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ldquoCruz_Driverrdquo mdash 201518 mdash 1813 mdash page i mdash 1

Fundamental Aspects of

Operational Risk andInsurance Analytics


ldquoCruz_Driverrdquo mdash 201518 mdash 1813 mdash page iii mdash 3


Operational Risk andInsurance AnalyticsA Handbook ofOperational Risk

MARCELO G CRUZ

GARETH W PETERS

PAVEL V SHEVCHENKO

ldquoCruz_Driverrdquo mdash 201518 mdash 1813 mdash page iv mdash 4

Copyright copy 2015 by John Wiley amp Sons Inc All rights reserved

Published by John Wiley amp Sons Inc Hoboken New JerseyPublished simultaneously in Canada

No part of this publication may be reproduced stored in a retrieval system or transmitted in any formor by any means electronic mechanical photocopying recording scanning or otherwise except aspermitted under Section 107 or 108 of the 1976 United States Copyright Act without either the priorwritten permission of the Publisher or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center Inc 222 Rosewood Drive Danvers MA 01923 (978) 750-8400fax (978) 646-8600 or on the web at wwwcopyrightcom Requests to the Publisher for permission shouldbe addressed to the Permissions Department John Wiley amp Sons Inc 111 River Street Hoboken NJ07030 (201) 748-6011 fax (201) 748-6008

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts inpreparing this book they make no representations or warranties with respect to the accuracy orcompleteness of the contents of this book and specifically disclaim any implied warranties ofmerchantability or fitness for a particular purpose No warranty may be created or extended by salesrepresentatives or written sales materials The advice and strategies contained herin may not besuitable for your situation You should consult with a professional where appropriate Neither thepublisher nor author shall be liable for any loss of profit or any other commercial damages includingbut not limited to special incidental consequential or other damages

For general information on our other products and services please contact our Customer CareDepartment with the US at 877-762-2974 outside the US 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 printhowever may not be available in electronic format

Library of Congress Cataloging-in-Publication Data

Cruz Marcelo GFundamental aspects of operational risk and insurance analytics a handbook of operational risk Marcelo G CruzGLeonard N Stern School of Business New York University New York NY USA Gareth W Peters Department ofStatistical Science University College of London London United Kingdom Pavel V Shevchenko Division ofComputational Informatics The Commonwealth Scientific and Industrial Research Organization Sydney Australia

pages cmIncludes bibliographical references and indexISBN 978-1-118-11839-9 (hardback)

1 Operational risk 2 Risk management I Peters Gareth W 1978ndash II Shevchenko Pavel V III TitleHD61C778 201465815prime5ndashdc23

2014012662

Printed in the United States of America10 9 8 7 6 5 4 3 2 1

ldquoCruz_Driverrdquo mdash 201518 mdash 1813 mdash page v mdash 5

To Virginia and NicholasMarcel G Cruz

To my dear wife Chen Mei-Peters your love patience supportand encouragement have made this book a reality To my motherLaraine Peters for teaching me the joy of scientific discovery ToYouxiang Wu the charity work is complete thank you for all

your supportGareth W Peters

To my father Vladimir and mother GalinaPavel V Shevchenko

ldquoCruz_Driverrdquo mdash 201518 mdash 1813 mdash page vi mdash 6

vi

To know is to know that you know nothingThat is the meaning of true knowledge

Socrates

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page vii mdash 7

Contents

Preface xvii

Acronyms xix

List of Distributions xxi

1 OpRisk in Perspective 1

11 Brief History 112 Risk-Based Capital Ratios for Banks 513 The Basic Indicator and Standardized Approaches for OpRisk 914 The Advanced Measurement Approach 10

141 Internal Measurement Approach 11142 Score Card Approach 11143 Loss Distribution Approach 12144 Requirements for AMA 13

15 General Remarks and Book Structure 16

2 OpRisk Data and Governance 17

21 Introduction 1722 OpRisk Taxonomy 17

221 Execution Delivery and Process Management 19222 Clients Products and Business Practices 21223 Business Disruption and System Failures 22224 External Frauds 23225 Internal Fraud 23226 Employment Practices and Workplace Safety 24227 Damage to Physical Assets 25

23 The Elements of the OpRisk Framework 25231 Internal Loss Data 26232 Setting a Collection Threshold and Possible Impacts 26233 Completeness of Database (Under-reporting Events) 27234 Recoveries and Near Misses 27235 Time Period for Resolution of Operational Losses 28

vii

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page viii mdash 8

viii Contents

236 Adding Costs to Losses 28237 Provisioning Treatment of Expected Operational Losses 28

24 Business Environment and Internal Control EnvironmentFactors (BEICFs) 29241 Risk Control Self-Assessment (RCSA) 29242 Key Risk Indicators 31

25 External Databases 3326 Scenario Analysis 3427 OpRisk Profile in Different Financial Sectors 37

271 Trading and Sales 37272 Corporate Finance 38273 Retail Banking 38274 Insurance 39275 Asset Management 40276 Retail Brokerage 42

28 Risk Organization and Governance 43281 Organization of Risk Departments 44282 Structuring a Firm Wide Policy Example of an OpRisk Policy 46283 Governance 47

3 Using OpRisk Data for Business Analysis 48

31 Cost Reduction Programs in Financial Firms 4932 Using OpRisk Data to Perform Business Analysis 53

321 The Risk of Losing Key Talents OpRisk in Human Resources 53322 OpRisk in Systems Development and Transaction Processing 54

33 Conclusions 58

4 Stress-Testing OpRisk Capital and the

Comprehensive Capital Analysis

and Review (CCAR) 59

41 The Need for Stressing OpRisk Capital Even Beyond 999 5942 Comprehensive Capital Review and Analysis (CCAR) 6043 OpRisk and Stress Tests 6844 OpRisk in CCAR in Practice 7045 Reverse Stress Test 7546 Stressing OpRisk Multivariate ModelsmdashUnderstanding the

Relationship Among Internal Control Factors and Their Impact onOperational Losses 76

5 Basic Probability Concepts in Loss

Distribution Approach 79

51 Loss Distribution Approach 7952 Quantiles and Moments 8553 Frequency Distributions 8854 Severity Distributions 89

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page ix mdash 9

Contents ix

541 Simple Parametric Distributions 90542 Truncated Distributions 92543 Mixture and Spliced Distributions 93

55 Convolutions and Characteristic Functions 9456 Extreme Value Theory 97

561 EVTmdashBlock Maxima 98562 EVTmdashRandom Number of Losses 99563 EVTmdashThreshold Exceedances 100

6 Risk Measures and Capital Allocation 102

61 Development of Capital Accords Base I II and III 10362 Measures of Risk 106

621 Coherent and Convex Risk Measures 107622 Comonotonic Additive Risk Measures 109623 Value-at-Risk 109624 Expected Shortfall 114625 Spectral Risk Measure 120626 Higher-Order Risk Measures 122627 Distortion Risk Measures 125628 Elicitable Risk Measures 126629 Risk Measure Accounting for Parameter Uncertainty 130

63 Capital Allocation 133631 Coherent Capital Allocation 134632 Euler Allocation 136633 Standard Deviation 138634 Expected Shortfall 139635 Value-at-Risk 140636 Allocation by Marginal Contributions 142637 Numerical Example 143

7 Estimation of Frequency and Severity

Models 146

71 Frequentist Estimation 146711 Parameteric Maximum Likelihood Method 149712 Maximum Likelihood Method for Truncated

and Censored Data 151713 Expectation Maximization and Parameter Estimation 152714 Bootstrap for Estimation of Parameter Accuracy 156715 Indirect InferencendashBased Likelihood Estimation 157

72 Bayesian Inference Approach 159721 Conjugate Prior Distributions 161722 Gaussian Approximation for Posterior (Laplace Type) 161723 Posterior Point Estimators 162724 Restricted Parameters 163725 Noninformative Prior 163

73 Mean Square Error of Prediction 164

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x Contents

74 Standard Markov Chain Monte Carlo (MCMC) Methods 166741 Motivation for Markov Chain Methods 167742 MetropolisndashHastings Algorithm 177743 Gibbs Sampler 178744 Random Walk MetropolisndashHastings within Gibbs 179

75 Standard MCMC Guidelines for Implementation 180751 Tuning Burn-in and Sampling Stages 180752 Numerical Error 185753 MCMC Extensions Reducing Sample Autocorrelation 187

76 Advanced MCMC Methods 188761 Auxiliary Variable MCMC Methods Slice Sampling 189762 Generic Univariate Auxiliary Variable Gibbs Sampler

Slice Sampler 189763 Adaptive MCMC 192764 RiemannndashManifold Hamiltonian Monte Carlo Sampler

(Automated Local Adaption) 19677 Sequential Monte Carlo (SMC) Samplers and Importance Sampling 201

771 Motivating OpRisk Applications for SMC Samplers 202772 SMC Sampler Methodology and Components 210773 Incorporating Partial Rejection Control into SMC Samplers 216774 Finite Sample (Nonasymptotic) Accuracy for Particle

Integration 21978 Approximate Bayesian Computation (ABC) Methods 22079 OpRisk Estimation and Modeling for Truncated Data 223

791 Constant Threshold - Poisson Process 224792 Negative Binomial and Binomial Frequencies 227793 Ignoring Data Truncation 228794 Threshold Varying in Time 232795 Unknown and Stochastic Truncation Level 236

8 Model Selection and Goodness-of-Fit

Testing for Frequency and Severity

Models 238

81 Qualitative Model Diagnostic Tools 23882 Tail Diagnostics 24083 Information Criterion for Model Selection 242

831 Akaike Information Criterion for LDA Model Selection 242832 Deviance Information Criterion 245

84 Goodness-of-Fit Testing for Model Choice (How to Accountfor Heavy Tails) 246841 Convergence Results of the Empirical Process

for GOF Testing 247842 Overview of Generic GOF TestsmdashOmnibus Distributional

Tests 256843 KolmogorovndashSmirnov Goodness-of-Fit Test and Weighted

Variants Testing in the Presence of Heavy Tails 260

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page xi mdash 11

Contents xi

844 Cramer-von-Mises Goodness-of-Fit Tests and WeightedVariants Testing in the Presence of Heavy Tails 271

85 Bayesian Model Selection 283851 Reciprocal Importance Sampling Estimator 284852 Chib Estimator for Model Evidence 285

86 SMC Sampler Estimators of Model Evidence 28687 Multiple Risk Dependence Structure Model Selection Copula Choice 287

871 Approaches to Goodness-of-Fit Testing for DependenceStructures 293

872 Double Parameteric Bootstrap for Copula GOF 297

9 Flexible Parametric Severity Models

Basics 300

91 Motivation for Flexible Parametric Severity Loss Models 30092 Context of Flexible Heavy-Tailed Loss Models in OpRisk and

Insurance LDA Models 30193 Empirical Analysis Justifying Heavy-Tailed Loss Models in OpRisk 30394 Quantile Function Heavy-Tailed Severity Models 305

941 g-and-h Severity Model Family in OpRisk 311942 Tail Properties of the g-and-h g h and hndashh Severity

in OpRisk 321943 Parameter Estimation for the g-and-h Severity in OpRisk 324944 Bayesian Models for the g-and-h Severity in OpRisk 328

95 Generalized Beta Family of Heavy-Tailed Severity Models 333951 Generalized Beta Family Type II Severity Models in OpRisk 333952 Sub families of the Generalized Beta Family Type II

Severity Models 336953 Mixture Representations of the Generalized Beta Family

Type II Severity Models 337954 Estimation in the Generalized Beta Family Type II

Severity Models 33996 Generalized Hyperbolic Families of Heavy-Tailed Severity Models 340

961 Tail Properties and Infinite Divisibility of the GeneralizedHyperbolic Severity Models 342

962 Subfamilies of the Generalized Hyperbolic Severity Models 344963 Normal Inverse Gaussian Family of Heavy-Tailed

Severity Models 34697 Halphen Family of Flexible Severity Models GIG and Hyperbolic 350

971 Halphen Type A Generalized Inverse Gaussian Familyof Flexible Severity Models 355

972 Halphen Type B and IB Families of Flexible Severity Models 361

10 Dependence Concepts 365

101 Introduction to Concepts in Dependence for OpRisk and Insurance 365102 Dependence Modeling Within and Between LDA Model Structures 366

1021 Where Can One Introduce Dependence Between LDAModel Structures 368

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page xii mdash 12

xii Contents

1022 Understanding Basic Impacts of Dependence ModelingBetween LDA Components in Multiple Risks 369

103 General Notions of Dependence 372104 Dependence Measures 387

1041 Linear Correlation 3901042 Rank Correlation Measures 393

105 Tail Dependence Parameters Functions and Tail Order Functions 3981051 Tail Dependence Coefficients 3981052 Tail Dependence Functions and Orders 4071053 A Link Between Orthant Extreme Dependence and Spectral

Measures Tail Dependence 410

11 Dependence Models 414

111 Introduction to Parametric Dependence Modeling Through a Copula 414112 Copula Model Families for OpRisk 422

1121 Gaussian Copula 4281122 t-Copula 4301123 Archimedean Copulas 4351124 Archimedean Copula Generators and the Laplace Transform

of a Non-Negative Random Variable 4391125 Archimedean Copula Generators l1-Norm Symmetric

Distributions and the Williamson Transform 4411126 Hierarchical and Nested Archimedean Copulae 4521127 Mixtures of Archimedean Copulae 4541128 Multivariate Archimedean Copula Tail Dependence 456

113 Copula Parameter Estimation in Two Stages Inference for the Margins 4571131 MPLE Copula Parameter Estimation 4581132 Inference Functions for Margins (IFM) Copula Parameter

Estimation 459

12 Examples of LDA Dependence Models 462

121 Multiple Risk LDA Compound Poisson Processes and Leacutevy Copula 462122 Multiple Risk LDA Dependence Between Frequencies via Copula 468123 Multiple Risk LDA Dependence Between the k-th Event TimesLosses 468

1231 Common Shock Processes 4691232 Max-Stable and Self-Chaining Copula Models 470

124 Multiple Risk LDA Dependence Between Aggregated Lossesvia Copula 474

125 Multiple Risk LDA Structural Model with Common Factors 477126 Multiple Risk LDA Stochastic and Dependent Risk Profiles 478127 Multiple Risk LDA Dependence and Combining Different

Data Sources 4821271 Bayesian Inference Using MCMC 4841272 Numerical Example 4851273 Predictive Distribution 487

128 A Note on Negative Diversification and Dependence Modeling 489

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page xiii mdash 13

Contents xiii

13 Loss Aggregation 492

131 Analytic Solution 4921311 Analytic Solution via Convolutions 4931312 Analytic Solution via Characteristic Functions 4941313 Moments of Compound Distribution 4961314 Value-at-Risk and Expected Shortfall 499

132 Monte Carlo Method 4991321 Quantile Estimate 5001322 Expected Shortfall Estimate 502

133 Panjer Recursion 503134 Panjer Extensions 509135 Fast Fourier Transform 511136 Closed-Form Approximation 514137 Capital Charge Under Parameter Uncertainty 519

1371 Predictive Distributions 5201372 Calculation of Predictive Distributions 521

138 Special Advanced Topics on Loss Aggregation 5231381 Discretisation Errors and Extrapolation Methods 5241382 Classes of Discrete Distributions Discrete Infinite Divisibility

and Discrete Heavy Tails 5271383 Recursions for Convolutions (Partial Sums) with Discretised

Severity Distributions (Fixed n) 5351384 Alternatives to Panjer Recursions Recursions for Compound

Distributions with Discretised Severity Distributions 5431385 Higher Order Recursions for Discretised Severity

Distributions in Compound LDA Models 5451386 Recursions for Discretised Severity Distributions in

Compound Mixed Poisson LDA Models 5471387 Continuous Versions of the Panjer Recursion 550

14 Scenario Analysis 556

141 Introduction 556142 Examples of Expert Judgments 559143 Pure Bayesian Approach (Estimating Prior) 561144 Expert Distribution and Scenario Elicitation Learning from

Bayesian Methods 563145 Building Models for Elicited Opinions Hierarchical Dirichlet Models 566146 Worst-Case Scenario Framework 568147 Stress Test Scenario Analysis 571148 Bow-Tie Diagram 574149 Bayesian Networks 576

1491 Definition and Examples 5771492 Constructing and Simulating a Bayesian Net 5801493 Combining Expert Opinion and Data in a Bayesian Net 5811494 Bayesian Net and Operational Risk 582

1410 Discussion 584

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page xiv mdash 14

xiv Contents

15 Combining Different Data Sources 585

151 Minimum Variance Principle 586152 Bayesian Method to Combine Two Data Sources 588

1521 Estimating Prior Pure Bayesian Approach 5901522 Estimating Prior Empirical Bayesian Approach 5921523 Poisson Frequency 5931524 The LogNormal Severity 5971525 Pareto Severity 601

153 Estimation of the Prior Using Data 6061531 The Maximum Likelihood Estimator 6061532 Poisson Frequencies 607

154 Combining Expert Opinions with External and Internal Data 6091541 Conjugate Prior Extension 6101542 Modeling Frequency Poisson Model 6111543 LogNormal Model for Severities 6181544 Pareto Model 620

155 Combining Data Sources Using Credibility Theory 6251551 BuumlhlmannndashStraub Model 6261552 Modeling Frequency 6281553 Modeling Severity 6311554 Numerical Example 6331555 Remarks and Interpretation 634

156 Nonparametric Bayesian Approach via Dirichlet Process 635157 Combining Using DempsterndashShafer Structures and p-Boxes 638

1571 DempsterndashShafer Structures and p-Boxes 6391572 Dempsterrsquos Rule 6411573 Intersection Method 6431574 Envelope Method 6441575 Bounds for the Empirical Data Distribution 645

158 General Remarks 647

16 Multifactor Modeling and Regression

for Loss Processes 649

161 Generalized Linear Model Regressions and the Exponential Family 6491611 Basic Components of a Generalized Linear Model Regression

in the Exponential Family 6501612 Basis Function Regression 654

162 Maximum Likelihood Estimation for Generalized Linear Models 6551621 Iterated Weighted Least Squares Maximum Likelihood

for Generalised Linear Models 6551622 Model Selection via the Deviance in a GLM Regression 657

163 Bayesian Generalized Linear Model Regressionsand Regularization Priors 6591631 Bayesian Model Selection for Regularlized GLM Regression 665

164 Bayesian Estimation and Model Selection via SMC Samplers 6661641 Proposed SMC Sampler Solution 667

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page xv mdash 15

Contents xv

165 Illustrations of SMC Samplers Model Estimation and Selection forBayesian GLM Regressions 6681651 Normal Regression Model 6681652 Poisson Regression Model 669

166 Introduction to Quantile Regression Methods for OpRisk 6721661 Nonparametric Quantile Regression Models 6741662 Parametric Quantile Regression Models 675

167 Factor Modeling for Industry Data 681168 Multifactor Modeling under EVT Approach 683

17 Insurance and Risk Transfer Products

and Modeling 685

171 Motivation for Insurance and Risk Transfer in OpRisk 685172 Fundamentals of Insurance Product Structures for OpRisk 688173 Single Peril Policy Products for OpRisk 692174 Generic Insurance Product Structures for OpRisk 694

1741 Generic Deterministic Policy Structures 6941742 Generic Stochastic Policy Structures Accounting for

Coverage Uncertainty 700175 Closed-Form LDA Models with Insurance Mitigations 705

1751 Insurance Mitigation Under the Poisson-Inverse-GaussianClosed-Form LDA Models 705

1752 Insurance Mitigation and Poisson-α-Stable Closed-FormLDA Models 712

1753 Large Claim Number Loss Processes Generic Closed-FormLDA Models with Insurance Mitigation 719

1754 Generic Closed-Form Approximations for InsuredLDA Models 734

18 Insurance and Risk Transfer Pricing

Insurance-Linked Derivatives

Reinsurance and CAT Bonds for OpRisk 750

181 Insurance-Linked Securities and CAT Bonds for OpRisk 7511811 Background on Insurance-Linked Derivatives and CAT

Bonds for Extreme Risk Transfer 7551812 Triggers for CAT Bonds and Their Impact on Risk Transfer 7601813 Recent Trends in CAT Bonds 7631814 Management Strategies for Utilization of Insurance-Linked

Derivatives and CAT Bonds in OpRisk 763182 Basics of Valuation of ILS and CAT Bonds for OpRisk 765

1821 Probabilistic Pricing Frameworks Complete and IncompleteMarkets Real-World Pricing Benchmark Approach andActuarial Valuation 771

1822 Risk Assessment for Reinsurance ILS and CAT Bonds 794

ldquoCruz_Driverrdquo mdash 201518 mdash 1818 mdash page xvi mdash 16

xvi Contents

183 Applications of Pricing ILS and CAT Bonds 7961831 Probabilistic Framework for CAT Bond Market 7961832 Framework 1 Assuming Complete Market

and Arbitrage-Free Pricing 7981833 Framework 2 Assuming Incomplete Arbitrage-Free Pricing 809

184 Sidecars Multiple Peril Baskets and Umbrellas for OpRisk 8151841 Umbrella Insurance 8161842 OpRisk Loss Processes Comprised of Multiple Perils 817

185 Optimal Insurance Purchase Strategies for OpRisk Insurance viaMultiple Optimal Stopping Times 8231851 Examples of Basic Insurance Policies 8261852 Objective Functions for Rational and Boundedly Rational

Insurees 8281853 Closed-Form Multiple Optimal Stopping Rules for Multiple

Insurance Purchase Decisions 8301854 Aski-Polynomial Orthogonal Series Approximations 835

A Miscellaneous Definitions and List

of Distributions 842

A1 Indicator Function 842A2 Gamma Function 842A3 Discrete Distributions 842

A31 Poisson Distribution 842A32 Binomial Distribution 843A33 Negative Binomial Distribution 843A34 Doubly Stochastic Poisson Process (Cox Process) 844

A4 Continuous Distributions 844A41 Uniform Distribution 844A42 Normal (Gaussian) Distribution 844A43 Inverse Gaussian Distribution 845A44 LogNormal Distribution 845A45 Studentrsquos t Distribution 846A46 Gamma Distribution 846A47 Weibull Distribution 846A48 Inverse Chi-Squared Distribution 847A49 Pareto Distribution (One-Parameter) 847A410 Pareto Distribution (Two-Parameter) 847A411 Generalized Pareto Distribution 848A412 Beta Distribution 848A413 Generalized Inverse Gaussian Distribution 849A414 d -variate Normal Distribution 849A415 d -variate t-Distribution 850

Bibliography 851

Index 892

ldquoCruz_Driverrdquo mdash 201518 mdash 1826 mdash page xvii mdash 17

Preface

Operational risk (OpRisk) has been through significant changes in the past few years withincreased regulatory pressure for more comprehensive frameworks Nowadays every mid-sizedand larger financial institution across the planet has an OpRisk department However if wecompare the pace of progress of OpRisk to market and credit risks we would realize thatOpRisk is not advancing as fast as its sister risks moved in the past Market risk managementand measurement had its major breakthrough in the early 1990s as JP Morgan released publiclyits Value-at-Risk (VaR) framework Only a couple of years after this release most of the 100global largest banks had developed a market risk framework and were using at least to a certainlevel VaR methods to measure and manage market risk A few years later the Basel Committeeallowed banks to use their VaR models for regulatory capital purposes From the release of JPMorganrsquos methodology to becoming accepted by Basel and local regulators it took only about4 years This is basically because the methods were widely discussed and the regulators couldalso see in practice how they would work As we see it one of the biggest challenges in OpRiskis to take this area to the same level that market and credit risk management are at Those tworisks are managed proactively and risk managers usually have a say if deals or businesses areapproved based on the risk level OpRisk is largely kept out of these internal decisions at thisstage and this is a very worrying issue as quite a few financial institutions have OpRisk as itsdominant exposure We believe that considerable effort in the industry would have to be putinto data collection and modeling improvements and making a contribution to close this gapis the main objective of our book

Unlike market and credit risks the methodologies and practices used in OpRisk still varysubstantially between banks Regulators are trying to close the methodological gap by hold-ing meetings with the industry and incentivizing convergence among the different approachesthrough more individualized guidance Although some success might be credited to these effortsthere are still considerable challenges and this is where the Fundamental Aspects of OperationalRisk and Insurance Analytics A Handbook of Operational Risk can add value to the industry

In addition by using this text as a graduate text from which to teach the key componentsof OpRisk in universities one will begin to achieve a concensus and understanding of the disci-pline for junior quantitative risk managers and actuaries These challenges involve the practicalbusiness environment regulator requirements as well as the serious and detailed quantitativechallenges in the modeling aspects

This book is a comprehensive treatment of all aspects of OpRisk management and insur-ance with a focus on the analytical and modeling side but also covering the basic quali-tative aspects The initial chapters cover the building blocks of OpRisk management andmeasurement There is broad coverage on the four data elements that need to be used in the

xvii

ldquoCruz_Driverrdquo mdash 201518 mdash 1826 mdash page xviii mdash 18

xviii Preface

OpRisk framework as well as how a risk taxonomy process should be developed Consider-able focus is given to internal loss data and key risk indicators as these would be fundamen-tal in developing a risk-sensitive framework similar to market and credit risks An example isalso shown of how OpRisk can be inserted into a firmrsquos strategic decisions In addition wecover basic concepts of probability theory and the basic framework for modeling and measur-ing OpRisk and how loss aggregation should work We conclude this part of the text with amodel to perform stress-testing in OpRisk under the US Comprehensive Capital Analysis andReview (CCAR) program

We continue by covering more special topics in OpRisk measurement For example diversemethods to estimate frequency and severity models are discussed Another very popular issuein this industry is how to select severity models and this is also comprehensively discussed Oneof the biggest challenges in OpRisk is that data used in measurement can be very different socombining them into a single measure is not trivial In this part of the book we show a numberof methods to do so

After the core risk measurement work is done there are still some issues to address thatcan potentially mitigate the capital and also indicate how to manage risks In the third partwe discuss correlation and dependency modeling as well as insurance and risk transfer toolsand methods This is particularly relevant when considering risk mitigation procedures for lossprocesses that may generate catastrophic losses due to for instance nature risk

This book provides a consistent and comprehensive coverage of all aspects of risk man-agement more specifically OpRiskndashorganizational structure methodologies policies andinfrastructurendashfor both financial and nonfinancial institutions The risk measurement andmodeling techniques discussed in the book are based on the latest research They are presentedhowever with considerations based on practical experience of the authors with the daily appli-cation of risk measurement tools

We have incorporated the latest evolution of the regulatory framework The book offers aunique presentation of the latest OpRisk management techniques and provides one-stop shop-ping for knowledge in risk management ranging from current regulatory issues data collec-tion and management to technological infrastructure hedging techniques and organizationalstructure

It is important to mention that we are publishing at the same time a companionbook Advances in Heavy Tailed Risk Modeling A Handbook of Operational Risk (Peters andShevchenko 2015) which although can be seen as an independent tome covers many impor-tant ideas in OpRisk and insurance modeling This book would be ideally treated as a mathe-matically detailed companion to this current text which would go hand in hand with a moreadvanced graduate course on OpRisk In this text we cover in detail significant components ofheavy-tailed loss modeling which is of key importance to many areas of OpRisk

We would like to thank our families for their patience in our absence while we were writingthis book

Acknowledgments

Dr Gareth W Peters also acknowledges the support of the Institute of Statistical Mathematics TokyoJapan and Prof Tomoko Matsui for extended collaborative research visits and discussions during thedevelopment of this book

Marcelo G Cruz Gareth W Peters and Pavel V Shevchenko

New York London Sydney

ldquoCruz_Driverrdquo mdash 201518 mdash 1833 mdash page xix mdash 19

Acronyms

ABC Approximate Bayesian ComputationALP Accumulated Loss PolicyAMA Advanced Measurement ApproachAPT Arbitrage Pricing Theoryas almost surelyAUM Assets under ManagementBDSF Business Disruption and System FailuresBCBS Basel Committee on Banking SupervisionBCRLB Bayesian CramerndashRao Lower BoundBEICF Business Environment and Internal Control FactorsBHC Banking Holding CompanyBIS Bank for International SettlementsCAT catastrophe bondCCAR Comprehensive Capital Analysis and ReviewCD codifferenceCLP Combined Loss PolicyCPI Consumer Price IndexCRLB Cramer Rao Lower BoundCV covariationCVaR Conditional Value-at-RiskDFT Discrete Fourier TransformES Expected shortfallEVI Extreme Value IndexEVT Extreme Value TheoryFED Federal Reserve BankFFT Fast Fourier TransformGAM Generalized Additive ModelsGAMLSS Generalized Additive Models for Location Scale and ShapeGAMM Generalized Additive Mixed ModelsGDP Gross Domestic ProductGLM Generalized Linear ModelsGLMM Generalized Linear Mixed ModelsHILP Haircut Individual Loss PolicyHMCR higher moment coherent risk measureiid independent and identically distributed

xix

ldquoCruz_Driverrdquo mdash 201518 mdash 1833 mdash page xx mdash 20

xx Acronyms

ILPC Individual Loss Policy CappedILPU Individual Loss Policy UncappedLDA Loss Distribution ApproachMC Monte CarloMCMC Markov chain Monte CarloMLE maximum likelihood estimatorMPT Modern Portfolio Theoryode ordinary differential equationOpRisk operational riskpgf probability generating functionPMCMC particle Markov chain Monte CarloPPNR pre-provision net revenuerv random variableSCAP Supervisory Capital Assessment ProgramSMC Sequential Monte CarloSRM spectral risk measureTCE tail conditional expectationTTCE tempered tail conditional expectationVaR Value-at-RiskVco variational coefficient

ldquoCruz_Driverrdquo mdash 201518 mdash 1833 mdash page xxi mdash 21

List of Distributions

Distribution Name Distribution Symbol

Asymmetric Laplace AsymmetricLaplace(middot)Beta Beta(middot)Binomial Binomial(middot)Chi-Squared ChiSquared(middot)Exponential Exp(middot)g-and-h distributions Tgh(middot)g-and-k distributions Tgk(middot)g distributions Tg(middot)Gamma Gamma(middot)Generalized Inverse Gaussian GIG(middot)Generalized Pareto Distribution GPD(middot)Inverse Gaussian InverseGaussian(middot)Inverse Gamma InverseGamma(middot)LogNormal LogNormal(middot)Normal (Gaussian) Normal(middot)Standard Normal Φ(middot)Negative Binomial NegBinomial(middot)Normal Inverse Gaussian NIG(middot)Pareto Pareto(middot)Poisson Poisson(middot)Tukey Transform h Th(middot)Tukey Transform k Tk(middot)Tukey Transform j Tj(middot)Tukey Transform hjk Thjk(middot)h distributions Th(middot)Double hndashh distributions Thh(middot)Generalized Beta GB2(middot)Log-t Log-t(middot)Generalized Gamma GG(middot)SinghndashMaddala or Burr Type III BurrIII(middot)Dagum or Burr Type XII BurrXII(middot)Log-Cauchy LogCauchy(middot)

xxi

ldquoCruz_Driverrdquo mdash 201518 mdash 1833 mdash page xxii mdash 22

xxii List of Distributions

Lomax Lomax(middot)Generalized Hyperbolic GH(middot)Laplace Laplace(middot)Halphen Type A Halphe(middot)

ldquoCruz_Driverrdquo mdash 201518 mdash 1047 mdash page 1 mdash 1

Chapter One

OpRisk in Perspective

11 Brief History

Operational risk (OpRisk) is the youngest of the three major risk branches the others beingmarket and credit risks The term OpRisk started to be used after the Barings event in 1995when a rogue trader caused the collapse of a venerable institution by placing bets in the Asianmarkets and keeping these contracts out of sight of management At the time these lossescould be classified neither as market nor as credit risks and the term OpRisk started to beused in the industry to define situations where such losses could arise It took quite some timeuntil this definition was abandoned and a proper definition was established for OpRisk Inthese early days OpRisk had a negative definition as ldquoevery risk that is not market and creditrdquowhich was not very helpful to assess and manage this risk Looking back at the history of riskmanagement research we observe that early academics found the same issue of classifying riskin general as Crockford (1982) noticed ldquoResearch into risk management immediately encoun-ters some basic problems of definition There is still no general agreement on where the bound-aries of the subject lie and a satisfactory definition of risk management is notoriously difficult toformulaterdquo

Before delving into the brief history of OpRisk it might be useful to first understand howrisk management is evolving and where OpRisk fits in this evolution Risk in general is a rela-tively new area that began to be studied only after World War II The concept of risk manage-ment came from the insurance industry and this was clear in the early daysrsquo definitions Accord-ing to Crockford (1982) the term ldquorisk managementrdquo in its earliest incarnations ldquoencompassedprimarily those activities performed to prevent accidental lossrdquo In one of the first textbooks on riskMehr and Hedges (1963) used a definition that reflected this close identification with insuranceldquo[T]he management of those risks for which the organization principles and techniques appropriateto insurance management is usefulrdquo Almost 20 years later Bannister and Bawcutt (1981) definedrisk management as ldquothe identification measurement and economic control of risks that threatenthe assets and earnings of a business or other enterpriserdquo which is much closer to the definitionused in the financial industry in the twenty-first century

The association of risk management and insurance came from the regular use of insuranceby individuals and corporations to protect themselves against these ldquoaccidental lossesrdquo It isinteresting to see that even early authors on the subject made a case for the separation betweenrisk management and risk-takers (the businesses) Crockford (1982) wrote that ldquooperational

Fundamental Aspects of Operational Risk and Insurance Analytics A Handbook of Operational RiskFirst Edition Marcelo G Cruz Gareth W Peters and Pavel V Shevchenkocopy 2015 John Wiley amp Sons Inc Published 2015 by John Wiley amp Sons Inc

1


2 CHAPTER 1 OpRisk in Perspective

convenience continues to dictate that pure and speculative risks should be handled by different func-tions within a company even though theory may argue for them being managed as onerdquo

New tools for managing risks started to emerge in the 1950s in addition to insurancewhen many types of insurance coverage became very costly and incomplete or certainly thisldquoincompletionrdquo started to be better noticed as risk management was beginning to evolve Sev-eral business risks were either impossible or too expensive to insure Contingent planning activ-ities an embryo of what is today called Business Continuity Planning (BCP) were developedand various risk prevention or self-prevention activities and self-insurance instruments againstsome losses were put in place Coverage for work-related illnesses and accidents also started tobe offered during the 1960s The 1960s were when a more formal organized scholarly intereststarted to blossom in academia on issues related to risk The first academic journal to show ldquoriskrdquoin their title was the Journal of Risk and Insurance in 1964 This journal was actually titled Jour-nal of Insurance until then Other specialized journals followed including Risk Managementmdashpublished by the Risk and Insurance Management Society (RIMS) a professional associationof risk managers founded in 1950 and the Geneva Papers on Risk and Insurance published bythe Geneva Association since 1976

Risk management had its major breakthrough as the use of financial derivatives by investorsbecame more spread out Before the 1970s derivatives were basically used for commodi-ties and agricultural products however in the 1970s but more strongly in the 1980s theuse of derivatives to manage and hedge risks began In the 1980s companies began to con-sider financial risk management of ldquorisk portfoliosrdquo Financial risk management has becomecomplementary to pure risk management for many companies Most financial institutionsparticularly investment banks intensified their market and credit risk management activitiesduring the 1980s Given this enhanced activity and a number of major losses it was no sur-prise that more intense scrutiny drew international regulatory attention Governance of riskmanagement became essential and the first risk management positions were created withinorganizations

A sort of ldquorisk management revolutionrdquo was sparked in the 1980s by a number of macroe-conomic events that were present during this decade as for example fixed currency paritiesdisappeared the price of commodities became much more volatile and the price fluctuationsof many financial assets like interest rates stock markets exchange rates etc became muchmore volatile This volatility and the many headline losses that succeeded revolutionized theconcept of financial risk management as most financial institutions had such assets in theirbalance sheets and managing these risks became a priority for senior management and board ofdirectors At the same time the definition of risk management became broader Risk manage-ment decisions became financial decisions that had to be evaluated based on their effect on afirm or portfolio value rather than on how well they cover certain risks This change in defini-tion applies particularly to large public corporations due to the risk these bring to the overallfinancial system

These exposures to financial derivatives brought new challenges with regard to risk assess-ment Quantifying the risk exposures given the complexity of these assets was (and stillremains) quite complex and there were no generally accepted models to do so The first andmost popular model to quantify market risks was the famous ldquoBlack amp Scholesrdquo developed byBlack and Scholes (1973) in which an explicit formula for pricing a derivative was proposedmdashinthis case an equity derivative The model was so revolutionary that the major finance journalsrefused to publish it at first It was finally published in the Journal of Political Economy in 1973An extension of this article was later published by Merton in the Bell Journal of Economicsand Management Science (Merton 1973) The impact of the article in the financial industry


11 Brief History 3

was significant and the risk coverage of derivatives grew quickly expanding to many distinctassets like interest rate swaps currencies etc

As risk management started to grow as a discipline regulation also began to get morecomplex to catch up with new tools and techniques It is not a stretch to say that financialinstitutions have always been regulated one way or another given the risk they bring to thefinancial system Regulation was mostly on a country-by-country basis and very uneven allow-ing arbitrages As financial institutions became more globalized the need for more symmetricregulation that could level the way institutions would be supervised and regulated increasedworldwide The G10 the group of 10 most industrialized countries started meetings in thecity of Basel in Switzerland under the auspices of the Bank for International Settlements (BIS)The so-called Basel Committee on Banking Supervision or Basel Committee was establishedby the central bank governors of the group of 10 countries at the end of 1974 and continuesto meet regularly four times a year It has four main working groups which also meet regularly

The Basel Committee does not possess any formal supranational supervisory authorityand its conclusions cannot and were never intended to have legal force Rather it formulatesbroad supervisory standards and guidelines and recommends statements of best practice inthe expectation that individual authorities will take steps to implement them through detailedarrangements statutory or otherwise which are best suited to their own national systemsIn this way the Committee encourages convergence toward common approaches and com-mon standards without attempting detailed standardization of member countriesrsquo supervisorytechniques

The Committee reports to the central bank governors and heads of supervision of its mem-ber countries It seeks their endorsement for its major initiatives These decisions cover a verywide range of financial issues One important objective of the Committeersquos work has beento close gaps in international supervisory coverage in pursuit of two basic principles that noforeign banking establishment should escape supervision and that supervision should be ade-quate To achieve this the Committee has issued a long series of documents since 1975 thatguide regulators worldwide on best practices that can be found on the websitewwwbisorgbcbspublicationshtm

The first major outcome of these meetings was the Basel Accord now called Basel I signedin 1988 (see BCBS 1988) This first accord was limited to credit risk only and required eachbank to set aside a capital reserve of 8 the so-called Cooke ratio of the value of the securitiesrepresenting the credit risk in their portfolio The accord also extended the definition of capitalto create reserves encompassing more than bank equity which were namely

bull Tier 1 (core capital) consisting of common stock holding in subsidiaries and somereserves disclosed to the regulatory body

bull Tier 2 (supplementary capital) made up of hybrid capital instruments subordinateddebts with terms to maturity greater than 5 years other securities other reserves

The Basel I Accord left behind one important risk component which was market risk Inthe meantime JP Morgan released publicly its market risk methodology called Risk Metrics(JP Morgan 1996) and the popularization of market risk measurement became widespread inthe early 1990s Reacting to that in 1996 the Basel Committee issued the market risk amend-ment (BCBS 1996) which included market risk in the regulatory framework The acceptanceof more sophisticated models like Value at Risk (VaR) as regulatory capital was a significantmilestone in risk management However this initial rule had a number of limitations as it did



not allow diversification that is the total VaR of the firm would be the sum of the VaR for allassets without allowing for correlation between these risks

As the global financial markets became increasingly interconnected and sophisticated aswell as financial products like credit derivatives it soon became clear to the Basel Committeethat a new regulatory framework was needed In June 1999 the Committee issued a proposalfor a revised Capital Adequacy Framework The proposed capital framework consisted of thefollowing three pillars

bull Pillar 1 Minimum capital requirements which seek to refine the standardized rules setforth in the 1988 Accord

bull Pillar 2 Supervisory review of an institutionrsquos internal assessment process and capital ade-quacy

bull Pillar 3 Market discipline focused on effective use of disclosure to strengthen marketdiscipline as a complement to supervisory efforts

Following extensive interaction with banks industry groups and supervisory authorities thatare not members of the Committee the revised framework (referred to as Basel II) BCBS (2004)was issued on June 26 2004 the comprehensive version was published as BCBS (2006) Thistext serves as a basis for national rule-making and for banks to complete their preparations forthe new frameworkrsquos implementation

With Basel II there also came for the first time the inclusion of OpRisk into the regulatoryframework The OpRisk situation was different from the one faced by market and credit risksFor those risks regulators were looking at the best practice in the industry and issuing regulationmirroring these The progress in OpRisk during the late 1990s and early 2000s was very slowSome very large global banks like Lehman Brothers did not have an OpRisk department until2004 so the regulators were issuing rules without the benefit of seeing how these rules wouldwork in practice This was a challenge for the industry

In order to address these challenges the Basel Committee allowed a few options for banksto assess capital The framework outlined and presented three methods for calculating OpRiskcapital charges in a continuum of increasing sophistication and risk sensitivity (i) the Basic Indi-cator Approach (BIA) (ii) the Standardized Approach (SA) and (iii) Advanced MeasurementApproaches (AMA) Internationally active banks and banks with significant OpRisk exposures(eg specialized processing banks) are expected to use an approach that is more sophisticatedthan the BIA and that is appropriate for the risk profile of the institution

Many models have been suggested for modeling OpRisk under Basel II for an overviewsee Chernobai et al (2007 chapter 4) Allen et al (2005) and Shevchenko (2011 Section 15)Fundamentally there are two different approaches used to model OpRisk

bull The topndashdown approach andbull The bottomndashup approach

The topndashdown approach quantifies OpRisk without attempting to identify the eventsor causes of losses while the bottomndashup approach quantifies OpRisk on a microlevel as it isbased on identified internal events The topndashdown approach includes the Risk Indicator mod-els that rely on a number of operational risk exposure indicators to track OpRisks and theScenario Analysis and Stress Testing Models that are estimated based on the what-if scenariosThe bottomndashup approaches include actuarial-type models (referred to as the Loss Distribution


12 Risk-Based Capital Ratios for Banks 5

Approach) that model frequency and severity of OpRisk losses In this book we provide adetailed quantitative discussion on a range of models some of which are appropriate for top-down modelling whilst others are directly applicable to bottom-up frameworks

12 Risk-Based Capital Ratios for Banks

Until the late 1970s banks in most countries were in general highly regulated and protectedentities This protection was largely a result of the bitter memories of the Great Depression inthe US as well as the role that high (or hyper) inflation played in the political developments inEurope in the 1930s and banks arguably play a significant part in the spreading of inflationDue to these memories the activities banks were allowed to undertake were tightly restricted bynational regulators and in return banks were mostly protected from competitive forces Thiscozy relationship was intended to ensure stability of the banking system and it succeeded inits goals throughout the reconstruction and growth phases which followed World War II Thisagreement held well until the collapse of Bretton Woods1 (Eichengreen 2008) in the 1970sThe resulting strain in the banking system was enormous Banks suddenly were faced with anincreasingly volatile environment but at the same time had very inelastic pricing control overtheir assets and liabilities which were subject not just to government regulation but also toprotective cartel-like arrangements The only solution seen by national authorities at this timewas to ease regulations on banks As the banking sector was not used to competitive pressuresthe result of the deregulation was that banks started to take too much risk in search of large pay-offs Suddenly banks were overlending to Latin American countries (and other emerging mar-kets) overpaying for expansion (eg buying competitors looking for geographic expansion)etc With the crisis in Latin America in the 1980s these countries could not repay their debtsand banks were once again in trouble Given that the problems were mostly cross-boundaryas the less regulated banks became more international the only way to address this situationwas at the international level and the Basel Committee was consequently established under theauspices of the BIS

In 1988 the Basel Committee decided to introduce an internationally accepted capitalmeasurement system commonly referred to as Basel I (BCBS 1988) This framework wasreplaced by a significantly more complex capital adequacy framework commonly known asBasel II (BCBS 2004) and more recently the Basel Committee issued the Basel III Accord(BCBS 2011 2013) which will add more capital requirements to banks Table 11 shows asummary of key takeaways of the Basel Accords

Basel I primarily focuses on credit risk and developed a system of risk-weighting of assetsAssets of banks were classified and grouped in five categories according to credit risk carryingrisk weights of 0 for the safest most liquid assets (eg cash bullion home country debtlike Treasuries) to 100 (eg most corporate debt) Banks with an international presence wererequired to at least hold capital equal to 8 of their risk-weighted assets (RWA) The conceptof RWA was kept in all Accords with changes on the weights and in the composition of assets bycategory An example of how risk-weighting works can be seen in Table 12 In this example thesum of the assets of this bank is $1015 however applying the risk-weighting rule establishedin Basel I the RWA is actually $675

1The Bretton Woods agreement was established in the summer of 1944 and put in place a system of exchangeand interest rate stability which ensured that banks could easily manage their exposures



table 11 Basel framework general summary

Accord Year Key points

Basel I 1988 Introduces minimal capital requirement for the banking bookIntroduces tier concept for capital requirementIncorporates trading book into the framework later on through theMarket Risk Amendment (MRA)

Basel II 2004 Allows usage of internal models and inputs in risk measurementIntroduces operational risk

Basel IIIII 2010 Increases capital requirement for trading book with significant increasefor correlation trading and securitizations

Basel III 2010 Motivated by the great financial crisis of 2008 increases capitalrequirements introduces leverage constraints and minimum liquidityand funding requirements

table 12 Example of risk-weighted assets calculation under Basel I

Risk-weight () Asset Amount ($) RWA ($)

0 CashTreasury billsLong-term treasury securities

1050100

000

20 Municipal bondsItems in collection

2020

44

50 Residential mortgages 300 150100 AA+ rated loan

Commercial loans AAA- ratedCommercial loans BB- ratedSovereign loans B- ratedFixed assets

205520020050

205520020050

Not rated Reserve for loan losses (10) (10)

Total 1015 675

Since Basel I a bankrsquos capital also started to be classified into Tier 1 and Tier 2 Tier 1capital is considered the primary capital or ldquocore capitalrdquo Tier 2 capital is the supplementarycapital The total capital that a bank holds is defined as the sum of Tier 1 and Tier 2 capitalsTable 13 provides a more detailed view of the components of each tier of capital The keycomponent of Tier 1 capital is the common shareholders equity This item is so important thata number of banks also report the so-called Tier 1 Common Equity in which only commonshareholder equity is considered as Tier 1 As shown in Table 13 the Basel Committee madecapital requirement much stricter in the latest Basel Accords by changing the definition ofsome of the current items but also by sending a couple of items to Tier 2 (eg trust preferredsecurities and remaining noncontrolling interest) making it more difficult for banks to complywith these new capital rules

Another important contribution from Basel I is the concept of capital ratios that remainsuntil today Basically a bank needs to assert its capital requirements based on the formula

Capital ratio =Eligible capital

RWA (11)









MARCELO G CRUZ

GARETH W PETERS

PAVEL V SHEVCHENKO












2014012662








vi


Socrates


Contents

Preface xvii

Acronyms xix










vii


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)








MARCELO G CRUZ

GARETH W PETERS

PAVEL V SHEVCHENKO












2014012662








vi


Socrates


Contents

Preface xvii

Acronyms xix










vii


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)





MARCELO G CRUZ

GARETH W PETERS

PAVEL V SHEVCHENKO












2014012662








vi


Socrates


Contents

Preface xvii

Acronyms xix










vii


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)




MARCELO G CRUZ

GARETH W PETERS

PAVEL V SHEVCHENKO












2014012662








vi


Socrates


Contents

Preface xvii

Acronyms xix










vii


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)












2014012662








vi


Socrates


Contents

Preface xvii

Acronyms xix










vii


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)







vi


Socrates


Contents

Preface xvii

Acronyms xix










vii


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


vi


Socrates


Contents

Preface xvii

Acronyms xix










vii


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


Contents

Preface xvii

Acronyms xix










vii


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


viii Contents









33 Conclusions 58










Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


Contents ix









Models 146






x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


x Contents











Models 238








Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


Contents xi







Basics 300


















xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


xii Contents












Estimation 459









Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


Contents xiii
















1410 Discussion 584


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


xiv Contents



















Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


Contents xv





and Modeling 685

















xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


xvi Contents












Bibliography 851

Index 892


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


Preface





xvii


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


xviii Preface








Acknowledgments





Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


Acronyms


xix


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


xx Acronyms






xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)





xxi





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)





Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


Chapter One


11 Brief History





1









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)









11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)


11 Brief History 3









































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)

































1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)




















1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)












1050100

000


2020

44



205520020050

205520020050


Total 1015 675




RWA (11)

Date post:	07-Jun-2020
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