Loss distribution approach to assessing operational risk

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

2

Risk ManagementRisk Management

Identify Assess Control Mitigate

Quantitative assessment

BIA: TSA:AMA: the ORC estimate is found from

bank’s internal model

3

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

4

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

7

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

13

01,1exp),,(Pr/1

xx

GEVxa

bM d

n

nn

Fxuux

GPDuXxuX

,11),()Pr(/1

15

Internal fraud lossesInternal fraud losses

Choosing the threshold uChoosing the threshold u

16

ME (u)=E(S-u|S>u)~

1

u

Parameter EstimationParameter Estimation

17

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

22

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Thank You for Your AttentionThank You for Your Attention!!

25

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