Operational risk a guide to basel II capital requirements, models, and analysis

Operational
Risk
A Guide to Basel II Capital
Requirements, Models, and Analysis

ANNA S. CHERNOBAI
SVETLOZAR T. RACHEV
FRANK J. FABOZZI

John Wiley & Sons, Inc.


Copyright c 2007 by Anna S. Chernobai, Svetlozar T. Rachev, and Frank J. Fabozzi. All
rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
Wiley Bicentennial Logo: Richard J. Pacifico
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in
any form or by any means, electronic, mechanical, photocopying, recording, scanning, or
otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright
Act, without either the prior written permission of the Publisher, or authorization through
payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222
Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the Web
at www.copyright.com. Requests to the Publisher for permission should be addressed to the
Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030,
(201) 748-6011, fax (201) 748-6008, or online at />Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their
best efforts in preparing this book, they make no representations or warranties with respect to
the accuracy or completeness of the contents of this book and specifically disclaim any implied
warranties of merchantability or fitness for a particular purpose. No warranty may be created
or extended by sales representatives or written sales materials. The advice and strategies
contained herein may not be suitable for your situation. You should consult with a

professional where appropriate. Neither the publisher nor author shall be liable for any loss of
profit or any other commercial damages, including but not limited to special, incidental,
consequential, or other damages.
For general information on our other products and services or for technical support, please
contact our Customer Care Department within the United States at (800) 762-2974, outside
the United States at (317) 572-3993 or fax (317) 572-4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in
print may not be available in electronic books. For more information about Wiley products,
visit our Web site at www.wiley.com.
ISBN: 978-0-471-78051-9
Printed in the United States of America.
10

9 8

7

6 5

4

3

2 1


ASC
To my husband, Makan, and my parents
STR
To the memory of my parents, Nadezda Racheva

and Todor Rachev
FJF
To my wife, Donna, and children, Francesco,
Patricia, and Karly


Contents
Preface

xv

About the Authors

xix

CHAPTER 1
Operational Risk Is Not Just ‘‘Other’’ Risks
Effects of Globalization and Deregulation: Increased Risk
Exposures
Examples of High-Magnitude Operational Losses
Orange County, 1994, United States
Barings Bank, 1995, United Kingdom
Daiwa Bank, 1995, New York
Allied Irish Banks, 2002, Ireland
The Enron Scandal, 2001, United States
MasterCard International, 2005, United States
Terrorist Attack, September 11, 2001, New York and
Worldwide
Operational Losses in The Hedge Fund Industry
Summary of Key Concepts

References

CHAPTER 2
Operational Risk: Definition, Classification, and Its Place among
Other Risks
What Is Risk?
Definition of Operational Risk
Operational Risk Exposure Indicators
Classification of Operational Risk
Internal versus External Operational Losses
Direct versus Indirect Operational Losses
Expected versus Unexpected Operational Losses
Operational Risk Type, Event Type, and Loss Type
Operational Loss Severity and Frequency

1
2
4
5
5
7
8
8
9
10
10
12
12

15

15
16
18
19
19
19
22
22
23

v


vi

CONTENTS

Topology of Financial Risks
Capital Allocation for Operational, Market, and Credit Risks
Impact of Operational Risk on the Market Value of Bank
Equity
Effects of Macroeconomic Environment on Operational Risk
Summary of Key Concepts
References

CHAPTER 3
Basel II Capital Accord
The Basel Committe (2004) (LDCE)
operational loss data, Dutta-Perry study, 177
Loss dependence (severity dependence), 260–261.

See also Aggregate loss dependence
Loss distribution approach (LDA), 45–47, 222
Loss distributions, 111
concepts, summary, 136
extensions. See Mixture loss distributions
nonparametric approach, 113–114
parametric approach, 114–125. See also
Continuous loss distributions
references, 144–145
tail behavior, 128t
Loss function test. See Lopez’s magnitude loss
function test
Loss given the event (LGE), 44
Loss of recourse. See Recourse
Loss severity
approaches, 112f
data, 78
demonstration, 50–51
distributions, 46
modeling, 80
process, 78–80
Low frequency/high severity events, presence, 247
Low-magnitude losses, management, 3
Low severity/high frequency losses, focus, 25
LR. See Likelihood ratio
Macroeconomic environment, impact, 31
MAD. See Median absolute deviation
MAE. See Mean absolute error
Market discipline, 48–49
Market distribution, 278

Market-related financial risks, 4
Market risk, 1, 16, 26
aggregation, copulas (usage), 272
allocation, 29
amendment, 63–64
capital allocation, 29
Market value, decline, 30
Marking to market, 77
MasterCard International (2005), high-magnitude
operational loss, 9


294
Maximum likelihood estimate (MLE), 115
estimators
closed form existence, absence, 118
existence, 122
method, 143
parameter, 129
estimates, 133
usage, 116, 153
Maximum likelihood parameter estimate, 195
Mean absolute error (MAE), 94, 99
minimization technique, 94
Mean Cluster Size Method, 229
Mean excess function, 167
Mean excess plot. See External operational loss
examples, 214f
usage, 202–204. See also Operational loss data
values, plotting, 202

Mean square error (MSE), 94, 99
Median absolute deviation (MAD), 251, 253
Medium-magnitude losses, management, 3
Mergers and acquisitions (M&As), increase, 3
Method of moments (MOM), 143
Minimum cutoff thresholds, usage. See Loss Data
Collection Exercise
Minimum Regulatory Capital (MRC)
ratios, 48
calculation, 29
percentage, 238
Mishandling losses, Laycock study, 103
Missing data, estimation (fraction), 191t
Mixture distributions, 93
usage, advantages, 126
Mixture loss distributions, extension, 125–127
MLE. See Maximum likelihood estimate
Modeling
classical approach, dangers. See Operational risk
dependence, 259
concepts, summary, 281
references, 262–263
Model risk
occurrence, 62
usage, 62
MOM. See Method of moments
Monotonicity, 235
Monte Carlo approach. See Aggregate loss
distribution
Moral hazard, 55, 57

Moscadelli study. See Loss Data Collection Exercise
MRC. See Minimum Regulatory Capital
MSE. See Mean square error

INDEX
¨
Muller
study. See Operational loss data
Multifactor causal models, 73–74
Multifactor equity pricing models, 69
Multi-indicator approach, 71
Naive approach, 185. See also Operational risk
comparison, 188–191
usage, 192f
Natural catastrophe insurance claims data
¨
(Chernobai-Burnec¸ki-Rachev-TruckWeron study), nonhomogeneous/
homogeneous Poisson processes, 100t
Natural disasters, unexpected losses, 22
Near-Miss Management Strategic Committee,
21–22
Near-miss (NM)
definition, 21
losses, 20–21, 76
management systems
levels, 21
structure, proposal, 21
Negative binomial distribution, 92, 95
fitting, 96
mean, value, 98

Negative binomial random variable, histogram
(illustration), 91f
Negative correlation, illustration, 263f
NHPP. See Nonhomogeneous Poisson process
Nikeei index, decrease, 6
NM. See Near-miss
Non-Gaussian case, 148
Nonhomogeneous Poisson process (NHPP // Cox
process), 92–94. See also Natural catastrophe
insurance claims data
algorithms, 93–94
stochastic intensity, inclusion, 93
Nonhomogeneous process, function, 92–93
Nonparametric approach, 111. See also Empirical
distribution
Nonparametric methods, 232
Nonrobust estimators, examples, 251
Nonsystematic risk, 16
Normal VaR, 279
Null hypothesis, 218
Numerical approximation, 224. See also Density
function
Occurrence, date, 77
Officers, liability coverage, 53
Off-site review, 48


Index
OLDC. See Operational Loss Data Collection
OLS. See Ordinary least squares

One-parameter Pareto random variable, 123
One-year regulatory capital charge, calculation, 45
Operating leverage models, 70
Operational 99% conditional value-at-risk,
illustration, 236f
Operational-event types/descriptions, 24t
Operational loss. See Expected aggregate
operational loss; Hedge funds
announcements, 30
contrast. See Internal operational losses
event
ex ante cause, 72
occurrence, 89
examples. See High-magnitude operational losses
frequency data, interarrival time distributions
(fitting). See Public operational loss data
frequency distributions, aggregation mechanism,
224f
historical insurance claims, 18
models. See Compound operational loss models
occurrence, process, 23f
severity/frequency, 23–26
percent, illustration, 50f–51f
transfer, determination, 53
types. See External type operational losses;
Human type operational losses; Processes
type operational losses; Relationship type
operational losses; Technology type
operational losses
Operational loss data

¨
(1950–2002), Muller
study, 129
description, sample, 131t
goodness-of-fit tests, 131t
parameter estimates, 131t
relative frequency histograms, 130f
alpha-stable distributions, applications, 154–157
¨
Chapelle, Crama, Hubner,
and Peters study,
272–274
business lines, Spearman’s rank correlation
coefficient (estimation), 273t
estimation approaches, operational capital
charge estimates (comparison), 275t
VaR estimates, 274t
Chavez-Demoulin and Embrechts study,
176–177
loss types, 176t
¨ study.
Chernobai, Menn, Rachev, and Truck
See Public operational loss data

295
Dalla Valle, Fantazzini, and Giudici study,
274–277
business line/event type combination,
correlation coefficient estimates, 276t
business line/event type combination,

dependence structure variation
(VaR/CVaR estimates), 277t
business line/event type combination,
frequency/severity distributions parameter
estimates, 276t
descriptive statistics, sample, 275t
descriptive statistics, sample. See Full operational
loss data; Top-5%-trimmed operational loss
data
empirical evidence, 129–136
empirical studies, 171–177, 191–199
histogram, example, 246f
inclusion. See Empirical analysis
Kuritzkes, Schuermann, and Weiner study,
277–278
Moscadelli study. See Loss Data Collection
Exercise
outliers, usage, 246–248
recording practices, problems, 184
robust methods, application, 253–255
Rosenberg and Schuermann study, 278–281
benchmark institution, correlation matrix,
280t
returns simulation, descriptive statistics
(sample), 280t
sample
mean excess plot, usage, 204f
Pareto quantiles, 203f
specifics, 75–81
usage. See Empirical studies

Operational Loss Data Collection (OLDC)
Exercises, 49
Operational loss severity
distribution, histogram (example), 75
modeling, Reynolds-Syer study, 135
Operational RAROC, 232–233
estimates, 233t
Operational risk, 26
aggregation, copulas (usage), 272
Bank of Tokyo-Mitsubishi definition, 18
Basel II Capital Accord classification, 23
BIS definition, 17
British Bankers Association definition, 17
capital allocation, 29
capital charge, assessment


296
Operational risk, (Continued)
AMA, usage, 44–47
approaches, 40–47
basic indicator approach, 41–42
standardized approach, 42–44
capital requirements, minimum, 37–47
causes, FIORI coverage, 54
classification, 15, 19–26, 31
concepts, summary, 12, 31–32
data, 148
specification, 185–187
definition, 10, 15, 16–18

dependence, types, 260–261
Deutsche Bank definition, 17
differences, 1
distributions, 31
economic capital, ratio, 29t
exposure, 55
indicators, 18–19
frequency/severity classification, 25f
impact. See Banks; Hedge funds
insurance products, 53
lognormal example, 188–191
macroeconomic environment, impact, 31
management responsibility, 60
minimum threshold, conditional approach, 185
fitted densities, 186f
minimum threshold, naive approach, 185
fitted densities, 186f
parameter estimation, 187–191
placement, 15
processes, productivity (improvement), 61
quantification, 67–68
references, 12–13, 32–33
SEC definition, 18
sources, 17
truncated model, 184–191
type, 22–23
Operational Risk data eXchange database, 59
Operational risk-driven returns, 278
Operational Risk Management document, 36
Operational risk modeling

challenges, 67
concepts, summary, 81–82
references, 82–83
classical approach, dangers, 248
naive approach, usage, 194–195
Operational risk models, 67–75
bottom-up approaches, basis, 72–75
top-down approaches, basis, 69–71

INDEX
topology, 68f
Operational 99% value-at-risk, illustration, 227f
Operational VaR
derivation, 222–228
performing, 72
usage, 226–228
Opportunity costs, 70
Orange County (1994), high-magnitude
operational loss, 5
ORC. See Corporate Operational Risk Committee
Ordinary least squares (OLS), 251
Outlier-resistant statistics method, 245–246
Outliers
detection
approach, influence functions (impact), 251
methods, 249–250
forwards-stepping rejection, 249
outside-in rejection, 249
rejection, 253–254
approach, 252

usage. See Operational loss data
Outside-in rejection. See Outliers
Paid-up share capital/common stock, 37
Panjer’s recursive method. See Aggregate loss
distribution
Parameter estimates. See Cr´edit Lyonnais loss data;
Expected aggregate operational loss
Parameter estimation methods, 143–144
Parameter value, variability, 93
Parametric approach, 111. See also Continuous
loss distributions
Parametric loss distribution models, 74
Parametric methods, 232
Parametric model, two-point mixture, 249
Pareto density, illustration, 122f
Pareto distribution, 80, 122–123. See also
Generalized Pareto distribution
application, 130–131
tail behavior, 123
versions, 123
Pareto-like distribution, indication, 167
Pareto quantiles. See Operational loss data
contrast. See Log-transformed QQ-plot
Past losses, reappearance, 113
Patriot Act, compliance, 28
PCS. See Property and Claims Services
PE. See Probability of event
Peak over threshold (POT) model, 164–169
conditional mean excess function, usage, 168

Index
excess, 163
illustration, 165f
investigation, empirical studies (usage), 171–172
value-at-risk, 168–169
violation, rarity, 173
Pearson’s chi-squared test, usage. See Goodness of
fit
Peer-group comparison, 71
People risk, 54
Percentiles, 141
Performance, measuring, 231
Physical assets
damage, operational event, 24t
risk, 54
Pickands estimator, 170
Poisson counting process, 85
Poisson distribution, 87–91
fitting, 96, 103
intensity parameter, 228
property, importance, 91
Poisson-gamma mixture, relaxation, 92
Poisson process, usage, 194
Poisson random variable
histogram, illustration, 90f
independence, 90–91
Political policies, changes, 28
Political risk, 28
Population

kurtosis coefficient, 142
mean, 141
median, 141
mode, 142
skewness coefficient, 142
standard deviation, 142
Population
variance, 142
Positive correlation, illustration, 263f
Positive homogeneity, 235
POT. See Peak over threshold
Power tail decay, 150–151
Probability of event (PE), 44
Process-based models, 72–74
Processes loss type, 101
Processes type operational losses, 216
Processing errors data, Laycock study, 103
Process management, operational event, 24t
Process map, 72
Property and casualty risk, characteristics (BIS
definition), 52
Property and Claims Services (PCS), 99

297
Office national index of catastrophe, 58
Property insurance, 53
Proprietary models, 75
Proprietary software, examples, 75
Provisioning, 39
Public disclosure, 48–49

Public loss data
(1980–2002), Chernobai, Menn, Rachev, and
¨ study, 155–156
Truck
goodness-of-fit statistic values, 156t
parameter estimates, 156t
(1950–2002) Chernobai and Rachev study, 157
Public operational loss data
(1950–2002), Chernobai-Rachev study,
101–103
operational loss frequency data, interarrival
time distributions (fitting), 103t
(1980–2002) Chernobai, Menn, Rachev, and
¨ study, 99–101, 194–197
Truck
external operational loss data,
non-homogeneous/homogeneous Poisson
processes (fitting), 102t
external type loss data, empirical
annual frequency/fitted Poisson/
nonhomogeneous Poisson process, 102f
(1980–2002) exploratory data analysis,
212f–214f
p-values. See Goodness of fit
Quadratic-type AD test, 207
Quantile-quantile (QQ) plots, 202
exponential comparison, 203f
log scale, 212f–213f
Quantiles, 141
Quantitative Impact Study (QIS) studies, 49–50,

54, 183
Random variables
expectation, 131
transformations, 142–143
Rank correlation, 265–266
RAPMs. See Risk-adjusted performance measures
RAROC. See Risk-adjusted return on capital
Raw moments, 151
calculation, 166
RB. See Retail Banking
Real data, studies, 95–103, 129
Recorded loss process, frequency, 187
Recourse, loss, 20t
Recursive method, 224


298
Regulatory capital charge guidelines. See Basel II
Capital Accord
Regulatory loss, 20t
Regulatory operational risk capital estimates (cutoff
levels), shape parameter (Hill estimates), 178t
Regulatory principles, 47–48
Regulatory risk, 54
Relationship loss type, 101
Relationship type operational losses, 211
Relative frequency histograms, 137
Reliability models, 73
Remedial action, 48
Reporting bias

impact. See Expected aggregate operational loss;
Lognormal distribution
problem, 183–184
Reputational risk, 28, 70
Reserves, disclosure, 37
Resources, inadequacy, 11
Restitution, 20t
Retail Banking (RB), capital charge, 42
Return, risk-free return, 69
Reynolds and Syer study. See Operational loss
severity
Right-skewed data, 138
Right-skewed distribution, 79
Risk
definition, 15–16
basis, 20–21
differences. See Operational risk
drivers, 73
exposures, increase, 2–4
human/technical errors/accidents, impact, 16
indicator. See Key risk indicator
models, 71
levels, comparison, 231
measures, 235–237
maximum loss, usage, 237
measures, alternatives. See Value-at-risk
illustration, 237f
negative consequences, 16
profile, 48
profiling models, 71

structure implications, Kuritzkes, Schuermann,
and Weiner study. See Capital
topology. See Financial risks
transfer, 62
type, 19
Risk-adjusted performance measures (RAPMs),
232

INDEX
Risk-adjusted return on capital (RAROC), 232. See
also Operational RAROC
Risk Management Group (RMG), 97
purpose, 36
Risk-reduction incentive, providing, 231
Risk-transfer products, usage, 59
Robust databases, 69
Robust estimators, examples, 251
Robust methods
application. See Operational loss data
usage, 62
Robust modeling, 245
concepts, summary, 255–256
references, 256–258
Robust statistics
advantages, 252
formal model, 249
methodology, overview, 248–252
Rosenberg and Schuermann study. See Banks;
Operational loss data; Simulated data
Rusnak, John, 8

Sample
characteristic function approach, 152
kurtosis coefficient, 138
mean, 137
excess function, 202
median, 137
mode, 137
variance, 138
visual inspection, 155
Scenario analysis, 70–71
usage, 76
Scorecard approach (ScA), 45
Scorecards, basis, 45
Security risk premium, 69
Sensitivity analysis. See Value-at-risk
Severity. See Operational loss
demonstration. See Loss severity
dependence. See Loss dependence
Shape parameter, 149
estimation, 169–170
Hill estimates. See Regulatory operational risk
capital estimates
Shapiro-Wilk statistic, 250
SIMEX. See Singapore Money Exchange
Simulated data
Reynolds-Syer study, 135
Rosenberg and Schuermann study, 136
studies, 103–105, 135–136

299

Index
Simulated Pareto random variable, Pareto
tails/exponential distributions (fitting), 128f
Singapore Money Exchange (SIMEX), equity
derivatives (leverage), 6
Sinusoidal rate function, 93
Six Sigma, 75
Skewed densities, illustration, 139f
Skewness, 138
coefficients, 115
Skilling, Jeffrey, 8–9
Spearman’s rank correlation coefficient, estimation,
273. See also Operational loss data
Stability, index, 149, 151
Standard deviation, product, 262
Standardized approach (TSA), 42–44, 71. See also
Alternative standardized approach;
Operational risk
advantages, 43
Standard & Poor’s 500 index, negativity, 58–59
Statistical methodology, proposal, 197
Statistical models, 74
Stochastic intensity, inclusion. See
Nonhomogeneous Poisson process
Stock returns, regression, 69
Strategic risk, 27–28, 70
Stress testing models, 70–71
Stress tests, usage, 76, 252

Studentized range, 250
Subadditivity, 234
Subjective probability, 72
Success
event, incidence (probability), 88
probability, 86
Supervisory response, 48
Survival, probability, 73
Symmetric alpha-stable distribution, 153
Symmetric alpha-stable models, 102
Symmetric alpha-stable random variable, 153
Symmetric densities, illustration, 139f
Tail behavior, 127–128. See also Loss
distributions
Tail events, 147
capture ability, 47
Tail risk, measure, 236
t-copulas, tail dependence (impact), 269f
Technology
failure, 71
loss type, 101
risk, 54

Technology type operational losses, 216
Terrorist attack (9/11/2001), high-magnitude
operational loss, 10
Terrorist attacks, unexpected losses, 22
Thin-tailed distribution, 134
Thin-tailed loss distribution, 127
Threshold

model. See Peak over threshold model
selection. See High threshold
value, estimates, 174t
Timing/data recording, problems, 77
Timing issues, 28
Top-down approaches, 40, 64, 67
Top-down quantitative methodologies, 75
Top-5%-trimmed operational loss data
descriptive statistics, sample, 254t
distribution fitting, parameters/mean/standard
deviation, 254t
one-year EL, estimation, 255t
VaR/CVaR values, estimation, 255t
Total recovery amounts, distribution, 56t
Trading
data, Lewis and Lantsman study. See
Unauthorized trading data
unauthorization. See Unauthorized trading
Transaction volume, impact, 18
Translation invariance, 234
Transparency Group, formation, 36
Truncated alpha-stable distribution, 153
Truncated alpha-stable random
variable, 154
Truncated distributions, 183
concepts, summary, 199–200
references, 200
Truncated model. See Operational risk
TSA. See Standardized approach
Two-parameter Pareto random variable, 123

Two-point Lognormal mixture density, illustration,
126f
Type I error, 218t
Type II error, 218t
UAT. See Unauthorized trading
UL. See Unexpected loss
Unauthorized trading (UAT), 11
activities, 85
data, Lewis-Lantsman study, 99, 193
losses, 99
Uncertainty, measurement, 15
Unemployment rate, 31


300
Unexpected loss (UL)
capital, 39–40
coverage, 39
sum, 248
United Parcel Service (UPS), information loss, 9
Upper-tail AD test, 210
Upper-tail tests, usage, 216
U.S. natural catastrophe insurance claims data,
Chernobai, Burnec¸ki, Rachev, and
¨
Truck-Weron
study, 99
U.S. Securities and Exchange Commission (SEC)
definition. See Operational risk
Value-at-risk (VaR), 221. See also Additive VaR;

Copula; Hybrid VaR; Normal VaR; Peak over
threshold model
amount, excess, 53
backtesting, 229–231
benefits, 231–233
coherent risk measures, 234–235
concepts, summary, 240–241
confidence level, 230t
definition, 221–222
equations, relationship, 227
derivation. See Operational VaR
determination, 221
estimates, 176t, 191, 239. See also Operational
loss data
estimation, 127
expected aggregate operational loss, impact, 192f

INDEX
illustration. See Operational 99% conditional
value-at-risk; Operational 99% value-at-risk
limitations, 231–237
measures, sum, 261
performing. See Operational VaR
pitfalls, 234
references, 241–243
risk measures, alternatives, 231–237
sensitivity analysis, 226–227
usage, 196t. See also Operational VaR
values, estimation. See Full operational loss
data; Top-5%-trimmed operational

loss data
Violations clustering, tests, 229
Visual tests. See Goodness of fit
examples, 201–202
Volatility approach, 70
Von Neumann Algorithm, usage, 116
Weibull density, illustration, 118f
Weibull distribution, 80, 117–119
application, 130–131
tail behavior, 127
Weibull random variable
inverse, 119
right tail behavior, 119
Winsorized standard deviation, 251
Workplace safety, operational
event, 24t
Write-downs, 20t