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 http://www.wiley.com/go/permission 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 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 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 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 5 8 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 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, 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, 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, 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, Mergers and acquisitions (M&As), increase, 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 ă (Chernobai-Burnecáki-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, 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 ă (19502002), Muller study, 129 description, sample, 131t goodness-of-fit tests, 131t parameter estimates, 131t relative frequency histograms, 130f alpha-stable distributions, applications, 154157 ă 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 ă 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, 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, 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 ă study, 155156 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 ă study, 99101, 194197 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, 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 ... 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... States of America 10 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... 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