ekaterina ovchinnikova finance academy under the government of the russian federation loss...
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Ekaterina OvchinnikovaEkaterina OvchinnikovaFinance Academy under the Government of Finance Academy under the Government of
the Russian Federationthe Russian Federation
Loss distribution approach to assessing
operational risk
State-of-the art methods and models for financial risk management
September 14-17,2009
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Risk ManagementRisk Management
Identify Assess Control Mitigate
Quantitative assessment
BIA: TSA:AMA: the ORC estimate is found from
bank’s internal model
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Loss distribution approachLoss distribution approach
F(frequency) – the number of risk events occurred during a set period
S(severity) – the amount of operational loss resulting from a single event
T(total risk) – the sum of F random variables S, i.e. total loss over the set period
The computation is carried out simultaneously for several homogeneous groups with due account for dependencies
OR capital estimate is calculated as Value-at-Risk – 90-99.9% quantile of the aggregate loss distribution T. Modeling is based on Monte-Carlo simulation
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External fraud: Modeling (1)External fraud: Modeling (1)
Risk event – illegal obtention of a retail loan and/or deliberate default
The law for Severity is chosen using sample data. Data is collected via the everyday monitoring of mass media. Distribution is fitted by checking statistical hypotheses. Parameters are estimated by maximum likelihood method
Frequency follows binomial or Poisson law (this could be derived from the credit undewriting workflow). Parameters are set according to the peculiar features of the institution
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External fraud: Modeling (2)External fraud: Modeling (2)
Prediction horizon – 1 month, α = 99% Amounts in terms of money are adjusted to
correspond the CPI level in May 2008 (RUR) Loss amount is considered without recovery The calculation is carried out for an abstract
credit institution
Type n p Limits
EXP* 81150 2,25% 3 000 - 300 000 RUR
AUTO 2830 0,78% 90 ths - 3 mio RUR
IPT 509 0,36% 300 ths- 30 mio RUR
* including express loans, immediate needs loans and credit cards
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Trial patternTrial pattern (1) (1)
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Trial patternTrial pattern (2) (2)
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ResultsResults (May(May 2008 2008))
VAR Structure
92,9%
57,1%
82,4%
7,1%
42,9% 84,3%
17,6%
0
20
40
60
80
100
120
140
160
EXP AUTO IPT Total Risk
Va
lue
s in
mill
on
s (R
UR
)
Expected loss Unexpected loss
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Results (ShortfallResults (Shortfall)) Disastrous loss estimate ES=E(T|T>VAR)
exceeds VAR by 2.2%
Stressed Simulation
x <= 86181912.005%
x <= 93292416.0095%
0
0,00000005
0,0000001
0,00000015
0,0000002
0,00000025
0,0000003
85000000 90000000 95000000 100000000 105000000 110000000
@RISK Trial VersionFor Evaluation Purposes Only@RISK Trial VersionFor Evaluation Purposes Only@RISK Trial VersionFor Evaluation Purposes Only@RISK Trial VersionFor Evaluation Purposes Only@RISK Trial VersionFor Evaluation Purposes Only
1-month 99%RUR Shortfall
WhWhуу use EVT use EVT??
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EVT cannot predict unpredictable. “But what EVT is doing is making the best use of whatever data you have about extreme phenomena”
“Fat” tails
EVTEVT
Probability Density Function
Histogram Gen. Pareto
x2,5E+92E+91,5E+91E+95E+80
f(x)
0,8
0,72
0,64
0,56
0,48
0,4
0,32
0,24
0,16
0,08
0
What is EVTWhat is EVT??
Block maxima method
Peaks over threshold method
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01,1exp),,(Pr/1
xx
GEVxa
bM d
n
nn
Fxuux
GPDuXxuX
,11),()Pr(/1
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Internal fraud lossesInternal fraud losses
Choosing the threshold uChoosing the threshold u
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ME (u)=E(S-u|S>u)~
1
u
Parameter EstimationParameter Estimation
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max1ln11
ln));,((1
n
iiSnSl
Distribution of Excesses Distribution of Excesses (S-u>s|S>u) (S-u>s|S>u)
GPD fit is №1 according to K-S test (33 other distributions checked) 18
Probability Density Function
Histogram Gen. Pareto
x2,5E+92E+91,5E+91E+95E+80
f(x)
0,72
0,64
0,56
0,48
0,4
0,32
0,24
0,16
0,08
0
Distribution of values below uDistribution of values below u
19Heavy tailed as well
Probability Density Function
Histogram Log-Gamma
x3,2E+72,8E+72,4E+72E+71,6E+71,2E+78E+64E+60
f(x)
0,48
0,44
0,4
0,36
0,32
0,28
0,24
0,2
0,16
0,12
0,08
0,04
0
Challenges and SolutionsChallenges and Solutions
?
X<--->Y
“Fat” tails Scarce Data Dependencies
EVTEVT Bayesian Bayesian ApproachApproach
CopulaeCopulae
Probability Density Function
Histogram Gen. Pareto
x2,5E+92E+91,5E+91E+95E+80
f(x)
0,8
0,72
0,64
0,56
0,48
0,4
0,32
0,24
0,16
0,08
0
The behavior of ML estimatesThe behavior of ML estimates
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u Exceedances ξ β
15 000 000,00 36 1,225414 33 000 000,00
20 000 000,00 30 1,061158 51 000 000,00
30 000 000,00 24 1,265289 43 000 000,00
35 000 000,00 23 1,065904 68 000 000,00
40 000 000,00 21 1,034900 78 000 000,00
50 000 000,00 18 0,933319 106 000 000,00
60 000 000,00 18 1,098955 81 000 000,00
SoftwareSoftware
Enterprise-wide OR management: SAS Oprisk, Oracle Reveleus, RCS OpRisk
Suite, Fermat OpRisk, Algo OpVar Russian vendors – Ultor, Zirvan
Distribution fitting and Monte-Carlo Simulation Palisade @Risk Mathwave EasyFit
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Thank You for Your AttentionThank You for Your Attention!!
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Consumer loanConsumer loan ( (EXP)EXP) Lognorm(87032; 145033) Shift=+2468,4
Va
lue
s x
10
^-5
Values in Thousands
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
0 50 100
150
200
250
300
350
400
450
>95,0%9,2 3261,1
Poisson(1825,9)
Va
lue
s x
10
^-2
Values in Thousands
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,7
2
1,7
4
1,7
6
1,7
8
1,8
0
1,8
2
1,8
4
1,8
6
1,8
8
1,9
0
1,9
2
1,9
4
< >5,0% 95,0%1,7560 1,9850
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Car loanCar loan ( (AVT)AVT) InvGauss(669367; 429365) Shift=+68678
Val
ues
x 10
^-6
Values in Millions
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
>95,0%0,157 11,300
Binomial(2830; 0,0077700)
Val
ues
x 10
^-2
0
1
2
3
4
5
6
7
8
9
-5 0 5 10 15 20 25 30 35
>5,0% 95,0%15,00 41,00
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MortgageMortgage ( (IPT)IPT) Pearson5(0,75372; 394099) Shift=-21966
Val
ues
x 10
^-6
Values in Millions
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0 2 4 6 8 10 12 14 16 18
< >95,0%0,14 89273,47
Binomial(509; 0,0036000)
0,00
0,05
0,10
0,15
0,20
0,25
0,30
-1 0 1 2 3 4 5 6 7
>5,0% 95,0%0,000 9,000