OpRiskHJF

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Quantifying Operational Risk:Possibilities and Limitations

Hansjorg FurrerSwiss Life

[email protected]

Risk-Based Supervision, ETH Zurich Summer 20041 June 2004

Quantifying OpRisk

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Contents

A. The New Basel Capital Accord (Basel II)

B. The OpRisk management process

C. OpRisk measurement for regulatory purposes

D. Conclusions

E. References

Quantifying OpRisk 1

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A. The New Basel Capital Accord (Basel II)

1988: Basel Accord (Basel I): minimum capital requirements against credit risk.One standardized approach

1996: Amendment to Basel I: market risk.

1999: First Consultative Paper on the New Basel Capital Accord (Basel II)

April 2003: Third Consultative Paper (CP3) on Basel II(www.bis.org/bcbs/bcbscp3.htmcp3)

Aug 2003: Publication of the comments received on CP3:

- criticism of credit risk approach- some comments on OpRisk methodology


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Oct 2003: Committee meeting in Madrid. Press release:

- credit risk approach will be reviewed- no mention of OpRisk aspects?!

May 2004: Committee meeting in Basel: Census achieved on the remainingtechnical issues regarding Basel II (e.g. specification of LDG parameters incredit risk)

June 2004: Publication of the new Basel II framework

year-end 2006: Implementation of the standardized approaches

year-end 2007: Implementation of the advanced approaches


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Whats new?

Standards on capital adequacy substantially revised

Rationale for the New Accord:

- improve risk management- enhance financial stability

- provide incentives to adopt the more advanced risk-sensitive approaches

Structure of the New Accord (compare with Solvency II):

Three-pillar framework: Pillar 1: minimal capital requirements (risk measurement)

Pillar 2: supervisory review of capital adequacy

Pillar 3: public disclosure


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Whats new? (contd)

Two options for the measurement of credit risk:

- standard approach

- internal rating based approach (IRB)

Pillar 1 sets out the minimum capital requirements:

total amount of capital

risk-weighted assets 8%

MRC (minimum regulatory capital)def= 8% of risk-weighted assets


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Whats new? (contd)

New regulatory capital for OpRisk:

OpRisk: The risk of losses resulting from inadequate or

failed internal processes, people and systems or

from external events

Note: This definition excludes

- strategic risk

- reputational risk

- systemic risk


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Rationale for the explicit treatment of OpRisk

Banks activities have become more complex and diverse (due toglobalization, deregulation, improved technology. Specifically: e-commerce,

large-volume transactions, outsourcing,. . . )

Risk mitigation techniques for credit and market risk may produceother forms of risk

Growing number of operational loss event types

* Credit Suisse Chiasso-affair (1997)

* Nick Leeson/Barings Bank, 1.3b (1995)* Enron (largest US bankruptcy so far) (2001)

* Banque Cantonale de Vaudoise, KBV Winterthur (2003)


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Rationale for the treatment of OpRisk (contd)

OpRisk management viewed as a comprehensive inclusive discipline(comparable to credit and market risk mgmt)

7 Loss event types: Internal fraudExternal fraudEmployment practices and workplace safety

Clients, products & business practices

Damage to physical assets

Business disruption and system failures

Execution, delivery & process management


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Basel II = Solvency II

The difference between the two prudential regimes goes further in thattheir actual objectives differ. The prudential objective of the Basel Accord isto reinforce the soundness and stability of the international banking system.To that end, the initial Basel Accord and the draft New Accord are directedprimarily at banks that are internationally active. The draft New Accord

attaches particular importance to the self-regulating mechanisms of amarket where practitioners are dependent on one another. In the insurancesector, the purpose of prudential supervision is to protect policyholdersagainst the risk of (isolated) bankruptcy facing every insurance company.The systematic risk, assuming that it exists in the insurance sector, has not

been deemed to be of sufficient concern to warrant minimum harmonizationof prudential supervisory regimes at international level; nor has it been thedriving force behind European harmonization in this field

(EU Insurance Solvency Sub-Committee (2001))


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Risks within the SST framework


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B. The OpRisk management process

Reference: Basel Sound practices [4] for the management andsupervision of OpRisks

The Sound practices principles form the basis for Pillar 2 and 3of the Basel proposals

OpRisk management process:

Identification

Assessment Monitoring

Control/Mitigation


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The OpRisk management process (contd)

Previous wording: identification, measurement, monitoring andcontrol.

compulsory for those banks that want to adopt the standardized orAMA approach

Possibly intended for all banks


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Responsibilities:

- Banking supervisors/board of directors: ensure that an OpRisk managementframework is in place

- Senior management: responsible for the implementation

/: Identification and Assessment of OpRisk:

- identify and assess the OpRisks inherent in all existing products, activities,processes and systems

- assess OpRisks before new products, activities, processes and systems areintroduced or undertaken


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How to identify/assess OpRisk?

- Self- or risk assessment (questionnaires, checklists, workshops,. . . )

- risk mapping

- KRI (key risk indicators). State variable: to be assessed. For example #

failed trades, staff turnovers, system downtime etc.- Scorecards, KRD (key risk drivers): Control variables. Translating qualitative

assessments into quantitative assessments. Examples of KRD: # transactions,system quality,. . .

KRI = +k

k KRDk +

- threshold, limits (tied to risk indicators)

- measurement (tracking and recording systematically the frequency and severityof individual loss events)


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Example: Questionnaire of the Erste Bank

Der Arbeitsaufwand kann im Rahmen der normalen Arbeitszeit erledigt werden(d)

80%Der Arbeitsaufwand kann zumeist im Rahmen der normalen Arbeitszeit erledigt werden, jedochkommt es in Spitzenzeiten zu berstunden

(c)

20%Der Arbeitsaufwand ist zumeist nur mit einer erheblichen Anzahl an berstunden zu erledigen(b)

Der Arbeitsaufwand ist kaum zu bewltigen. Mitarbeiter arbeiten regelmsssig auch am Wochenende(a)

AuswertungWie wrden Sie die Auslastung der Mitarbeiter in ihrem Fachbereich einstufen in Bezug aufgeleistete berstunden?

38

Es stellt kein Problem dar, geeignetes Fachpersonal zu finden(c)

Es ist nicht immer einfach, sofort die richtige Arbeitskraft fr eine offene/neue Stelle zu finden,jedoch gelingt dies letztendlich doch immer wieder ohne allzu grossen Zeitaufwand

(c)

100%Es ist sehr schwierig und zeitaufwndig eine offene/neue Stelle zu besetzen, da geeignetes Personalnur sehr schwer zu finden und oft erst nach einer intensiven Einschulung einsetzbar ist.

(b)

Es ist fast unmglich, stets das richtige Personal fr offene/neue Stellen zu finden. Es ist meistausschliesslich nur durch zeitaufwndige, interne Schulungen mglich eine neue/offene Stellenachzubesetzen

(a)

AuswertungWie sieht es aus mit der Verfgbarkeit von Fachpersonal? Ist es leicht oder schwierig, dieseswieder nachzubesetzen

22


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C. OpRisk measurement for regulatory purposes

Recall:total amount of capital

risk-weighted assets 8%

Under Basel II: risk-weighted assets must include capital charge for OpRisk

Notation: COP: capital charge for OpRisk

Three distinct approaches for determining COP:

Basic Indicator Approach Standardized Approach

Advanced Measurement Approaches (AMA)


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Basic Indicator Approach

Capital charge:

CBIAOP = GI

CBIAOP : capital charge under the Basic Indicator Approach

GI: average annual gross income over the previous three years

= 15% (set by the Committee)

No risk mitigation via insurance allowed


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Standardized Approach

Similar to the BIA, but on the level of each business line:

CSAOP =

8i=1

i GIi i [12%, 18%], i = 1, 2, . . . , 8

8 business lines:

Corporate finance Payment & SettlementTrading & sales Agency Services

Retail banking Asset managementCommercial banking Retail brokerage

No risk mitigation via insurance allowed


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Advanced Measurement Approaches (AMA)

Allows banks to use their own methods for assessing their exposure to OpRisk significant capital reduction should result compared to BIA and SA

Preconditions: Bank must meet

- qualitative and- quantitative

standards before using the AMA

Qualitative standards: OpRisk management framework must be in place, seeSection B.


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Quantitative standards

the Committee does not stipulate which (analytical) approach banks must use. . .

. . . however, banks must demonstrate that their measurement system issufficiently granular to capture severe tail loss events, e.g 99.9% VaR

Capital charge defined in the following way:

MRC = EL + UL

If ELs are already captured in a banks internal business practices, then capitalcharge set at the unexpected loss alone:

MRC = UL


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Quantitative standards (contd)

In a normally distributed world with = 0.999:

UL = VaR(X) = + 3.09 , X N(, 2)

Internally generated OpRisk measures must be based on a 5-year observationperiod

Internal data: banks must record internal loss data. Problem: the data formany (business line/loss event type) cells is sparse. Therefore: aggregation with

External data: A banks OpRisk measurement system must also include externaldata


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External consortium data

Data consortia (e.g. Operational Risk data eXchange ORX)exchange loss data from member banks anonymously

ORX member banks: ABN Amro, BNP Paribas, Commerzbank,Deutsche Bank, JP Morgan Chase,. . .(number of member banks increasing)

Mathematical problem: How to scale severity and frequency of the

external data to fit into the internal loss data collection?


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Scaling of OpRisk Data

Example:

- Bank ABC: B/S: CHF 250b

- Bank ORX: B/S: CHF 415b, OpRisk loss CHF 82m for cell (i, k).

- Scaling process:

82 250

415= 49.4

Is this reasonable? Does a relationship between size and risk exist?

If so, is this relationship linear?


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OpRisk Loss Data

QIS2 exercise ([3]): gathering information concerning OpRisk loss events

loss data mapped according to the 8 7 business line/loss event type cells

- # of participating banks: 30 (11 countries)

- time span: three years (1998-2000)- # reported loss events: 11,300- total loss amount EUR 2.6b (only events exceeding EUR 10,000)

- largest contributions:

(Retail Banking/Clients, Products and Business Services)

(Trading and Sales/Execution, Delivery, and Process Management)

(Commercial banking/External Fraud)

- two cells have no reported losses- extraordinary losses presumably absent from this database


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OpRisk Loss Data (contd)

LDCE exercise ([5]): Loss Data Collection Exercise for OpRisk

extension and refinement of the QIS2-exercises

Characteristics of the LDCE:

- # of participating banks: 89 (19 countries)

- time span: 1 year (2001)

- # reported loss events: 47,200- total loss amount EUR 7.8b (only events exceeding EUR 10,000)

- considerable clustering around certain business lines/event type cells


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Comparison of the LDCE with the QIS2 data

Figure1a: Percent Frequency by Business Line

0%

10%

20%

30%

40%

50%

60%

70%

Corporate Finance Trading and Sales Retail Banking Commercial

Banking

Payment and

Settlement

Agency and

Custody Services

Asset

Management

Retail Brokerage No Information

2000 2001


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Figure 1b: Percent Frequency by Event Type

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

Internal Fraud External Fraud Employment

Practices and

Workplace Safety

Clients, Products

and Business

Services

Damage to Physical

Assets

Business Disruption

and System Failures

Execution, Delivery,

and Process

Management

No Information

2000 2001


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Figure 2a: Percent Severity by Business Line

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Corporate Finance Trading and Sales Retail Banking Commercial

Banking

Payment and

Settlement

Agency and

Custody Services

Asset

Management

Retail Brokerage No Information

2000 2001


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Figure 2b: Percent Severity by Event Type

0%

5%

10%

15%

20%

25%

30%

35%

40%

Internal Fraud External Fraud Employment

Practices and

Workplace Safety

Clients, Products

and Business

Services

Damage to Physical

Assets

Business Disruption

and System Failures

Execution, Delivery,

and Process

Management

No Information

2000 2001


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Note:

- the QIS2 data shown in the previous graphs (highlighted in orange) onlydepicts the data collected in 2000 (enabling an annual comparison)

- significant differences in the samples of participating banks!- Frequency of loss events: roughly no changes by business line (Figure 1a)

by event type (Figure 1b), we observe an increase in External Fraud and Employment

Practices, whereas the share in Execution, Delivery, and Process Mgmnt decreased

- Severity of loss events: Striking changes by event types (Figure 2b): the distribution of loss amounts is sensitive

to low frequency/high severity events (e.g. 09/11)


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To assess the extent of risk, it is necessary to assess the extent ofvariability of both number and amount of loss events.

The RMG is undertaking internal analysis to address such issues,see also, among others, the papers by Pezier [14].


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Some internal datatype 1

1992 1994 1996 1998 2000 2002

0

10

20

30

40

type 2

1992 1994 1996 1998 2000 2002

0

5

10

15

20

type 3

1992 1994 1996 1998 2000 2002

0

2

4

6

8

pooled operational losses

1992 1994 1996 1998 2000 2002

0

10

20

30

40


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Modeling issues

Stylized facts about OP risk losses

- Loss occurrence times are irregularly spaced in time

(selection bias, economic cycles, regulation, management interactions,. . . )

- Loss amounts show extremes

Large losses are of main concern!

Repetitive vs non-repetitive losses ([14])

Repetitive losses: loss events that may occur more than once aweek (e.g. settlement risk, minor external fraud, human error in transaction

processing)


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Modeling issues (contd)

Non-repetitive losses:

- ordinary: from once a week to once in a generation ( 2/3 of the riskcategories reported in the QIS studies)

- extraordinary: large but rare

Immaterial losses: to be ignored (both EL and UL are negligible)

Red flag: Are observations in line with modeling assumptions?

Example: iid assumption implies1 NO structural changes in the data as time evolves

1 Irrelevance of which loss is denoted X1, which one X2,. . .


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A mathematical (actuarial) model

OpRisk loss databaseX

(t,k) , t {T n + 1, . . . , T 1, T} (years),

k {1, 2, . . . , 7} (loss event type),

{1, 2, . . . , N (t,k)} (number of losses) 7 loss event types: Internal fraud

External fraud

Employment practices and workplace safetyClients, products & business practices

Damage to physical assets

Business disruption and system failures

Execution, delivery & process managementQuantifying OpRisk 35

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A mathematical (actuarial) model (contd)

TruncationX

(t,k) = X

(t,k) 1

X(t,k)

>d(t,k)

A further index j, j {1, . . . , 8} indicating business line can be introduced(suppressed in the sequel)

Estimate a risk measure for FL(T+1,k)(x) = P

L(T+1,k) x

like

1 Op-VaR(T+1,k) = F

L(T+1,k)()

1 Op-EST+1 = E

L(T+1,k)|L(T+1,k) > Op-VaR(T+1,k)

where

L(T+1,k) =N(T+1,k)

=1

X(T+1,k) : OpRisk loss for loss event type k

over the period [T, T + 1].Quantifying OpRisk 36

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A mathematical (actuarial) model (contd)

Discussion: Recall the stylized facts

- Xs are heavy-tailed

- N shows non-stationarity

Conclusions:

- FX(x) and FL(t,k)(x) difficult to estimate

- In-sample estimation of VaR ( large) almost impossible!

- actuarial tools may be useful:

Approximation (translated gamma/lognormal) Inversion methods (FFT) Recursive methods (Panjer) Simulation Extreme Value Theory (EVT)


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How accurate are VaR-estimates?

Make inference about the tail decay of the aggregate loss L(t,k) via the taildecay of the individual losses X(t,k):

L =N=1

X , 1 FX(x) xh(x) , x

1 FL(x) E[N] xh(x) , x .

Assumptions: (Xm) iid F and for some , and u large

Fu(x) := P[X u x|X > u] = G,(u)(x)

where

G,(x) =

1

1 + x(u)

1/, = 0,

1 ex/ , = 0.Quantifying OpRisk 38

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How accurate are VaR-estimates? (contd)

Tail- and quantile estimate:

1

FX(x) =

Nu

n 1 + x u

1/

, x > u.

VaR = q = u

1

Nun(1 )

(1)

Idea: Comparison of estimated quantiles with the correspondingtheoretical ones by means of a simulation study ([13]).


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Simulation procedure:

Choose F and fix 0 < < 1, Nu {25, 50, 100, 200}(Nu: # of data points above u)

Calculate u = q0 and the true value of the quantile q

Sample Nu independent points ofF above u by the rejection method. Recordthe total number n of sampled points this requires

Estimate , by fitting the GPD to the Nu exceedances over u by means ofMLE.

Determine q according to (1)

Repeat N times the above to arrive at estimates of Bias(q) and SE(q)


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Accuracy of the quantile estimate expressed in terms of bias andstandard error:

Bias(q) = E[q q], SE(q) = E

(q q)21/2

Bias(q) =1

N

Nj=1

qj q ,SE(q) =

1N

Nj=1

(qj q)21/2

For comparison purposes (different distributions) introduce

Percentage Bias :=Bias(q)

q, Percentage SE :=

SE(q)

q


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Criterion for a good estimate: Percentage Bias andPercentage SE should be small, e.g.

= 0.99 = 0.999

Percentage Bias 0.05 0.10

Percentage SE 0.30 0.60


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Example: Pareto distribution 1 FX(x) = x1 FX(x) = x1 FX(x) = x, = 2 = 2 = 2

u = F(xq) Goodness of VaR0.99 A minimum number of 100 exceedances

(corresponding to 333 observations) is requiredto ensure accuracy wrt bias and standard error.

q = 0.7

0.999 A minimum number of 200 exceedances(corresponding to 667 observations) is requiredto ensure accuracy wrt bias and standard error.

0.99 Full accuracy can be achieved with the minimumnumber 25 of exceedances (corresponding to 250observations).

q = 0.90.999 A minimum number of 100 exceedances

(corresponding to 1000 observations) is requiredto ensure accuracy wrt bias and standard error.


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Example: Pareto distribution 1 FX(x) = x1 FX(x) = x1 FX(x) = x, = 1 = 1 = 1

u = F(xq) Goodness of VaR0.99 For all number of exceedances up to

200 (corresponding to a minimum of 667observations) the VaR estimates fail to meetthe accuracy criteria.

q = 0.7 0.999 For all number of exceedances up to200 (corresponding to a minimum of 667observations) the VaR estimates fail to meetthe accuracy criteria.

0.99 A minimum number of 100 exceedances(corresponding to 1000 observations) is requiredto ensure accuracy wrt bias and standard error.

q = 0.90.999 A minimum number of 200 exceedances

(corresponding to 2000 observations) is requiredto ensure accuracy wrt bias and standard error.Quantifying OpRisk 44

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Large number of observations necessary to achieve targetedaccuracy.

Minimum number of observations increases as the tails becomethicker ([13]).

Remember: The simulation study was done under idealisticassumptions. OpRisk losses, however, typically do NOT fulfill

these assumptions.


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Pricing risk under incomplete information

Recall: L(T+1,k): OpRisk loss for loss event type k over the period [T, T + 1]

L(T+1,k) =N(T+1,k)

=1

X(T+1,k)

Question: Suppose we have calculated risk measures (T+1,k) , k {1, . . . , 7}

for each loss event type. When can we consider

7k=1

(T+1,k)

a good risk measure for the total loss LT+1 =7

k=1 L(T+1,k) ?


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Pricing risk under incomplete information (contd)

Answer: Ingredients

- (non-) coherence of risk measures (Artzner, Delbaen, Eber, Heath

framework)

- optimization problem: given (T+1,k) , k {1, . . . , 7}, what is

the worst case for the overall risk for LT+1?

Solution: using copulas in [9] and references therein.

- aggregation of banking risks [1]


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A ruin-theoretic problem motivated by OpRisk

OpRisk process:

V(k)t = u

(k) +p(k)(t) L(k)t , t 0

for some initial capital u(k)

and a premium function p(k)

(t) satisfyingP

[L

(k)

t p(k)(t) ] = 1.

Given > 0, calculate u(k)() such that

P

inf

TtT+1u(k)() +p(k)(t) L

(k)t

< 0

(2)

u(k)() is a risk capital charge (internal)


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Ruin-theoretic problem (contd)

Solving for (2) is difficult

- complicated loss process L(k)t

- heavy-tailed case

- finite time horizon [T, T + 1]

Classical risk theory revisited:

Y(t) = u + ct

N(t)

k=1

Xk = u + ct SXN(t)

(u) = P

supt0

SXN(t) ct

> u


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Pro memoria: Cramer-Lundberg Theorem (light-tailed case):Assume that there exists a constant > 0 fulfilling

h(r) =

rc

, h(r) :=Ee

rX

1and that

0

xexd

GI(x)/c

=: < . Then

(u)

1 /c

eu

, u .


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Important: Net-profit condition: P

limt

SXN(t) ct

=

= 1

Heavy-tailed case: Let the claim size distribution be such that P[X1 > x] x(+1)L(x), L slowly varying. Then

(u) uL(u) , u .

Now assume for some general loss process (S(t))

P limt

S(t) ct = = 11(u) = P

supt0

S(t) ct

> u

uL(u) , u . (3)


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Question: How much can we change S keeping (3)?

Solution: use time change S(t) = S((t))

(u) = Psupt0S(t) ct > uUnder some technical conditions on and S, general models are

given so that

limu

(u)

1(u) = 1

i.e. ultimate ruin behaves similarly under the time change


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Example:

- start from the homogeneous Poisson case (classical Cramer-

Lundberg, heavy-tailed case)

- use to transform to changes in intensities motivated by

operational risk, see [11].


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D. Conclusions

OP risk =market risk, credit risk

all risk types (market, credit, Op) must be consideredsimultaneously, as the reduction in one risk type is at the expense

of an increase in another type

(Internal) OpRisk loss databases must grow

Standard actuarial methods (including EVT) aiming to derive

capital charges for OpRisks are of limited use due to- lack of data

- inconsistency of the data with the modeling assumptions


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Conclusions (contd)

interesting source of mathematical problems

challenges: choice of risk measures, aggregation of risk measures

Pillar 2 and 3 (c.f. Basel Sound Practices [4]) important part in

the OpRisk management process


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E. References

[1] Alexander, C., and Pezier, P. (2003). Assessment and aggregation of bankingrisks. 9th IFCI Annual Risk Management Round Table, International FinancialRisk Institute (IFCI).

[2] Basel Committee on Banking Supervision. Working Paper on the RegulatoryTreatment of Operational Risk. September 2001. BIS, Basel, Switzerland,

www.bis.org/publ/bcbs wp8.htm

[3] Basel Committee on Banking Supervision. The Quantitative ImpactStudy for Operational Risk: Overview of Individual Loss Data

and Lessons Learned. January 2002. BIS, Basel, Switzerland,www.bis.org/bcbs/qis/qisopriskresponse.pdf

[4] Basel Committee on Banking Supervision. Sound Practices for theManagement and Supervision of Operational Risk. July 2002. BIS, Basel,Switzerland, www.bis.org/publ/bcbs91.htm


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[5] Basel Committee on Banking Supervision. The 2002 Loss DataCollection Exercise for Operational Risk: Summary of the Data Collected.

March 2003. BIS, Basel, Switzerland, www.bis.org/bcbs/qis/ldce2002.pdf

[6] Basel Committee on Banking Supervision. Third Consultative Paper onThe New Basel Capital Accord. 29 April 2003. BIS, Basel, Switzerland,www.bis.org/bcbs/bcbscp3.htm

[7] Center for Financial Studies. Latest Developments in Managing OperationalRisk. March 2004. CFS Research Conference, Eltville. www.ifk-cfs.de/English

[8] Embrechts, P., Furrer, H.J., and Kaufmann, R. (2003). Quantifying RegulatoryCapital for Operational Risk. Derivatives Use, Trading and Regulation,Vol. 9, No. 3, 217-233. Also available on www.bis.org/bcbs/cp3comments.htm

[9] Embrechts, P., Hoeing, A., and Juri, A. (2003). Using copulae to boundthe Value-at-Risk for functions of dependent risks. Finance and Stochastics,Vol. 7, No 2, 145-167.


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[10] Embrechts, P., Kaufmann, R., and Samorodnitsky, G. (2002). Ruin theoryrevisited: stochastic models for operational risk. Submitted.

[11] Embrechts, P., and Samorodnitsky, G. (2003). Ruin problem and how faststochastic processes mix. Annals of Applied Probability, Vol. 13, 1-36.

[12] Geiger, H. (2000). Regulating and Supervising Operational Risk for Banks.Working paper, University of Zurich.

[13] McNeil, A. J., and Saladin, T. (1997) The peaks over thresholds methodfor estimating high quantiles of loss distributions. Proceedings of XXVIIthInternational ASTIN Colloquium, Cairns, Australia, 23-43.

[14] Pezier, J. (2002) Operational Risk Management. ISMA Discussion Papersin Finance 2002-21. To appear in Mastering Operational Risk, FT-PrenticeHall, 2003.


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