operational risk modelling - mathworks · analysis with risk modeling was the most effective way to...

Operational Risk Modelling

Aniruddho “Ani” Sanyal, PhD

Senior Consultant

Wolters Kluwer Financial Services

April 9, 2014, New York

Agenda

• Operational Risk management –latest trends

• Economic Rationale of the methodology – avoiding

certain pitfalls.

• Getting an AMA-compliant measure of Op Risk capital

that ties in the requisite components –

– The Change of Measure (COM) approach

• Implementing the COM approach

– in the MS Excel© environment and a proprietary Add-In

file built by WKFS using Matlab Excel Builder

– Heavy-lifting only possible because of the MCR

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Agenda


• Economic Rationale of the methodology – avoiding the

pitfalls.


that tie in the requisite components –




file built by WKFS


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ORM – Latest trends

• Inadequate controls and procedures leading to events

such as JP Morgan’s “London Whale” or rogue trader

Kweku Adoboli at UBS –image problem

• Shareholder have joined regulators in seeking

transparency

• No longer a silo-ed part of risk but important toolkit for

running the bank: AML, Compliance overlap with ORM

• Capital calculation directive remains the same as under

Base II but capital got more expensive under Basel III.

– BIA and STA – punitive, unsuitable for stress-testing.

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ORM – Latest trends

• The cross-over between Pillars I and II is getting the

business managers involved in op risk quantification

rather than just quant specialists. Weak Pillar I leads to

weak Pillar II and additional charges

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Agenda



pitfalls.






file built by WKFS


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Economic Rationale

• Collaborated with Dr. Kabir Dutta – recognized OpRisk

expert from Wharton Business School and the Federal

Reserve Bank of Boston.

• His paper with Jason Perry: “A Tale of Tails” is the one

of the most downloaded in the Op Risk Literature

• His Change of Measure Approach to incorporating

scenarios is gaining a lot of attention in the US, the UK,

the Middle East and elsewhere .

• A way to layer scenario analysis on ILD and more

intuitive and pragmatic alternative to Bayesian Belief

Network (BBN).

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Economic Rationale Capital Calculation

Scenario Analysis

Stress Testing

Regulatory

Guidance

Internal Loss Data

External Loss Data ?

BEICF/RCSA

Economic Rationale

• Dutta-Perry standards in AMA modeling

– Good Fit — Statistically how well does the method fit the

data?

– Realistic — If a method fits well in a statistical sense, does

it generate a loss distribution with a realistic capital

estimate?

– Well-Specified — Are the characteristics of the fitted data

similar to the loss data and logically consistent?

– Flexible — How well is the method able to reasonably

accommodate a wide variety of empirical loss data?

– Simple — Is the method easy to apply in practice?

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Economic Rationale

• “My view, when I was a regulator, was that coupling scenario

analysis with risk modeling was the most effective way to go. No

model will capture all types of risk, but models allow for systematic

data analysis, which should be an important part of, but not the

whole of, op risk management. Scenario analysis allows you to

consider risks not well captured in the model and, thereby, increase

awareness of – and monitoring of – those risks. The supervisory

process should consider current and prospective risks, which may

not be fully reflected in historical data, and how to mitigate them”

• Randall Kroszner, professor of economics at University of Chicago Booth

School of Business, and a former governor of the Federal Reserve system

from 2006 to 2009.

• COM provides hitherto the most robust way of achieving this.

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Economic Rationale

• Humans are not “Econs”

– Systems 1 and 2

– Remembering vs. Experiencing

selves

– Cognitive illusions • Biases

• Priming

• Anchoring

– Framing • “Sausages are 90% fat free” sounds

healthier than “containing 10% fat”!

– Heuristics • Mental shortcuts and rules of thumb

• Dependence on readily available data

rather than due diligence

– “Availability heuristic”

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Economic Rationale

• Immediate implications

– Gather data in the range-

frequency format • At the level of factors rather than

processes.

• Frequency as “once in n years” – not

“probabilities”

– Deprecate “median and 95

percentile loss” kind of thinking! • Can be very misleading due to anchoring

effects

• Cannot accommodate multiple

overlapping perceptions

• Too often GIGO!

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Agenda



pitfalls.






file built by WKFS


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AMA-compliant measure of Op Risk capital

• Relating to operational risk

• Applying the Dutta-Babel (2012) COM approach

– Methodology applied in 12 major US/Canadian institutions

– WKFS: first packaged implementation of the above model

– The only approach that can combine internal loss data

with scenario analysis to get to a single capital number.

– Using the familiar Excel front-end that uses a compiled

Matlab® engine in the background

– Follows the paper closely including the choice of key

severity distributions (can add more!)

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Essence of the methodology – the

“residual” approach 1. m events are supposed to

occur in t years

2. t sets of observations are

taken, each of length ni

3. nTot observations: k

occurrences actually found in

[a,b] while m is predicted by

the scenario

4. If m>k, m-k additional samples

are taken from [a,b] and

added to nTot

5. Parameters p1, p2, and

frequency are re-estimated

and VaR calculated using SLA

6. Steps 2 through 5 are repeated

10,000 times

7. Median of 10,000 VaR

observations is taken.

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Summary Statistics using Internal Data. (Generate Data if internal data does not exists)

Parameter Estimation (Lognormal, Loglogistic, Loggamma, and Weibull)

GOF (AD, KS, Chi-Square, QQ-Plots)

Change of Measures on some or all distributions using scenarios (10,000 Trials). Re-estimate parameters using MLE

Estimate Capital using the new distribution. SLA is used for most distributions. Monte Carlo with 1,000,000 trials is used for Empirical distribution

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Agenda



pitfalls.






file built by WKFS


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Implementing COM – Demonstration!

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Can accommodate varied

perceptions? There is no need

to build artificial consensus.

Implementing the COM approach

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• Industry-standard Goodness-of-Fit tests

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$248,933

$748,933

$1,248,933

$1,748,933

$2,248,933

$2,748,933

$3,248,933

$3,748,933

$4,248,933

$248,933 $748,933 $1,248,933 $1,748,933 $2,248,933 $2,748,933 $3,248,933 $3,748,933 $4,248,933

Lognormal

Loglogistic

Loggamma

Weibull

Observed

Linear (Observed)


Chosen percentile (e.g.,99, 99.9, 99.95) reflects risk appetite.

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OpVaR based on ILD

Distributions Param 1 Param 2 Frequency 99 99.9 99.95 Percentiles UOM

Lognormal 9.9625555 1.4957571 10 2,742,665$ 6,112,252$ 7,729,540$ 50 31,867$

Loglogistic 9.96657069 0.8482016 10 8,571,680$ 53,738,478$ 95,856,331$ 75 67,142$

Loggamma 43.1285805 0.2309966 10 5,225,300$ 17,154,322$ 24,409,400$ 85 102,301$

Weibull 44924.1393 0.6480781 10 1,440,566$ 1,935,826$ 2,099,504$ 90 133,841$

Empirical - - 10 4,983,625$ 6,333,945$ 6,851,424$ 95 251,213$

97 361,347$

99 971,416$

OpVaR based on ILD and Scenario Data 99.9 3,941,731$

Distributions Param 1 Param 2 Frequency 99 99.9 99.95 99.97 4,731,303$

Lognormal 10.0157787 1.5773649 9.8225806 3,589,584$ 8,526,057$ 10,965,963$ Count 800

Loglogistic 9.89408297 0.8871885 9.5483871 10,075,948$ 68,635,229$ 125,795,686$ Aggregate Loss Amount 64,152,727$

Loggamma 39.4140262 0.2518867 10.306452 6,574,492$ 23,316,968$ 33,914,233$ Min 10,173$

Weibull 56200.3688 0.5733778 10.193548 2,470,153$ 3,537,540$ 3,902,428$ Max 4,731,303$

Empirical - - 10.080645 9,382,157$ 12,735,458$ 13,393,003$ Mean 80,191$

std 231942.02

skewness 12.57

kurtosis 218.97

Based on selected

risk appetite –

represented here

by the percentile

we get a SINGLE

number that is

inclusive of own

loss experience and

scenario data.


• Why we chose the Excel Builder

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Interactive debugging from the Function

Wizard alongside standard Excel VBA

coding and debugging.


• Stand-alone – can be used with other platforms

• Runs 50K simulations in 20 minutes and 10 billion

simulations in 12 hours (Windows 7, 32-bit Excel)

– Faster with 64 bit Excel

– May be speeded up with Matlab Production Server

• Matlab is the pre-eminent platform for AMA modeling –

distantly followed by open source alternatives

• Great support

• Excel is center of workflow (can be replaced with in-

house platform, plugging in C++ component)

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• Combines multiple elements of AMA – ILD and Scenarios

• Cross checks scenarios for redundancy

• External data can be included to inform scenarios and/or choose

starter distributions when there is no internal data

• Scenario Selection can be made using RCSA, BEICF, and other

qualitative information on self assessments

– Scenarios should be prioritized based on the riskiness of the

business evaluated by the qualitative assessments

• Stabler than conventional AMA

– Finite capital estimates (instability – scourge of older models)

• Espousing this methodology will be simpler and more intuitive for

bankers- Analyst/Risk Mgr collects data and generates reports

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• Can accommodate LOB/event types with little or no loss

data.

• Can make the model more heavily weighted toward

scenarios – using the Empirical distribution approach

– Takes much longer to run – but not years to gather data!

– There always are Op Risk losses that can be gathered from

the general ledger

• Works better than the BBN

– Easier for bankers to understand.

– Don’t have to maintain/transfer complex NPT (node

probability tables)- when key people move on.

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Used ReportBuilder and SSIS to integrate with platform

Q&A

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