Modelling Operational Risk - Univerzita Karlovamazurova/OperationRisk2016.pdf · 2018-12-17 · 1...

Modelling Operational Risk

Lucie Mazurova

19.10.2018

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Contents

1 Operational Risk Definition

2 Operational Risk in Banks

3 Operational Risk Management

4 Capital Requirement for Operational RiskBasic Indicator ApproachThe Standardized ApproachAdvanced Measurement ApproachFurther Development

5 Loss Distribution ApproachProbability DistributionsModelling Large LossesModelling Dependence

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Operational Risk Definition

Operational risk - risk of losses arising from operation of a company, itdoes not concern the production or services provided by the company (i.e.losses from an insurance portfolio or from a portfolio of bank loans).

OR according to Basel 2

Operational risk is defined as the risk of loss resulting from inadequate orfailed internal processes, people and systems or from external events. Thisdefinition includes legal risk, but excludes strategic and reputational risk.

OR according to Solvency 2

Operational risk means the risk of loss arising from inadequate or failedinternal processes, personnel or systems, or from external events.Operational risk . . . shall include legal risks, and exclude risks arising fromstrategic decisions, as well as reputation risks.

legal risk - includes exposure to fines, penalties or punitive damagesresulting from supervisory actions, as well as private settlements

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Operational Loss Event Type Classification

Basel 2:

3 levels

event-type categories → categories → activity examples

Internal fraud(Losses due to acts of a type intended to defraud, misappropriateproperty or circumvent regulations, the law or company policy, whichinvolves at least one internal party)→ Unauthorised Activity, Theft and Fraud

External Fraud(Losses due to acts of a type intended to defraud, misappropriateproperty or circumvent the law, by a third party)→ Theft and Fraud, Systems Security

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Employment Practices and Workplace Safety(Losses arising from acts inconsistent with employment, health orsafety laws or agreements, from payment of personal injury claims, orfrom diversity / discrimination events)→ Employee Relations, Safe Environment, Diversity andDiscrimination

Clients, Products and Business Practices(Losses arising from an unintentional or negligent failure to meet aprofessional obligation to specific clients, or from the nature or designof a product)→ Suitability, Disclosure and Fiduciary, Improper Business or MarketPractices, Product Flaws, Selection, Sponsorship and Exposure,Advisory Activities

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Damage to Physical Assets(Losses arising from loss or damage to physical assets from naturaldisaster or other events)→ Disasters and other events

Business disruption and system failures(Losses arising from disruption of business or system failures)→ Systems

Execution, Delivery and Process Management(Losses from failed transaction processing or process management,from relations with trade counterparties and vendors)→ Transaction Capture, Execution Maintenance, Monitoring andReporting, Customer Intake and Documentation, Customer / ClientAccount Management, Trade Counterparties, Vendors and Suppliers

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Examples from history

1995 bankruptcy of Barings Bank (founded 1762)- due to unauthorized trading by its head derivatives trader inSingapore, Nick Leeson- failure of internal control, unauthorized trading, internal fraud,external factors (earthquake in Japan)- loss US$1.3 billion - twice the bank’s available trading capital

September 11, 2001 terrorist attack- damage to physical assets, business disruption, dead employees- Bank of New York - loss US$ 140 million

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Operational Risk in Banks

Basel Comittee for Bank Supervision

The Basel Committee is the primary global standard-setter for theprudential regulation of banks and provides a forum for cooperation onbanking supervisory matters.

- established in 1974 by the central bank governors of the G10 countries- Secretariat is located at the Bank for International Settlements in Basel,Switzerland- 28 members (countries represented by their central banks, EU)- publishes:standards ( BCBS expects full implementation of its standards by BCBSmembers and their internationally active banks)guidelines (elaborate the standards)sound practices (describe actual observed practices)

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3 generations of standards

Basel I: the Basel Capital Accord- released 1988- a minimum ratio of capital to risk-weighted assets

Basel II: the New Capital Framework- released 2004, comprehensive document 2006- 3 pillars: minimum capital requirements, supervisory review of aninstitution’s capital adequacy and internal assessment process,effective use of disclosure

Basel III- reacts to financial crisis- enhanced capital requirements, liquidity risk management,systemically important banks, . . .

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Operational Risk Management

BCBS: Principles for the Sound Management of Operational Risk (2011)

Strong risk management culture

Framework fully integrated into the bank’s overall risk managementprocesses

Governance structure with well defined, transparent and consistentlines of responsibility

Identification and assessment of the operational risk inherent in allmaterial products, activities, processes and systems

Monitoring and reporting

Control and mitigation

Business resiliency and continuity plans

Disclosure

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Capital Requirement for Operational Risk

Under the Basel II framework, three approaches can be used to quantifythe operational risk annual capital charge.

Elementary approaches

the basic indicator approach (BIA)the standardized approach (TSA)

- use gross income as a volume measure of the exposition to OR

Internal risk measurement system

advanced measurement approach (AMA)

- mathematical modelling of OR losses based on internal and external data

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Basic Indicator Approach

Banks using the Basic Indicator Approach must hold capital foroperational risk equal to the average over the previous three years of afixed percentage (denoted alpha) of positive annual gross income.

C tBI =

1

Zt

3∑i=1

α max(GI t−i , 0),

Zt =3∑

i=1

χ[GI t−i>0]

GI j - gross income in year jBased on QISs: α = 0, 15.

GI is net interest income plus net non-interest income (gross of anyprovisions (e.g. for unpaid interest), gross of operating expenses, excludesrealised profits/losses from the sale of securities and extraordinary orirregular items as well as income derived from insurance).

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The Standardized Approach

In the Standardised Approach, banks’ activities are divided into eightbusiness lines: corporate finance, trading & sales, retail banking,commercial banking, payment & settlement, agency services, assetmanagement, and retail brokerage.The capital charge for each business line is calculated by multiplying grossincome by a factor (denoted βj) assigned to that business line.

C tS =

1

3

3∑i=1

max

8∑j=1

βj GIt−ij , 0

Values of βj : 0,12 - 0,18.

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The Alternative Standardized Approach

Under the ASA, the operational risk capital charge/methodology is thesame as for the Standardised Approach except for two business lines —retail banking and commercial banking. For these business lines, loans andadvances — multiplied by a fixed factor m — replaces gross income as theexposure indicator. The betas for retail and commercial banking areunchanged from the Standardised Approach. The ASA operational riskcapital charge for retail banking:

Crb = βrb mLArb

where m = 0, 35 and LArb are total outstanding retail loans and advances.

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Advanced Measurement Approach

Under the AMA, the regulatory capital requirement will equal the riskmeasure generated by the bank’s internal operational risk measurementsystem using prescribed quantitative and qualitative criteria. Use of theAMA is subject to supervisory approval.- qualification criteria for AMA must be fulfilled

Use of data:

internal data- collected over a minimum five-year period- classified according to different business lines and loss-event types- usually truncated by a reporting threshold (e.g. 10000EUR)- for many risk cells contain few low-frequency/high-severity losses ornone

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external data- public data and/or pooled industry data- industry data available through external databases from vendors andconsortia of banks-difficult to use directly due to different volumes- survival bias as typically the data of all collapsed companies are notavailable

scenario analysis- in conjunction with external data to evaluate the exposure tohigh-severity events- rough quantitative assessment of the risk frequency and severitydistributions can be obtained- very subjective

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business environment and internal control factors

exposure indicators- influence the frequency and severity of losses- e.g. gross income, number of transactions, number of staff and assetvalues

near-miss losses- losses that could occur but were prevented- included in internal datasets to estimate severity of losses butexcluded in the estimation of frequency

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Further Development

Standardised Measurement Approach for operational risk- consultative document issued in 2016

withdrawal of internal modelling for operational risk regulatory capital(AMA) from the Basel Framework

- for complexity of the AMA and the lack of comparability arising from awide range of internal modelling practices

introduction of the Standardised Measurement Approach (SMA)

The Business Indicator (BI)- similar to gross income, combines P&L items in different way- multiplied by coefficient dependent on the size of BI (no segmentationinto lines of business)

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Further Development

The operational risk capital is determined as follows:

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Loss Distribution Approach

Data on OR losses classified according to the above mentioned businesslines and loss-event types.For computing the capital requirement for year t based on the experiencefrom the past T years (T ≥ 5) we have observations

X t−i ,b,lk , i = 1, . . . ,T , b = 1, . . . , 8, l = 1, . . . , 7, k = 1, . . . ,Nt−i ,b,l ,

whereX t−i ,b,lk is the k-th loss of type l in business line b in year t − i ,

Nt−i ,b,l is the number of losses of type l in business line b in year t − i .

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For each category (i , b, l) there can be a reporting threshold (typically ofthe order of 10000 EUR).

→ X t−i ,b,lk has a distribution truncated from the left (i.e. conditional

distribution (X |X > d), where X ≥ 0 denotes the size of loss withoutreporting threshold).

The aggregate loss in business line b in year t − i is

Lt−i ,b =7∑

l=1

Nt−i,b,l∑k=1

X t−i ,b,lk .

and the aggregate loss in year t − i is

Lt−i =8∑

b=1

Lt−i ,b.

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The aim is to estimate from data the distribution of total loss in year t,Lt , and to determine an appropriate risk measure for that distribution.ρα - risk measure at confidence level α (typically α between 0,99 - 0,999)Capital requirement: C t

AM = ρα(Lt).We need to know the dependence structure of losses in different cellsdefined by business lines end loss-event types. Simple aggregation ofpartial risk measures gives

C tAM =

8∑b=1

ρα(Lt,b).

It is correct for rhoα = Varα in case of comonotonic losses. It does nottake into account diversification effects.

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Risk Measures

Value at risk

ρα(L) = VaRα(L)

VaRα(L) = inf {l ∈ R |P(L > l) ≤ 1− α}

Conditional value at risk

ρα(L) = CVaRα(L) = E (L|L > VaRα(L))

CVaRα(L) = Varα(L) + e (VaRα(L)) ,

where e(u) = E(L− u|L > u) is the mean excess value of the loss abovethe threshold u.

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Probability Distributions

For modelling the sumsNt−i,b,l∑k=1

X t−i ,b,lk

a compound distribution can be used. For computing its distributionfunction various recursive methods (e.g. Panjer formula, Fast Fouriertransform), numerical methods or approximations are applicable.

Examples of the most commonly used probability distributions of loss sizesareGamma: f (x) = (x/θ)α e−x/θ

x Γ(α) , α > 0, θ > 0

Lognormal: f (x) = 1√2πσ x

exp

[−1

2

(ln x−µσ

)2], µ ∈ R, σ > 0

Pareto: f (x) = αθα

(x+θ)α+1 , α > 0, θ > 0.

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Probability Distributions

Basel committee: ”Observed range of practice in key elements ofAdvanced Measurement Approach (AMA)”(2009)- survey of practice of the banks using AMA approach (or candidates forapproval of AMA approach)

Probability distributions used in OR losses:

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Claim Severity Distributions

”body”- the part of distribution describing losses of common size

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”tail”- the part of distribution describing large losses

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one distributional model for both common and large losses

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Claim Frequency Distributions

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Modelling Large Loses

For modelling the tail of the loss distribution (extreme losses) POTmethod based on data exceeding certain threshold is often used.

Generalized Pareto distribution d.f.

Wγ,β(x) = 1− (1 + γ x/β)−1/γ , γ 6= 0

W0,β(x) = 1− exp(−x/β),

where β > 0;x ≥ 0 pro γ ≥ 0,0 ≤ x ≤ −β/γ pro γ < 0.

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Modelling Dependence

For modelling the aggregate loss in year t

Lt =8∑

b=1

Lt,b

the joint disribution of losses in different lines of business is needed.Simple aggregation

C tAM =

8∑b=1

ρα(Lt,b)

in case of the risk measure represented by value at risk is correct only forcomonotonic partial losses.To allow for diversification effects, more realistic modelling of dependenceby means of copulas is often used. In the BCBS document on the observedrange of practice from 2009 the following use of copula models wasrecorded:

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Modelling Dependence

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References

Basel Committee for Bank Supervision (2006)

Basel II: International Convergence of Capital Measurement and Capital Standards:A Revised Framework - Comprehensive Version

http://www.bis.org/publ/bcbs128.htm


Observed range of practice in key elements of Advanced Measurement Approaches(AMA)

http://www.bis.org/publ/bcbs160b.pdf


Standardized Measurement Approach for Operational Risk - ConsultativeDocument

http://www.bis.org/bcbs/publ/d355.pdf

Shevchenko, P.V. (2011)

Modelling operational risk using Bayesian inference. Berlin: Springer.

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Modelling Operational Risk - Univerzita Karlovamazurova/OperationRisk2016.pdf · 2018-12-17 · 1...

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