=0.5)

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1 1.2

PD

K

residential revolving other retail corporate

Impact of Basel Accordon credit scoring development


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on credit scoring development

Need to estimate calibration of scorecard not justdiscrimination

Small numbers of defaults(180 days overdue) meanstake all defaults not just ones in 12 month period

Estimate risk with data of different time periods

Coxs proportional hazards models

Loss given default ( or Recovery Rate) completely newproblem where outcome is mix of

decisions by lenders ( collect in house/use agent/sell off debt)

uncertainty of borrower willing/able to pay back

Stress testing and need for long run average PD meanshave to incorporate economic variables into defaultmodels or at least the dynamics of the default models

Mimic corporate credit risk models??

Problems with validatingLow Default Portfolios (LDP)


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Low Default Portfolios (LDP)

Problems:

Very few defaults to use in back testing soone extra default makes a huge difference

Procyclicality will be more obvious

Subprime market is always in recession

Solutions:

Use as much data as you can

Make prudent assumptions

Low default portfolios:Pluto and Tasche (2005)


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No defaults, assumption of independence

Use largest set possible

take PD value whose lowest confidence limit is 0

Rating grades A, B, C with nA, nB, nC obligors

Assume borrower ranking to be correct

PDA PDB PDC

Most prudent estimate of PDAobtained under assumption

PDA=PDC, or PDA=PDB=PDC

Determine confidence region for PDAat confidence level (e.g. =90%)

Confidence region is values of PDAsuch that probability of not observingany default is higher than 1-

Confidence limits;


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usual and P and T

PD from actual data

Best estimateof PD

Lowe

r-confidencelimitofPD

Upper-confidencelimitofPD

Ifestimatetrue

wha

tcouldhappenin

ofcases

Low

err-confidenceli

mitofPD

Ifestimatetrue

wha

tcouldhappenin

ofcases

Highest value of PDThat gets lower

limit to agreewith actual data

Low Default Portfolios:Using survival analysis directly


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g y y

Problem; How to calculate PDas default in first 12 months if

using data including defaultsand bads at any time ?

Answer 1:Use survival analysis-proportional hazard models -to

estimate when loan willdefault/bad rather thanprobability it goes bad in 12months? Take data on whole

portfolio for as long as you haveit

Survival analysis

Use Coxs proportional hazardmodels to estimate hazard unction

h(s,x) for loan with characteristics x

So obtain PD for 12 month time

horizon

( )

12

0

( , )

12

h s ds

S e

= x

Modelling Loss Given Default


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Very little work done on modelling this until mid 90s

Regression models used for LGD corporate loan models

Modelling approaches Regression on type of loan/company, economic conditions

( needs lots of data points)

Segment and use historic averages ( need lots of defaults) Build model of collections process

For consumer loans, modelling collection process onlyoption

LGD models in consumer lending has mix of randomevents ( defaulter will not pay, cannot pay) and decisions

by lender (what collection strategy to use)

Collections strategy


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Strategic level

Collect in house 0 LGD 1 ( though can exceed bothbounds)

Use agency ( who keep 40% collected) 0.4 LGD 1

Sell off debt ( say at 5p in 1) LGD = 0.95

Operational level

What sequence of contacts to make

Telephone contact possible?

Arrange repayment schedule Letters nice

Letters nasty

Legal proceedings

LGD model for credit cardsDecision tree approach


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Default

No trace Trace

Agent Sell off In house Agent

Satisfactory

Sell off

SatisfactoryNot

satisfactory

Sell off

SatisfactoryNot

Satisfactory

Agent Sell off

SatisfactoryNot

satisfactory

Not

satisfactory

Sell off

Second

agent Sell off

SatisfactoryNot

satisfactory

Sell off

Distribution of LGD for in house


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collections

- 0 . 1 0 0 0 . 0 7 5 0 . 2 5 0 0 . 4 2 5 0 . 6 0 0 0 . 7 7 5 0 . 9 5 0 1 . 1 2 5

LGD

D

e

n

s

i

t

y

Actual LGD can stray outside 0 to 1LGD has spikes at LGD =1 and LGD =0For agent/sold debt, spike at LGD=1 predominates

Distribution 0


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Need to model as a mixed distribution; Here seemed to bethree classes:

Agree and abide by repayment schedule LGD=0

Pay back reduced amount LGD


76/85

Corporate credit risk models have been developed for last decade and some include economicparameters which can be used for stress testing

Corporate credit risk models split into four classes

Structural models

Assume companies default when debts exceed assets ( Merton model)

Try to model the dynamics of their assets

Basel formula based on very simple version of this

Reduced form models

Cuts to the chase when will firms default as function of economic conditions

Hazard( survival analysis) or intensity models build a model of hazard rate hi (t) chance firm I will default at t given not done so before

Markov chain rating based models. Models how firms credit ratings change dynamically withone rating being defaulted

Actuarial models

Models at segment level not individual level. Estimated default rate and LGD rate using actuarial

distributions and historic parameter estimates.

Very few assumptions so can be used in retail area but where are economy variables in it. Scorecard based

z scores, less successful as consumer credit scoring and no economic effects in them

Can we use these models to build stress tests for consumer loan portfolios ?

No. Assumption and data available are so different but appoach might work.

Introduce economic variables


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into consumer credit risk models

Introducing economic variables into credit risk modelsallows

Estimating Long run average PD for Basel

Stress testing required by Basel

Ways of building correlation between defaults of different loans

Pricing portfolios for securitization

Comparison of retail and corporaterisk environments and models


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corporate loans

Objective is to price bonds

well established market

market price continuously available

bonds only infrequently withdrawn

contingent claim model says default iswhen loans exceeds assets

Correlation of defaults related tocorrelation of assets related tocorrelation of share prices

Economic conditions built into models

consumer loans

Objective is to rank borrowers

no established market-only occasionalsecuritization sales

no price available as no public sales

consumers often leave lender (attrition)

default caused by cash flow (consumerhas no idea of assets nor can realise

them)

no share price surrogate for correlationof defaults

Economic conditions not in models

Corporate credit risk modelling


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Corporate credit risk models include

Structural models

Assume default when debts exceed assets ( Merton model)

Model dynamics of their assets ( Basel formula simple version)

Reduced form models

Default mode: Hazard( survival analysis) or intensity models

build a model of hazard rate Mark to Market: Markov chain rating based models. Actuarial models

Models at segment level not individual level. Estimate PD and LGDusing actuarial distributions/ historic parameter estimates.

Factors ( risk) used to give dynamics and correlations

it

2

t 1

i,t 1 1

Basel Model: R R is assets of firm; c is loan;

(1 ) F is systemic factor ( world economy); U is idiosyncratic

c z is economic factors

( , ) Pr{ 1| , ) (

t

it t it

t

t it t t

c

R wF w U

z

p f z D f z N z

Value of credit worthiness

Translates into behavioural score above debt cut-off Model dynamics of behavioural score

Affordability

Repay if cash flow means can afford repayment

Model dynamics of cash flow

Consumer credit Default Modereduced form models


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Extend Cox Proportional Hazard Models to get these

If t is time since loan started, the hazard of default at

time t for a person iwith economic conditions EcoVar(t)and behavioural scoreBehScr(t) is

( ) ( ) ( )( )iii VintageEcoVarBehScri

ethth ++= tt )(

0

Cox Regression estimates , and and then use Kaplan-Meier form

of distribution function to recover baseline hazard function

Idiosyncratic Risk

IdiosyncrIdiosyncr

atic Riskatic RiskSystemic

Risk

SystemicSystemic

RiskRisk

Months

on BooksFactor

MonthsMonths

on Bookson BooksFactorFactor

VintageFactor

VintageVintage

FactorFactor

Consumer credit reduced form


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mark to market model:Markov chain approach

Think of rating grades as states of Markov Chain

So state is score band or default status ( 0,1,2,3+ overdue) At least one state corresponds to default

Markov assumption is states of system describes allinformation concerning credit risk of customer

Estimate transition probabilities of moving from state ito state j in next time period

Use logistic regression to get transition probabilities tobe functions of economic variables

In stress test choose the economic variables for a stressedscenario ( scenario could last over several periods)

Are securitization problems


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due to credit scoring? Securitized products were priced top down

What was market paying last week

Assumption all products were essentially the same ( or could be madeso)

Little investigation of borrowers credit scores and individual product

features

No model of correlation between default risks

Previous portfolio credit risk models would allow a bottom up approach


84/85

US Sub prime mortgage crisis Other half of the disaster

Main reason was conspiracy of optimism

Lenders : scores were low but no one had defaulted for ages

Borrowers: house prices will go up, so can refinance before payments gethigh

Some lessons for scoring

Products had hike in repayments

Allow for affordability in default probability (recall pricing)

Survival analysis (allow for rate terms)

If scorecard known, borrowers will work the system

Scorecard doctors guaranteed increase FICO score by 150

Conclusions


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Profit scoring, pricing and customizing products , credit risk ofportfolios of credit loans are just a few of the new problems in the area.

Still exciting area where many different statistical, probability and OR

techniques- Markov chains, survival analysis, Support vector machines,Brownian processes prove very useful

After 50 years, research in credit scoring is as vital as ever, and willcontinue.

All progress is based upon a universal innate desire of every organism

to live beyond its income. (Samuel Butler)

Documents

Lyn Thomas-Book