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8/10/2019 Lyn Thomas-Book
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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
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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
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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.
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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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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
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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
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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.
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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?
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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
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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
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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
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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
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Default risk with age
0
5
10
15
20
25
30
18 24 30 36 42 48 54 60 66 72 78
default risk
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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)
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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
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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
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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.
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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.
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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)
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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)
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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.
( )
( )
+
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
=
=
+
= +
+ +
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Plots of profits at for loans
of different durations
Default score: Increasing default probability
M k Ch i M d l
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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
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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
= +
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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
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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%
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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)
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Pr { Take} as function of Pr{Good}
Common risk free
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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
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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
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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)
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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
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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
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Profit scoring and pricing
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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
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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
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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
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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-
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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
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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
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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)