Marcelo G. Cruz, Gareth W. Peters, Pavel V. Shevchenko
Fundamental Aspects of Operational Risk and Insurance Analytics
A Handbook of Operational Risk
Marcelo G. Cruz, Gareth W. Peters, Pavel V. Shevchenko
Fundamental Aspects of Operational Risk and Insurance Analytics
A Handbook of Operational Risk
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A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk
Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary…mehr
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A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk
Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements.
Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk , the handbook also features:
Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework
Guidelines for how operational risk can be inserted into a firm's strategic decisions
A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program
A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.
Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements.
Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk , the handbook also features:
Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework
Guidelines for how operational risk can be inserted into a firm's strategic decisions
A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program
A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.
Produktdetails
- Produktdetails
- Wiley Handbooks in Financial Engineering and Econometrics
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 928
- Erscheinungstermin: 23. Februar 2015
- Englisch
- Abmessung: 240mm x 161mm x 54mm
- Gewicht: 1557g
- ISBN-13: 9781118118399
- ISBN-10: 1118118391
- Artikelnr.: 41376886
- Wiley Handbooks in Financial Engineering and Econometrics
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 928
- Erscheinungstermin: 23. Februar 2015
- Englisch
- Abmessung: 240mm x 161mm x 54mm
- Gewicht: 1557g
- ISBN-13: 9781118118399
- ISBN-10: 1118118391
- Artikelnr.: 41376886
Marcelo G. Cruz, PhD, is Adjunct Professor at New York University and a world-renowned consultant on operational risk modeling and measurement. He has written and edited several books in operational risk, and is Founder and Editor-in-Chief of The Journal of Operational Risk. Gareth W. Peters, PhD, is Assistant Professor in the Department of Statistical Science, Principle Investigator in Computational Statistics and Machine Learning, and Academic Member of the UK PhD Centre of Financial Computing at University College London. He is also Adjunct Scientist in the Commonwealth Scientific and Industrial Research Organisation, Australia; Associate Member Oxford-Man Institute at th Oxford University; and Associate Member in the Systemic Risk Centre at the London School of Economics. Pavel V. Shevchenko, PhD, is Senior Principal Research Scientist in the Commonwealth Scientific and Industrial Research Organisation, Australia, as well as Adjunct Professor at the University of New South Wales and the University of Technology, Sydney. He is also Associate Editor of The Journal of Operationa Risk. He works on research and consulting projects in the area of financial risk and the development of relevant numerical methods and software, has published extensively in academic journals, consults for major financial institutions, and frequently presents at industry and academic conferences.
Preface xxi Acronyms xxv 1 OpRisk in Perspective 1 1.1 Brief History 1 1.2
Risk-Based Capital Ratios for Banks 5 1.3 The Basic Indicator and
Standardized Approaches for OpRisk 9 1.4 The Advanced Measurement Approach
11 1.5 General Remarks and Book Structure 16 2 OpRisk Data and Governance
17 2.1 Introduction 17 2.2 OpRisk Taxonomy 18 2.3 The Elements of the
OpRisk Framework 25 2.4 Business Environment and Internal Control
Environment Factors (BEICFs) 29 2.5 External Databases 32 2.6 Scenario
Analysis 33 2.7 OpRisk Profile in Different Financial Sectors 36 2.8 Risk
Organization and Governance 43 3 Using OpRisk Data for Business Analysis 49
3.1 Cost Reduction Programs at Financial Firms 50 3.2 Using OpRisk Data to
Perform Business Analysis 54 3.3 The Risk of Losing Key Talents: OpRisk in
Human Resources 55 3.4 Systems Risks: OpRisk in Systems Development and
Transaction Processing 56 3.5 Conclusions 59 4 Stress Testing OpRisk
Capital and CCAR 61 4.1 The Need for Stressing OpRisk Capital Even Beyond
the 99.9% 61 4.2 Comprehensive Capital Review and Analysis (CCAR) 62 4.3
OpRisk and Stress Tests 68 4.4 OpRisk in CCAR in Practice 69 4.5 Reverse
Stress Test 75 4.6 Stressing OpRisk Multivariate Models 75 5 Basic
Probability Concepts in Loss Distribution Approach 79 5.1 Loss Distribution
Approach 79 5.2 Quantiles and Moments 84 5.3 Frequency Distributions 87 5.4
Severity Distributions 88 5.5 Convolutions and Characteristic Functions 93
5.6 Extreme Value Theory 95 6 Risk Measures and Capital Allocation 101 6.1
Development of Capital Accords Base I, II and III 102 6.2 Measures of Risk
105 6.3 Capital Allocation 130 7 Estimation of Frequency and Severity
Models 143 7.1 Frequentist Estimation 143 7.2 Bayesian Inference Approach
155 7.3 Mean Square Error of Prediction 160 7.4 Standard Markov Chain Monte
Carlo Methods. 161 7.5 Standard MCMC Guidelines for Implementation 174 7.6
Advanced Markov chain Monte Carlo Methods 182 7.7 Sequential Monte Carlo
Samplers and Importance Sampling 194 7.8 Approximate Bayesian Computation
(ABC) Methods 212 7.9 Modelling Truncated Data 215 8 Model Selection and
Goodness of Fit Testing 231 8.1 Qualitative Model Diagnostic Tools 231 8.2
Information Criterion for Model Selection 235 8.3 Goodness of Fit Testing
for Model Choice (How to Account for Heavy Tails!) 239 8.4 Bayesian Model
Selection 274 8.5 SMC Samplers Estimators of Model Evidence 276 8.6
Multiple Risk Dependence Structure Model Selection: Copula Choice 277 9
Flexible Parametric Severity Models: Basics 289 9.1 Motivation for Flexible
Parametric Severity Loss Models 289 9.2 Context of Flexible Heavy Tailed
Loss Models in OpRisk and Insurance LDA Models 290 9.3 Empirical Analysis
Justifying Heavy Tailed Loss Models in OpRisk 292 9.4 Flexible
Distributions for Severity Models in OpRisk 294 9.5 Quantile Function Heavy
Tailed Severity Models 294 9.6 Generalized Beta Family of Heavy Tailed
Severity Models 321 9.7 Generalized Hyperbolic Families of Heavy Tailed
Severity Models 328 9.8 Halphen Family of Flexible Severity Models: GIG and
Hyperbolic 338 10 Modelling Dependence 353 10.1 Dependence Modelling Within
and Between LDA Model Structures 353 10.2 General Notions of Dependence 358
10.3 Dependence Measures and Tail Dependence 364 10.4 Introduction to
Parametric Dependence Modeling Through a Copula 380 10.5 Copula Model
Families for OpRisk 387 10.6 Copula Parameter Estimation in Two Stages:
Inference For the Margins 416 10.7 Multiple Risk LDA Compound Poisson
Processes and Lévy Copula 420 10.8 Multiple Risk LDA: Dependence Between
Frequencies via Copula 425 10.9 Multiple Risk LDA: Dependence Between the
k-th Event Times/Losses 425 10.10 Multiple Risk LDA: Dependence Between
Aggregated Losses via Copula 430 10.11 Multiple Risk LDA: Structural Model
with Common Factors 432 10.12 Multiple Risk LDA: Stochastic and Dependent
Risk Profiles 434 10.13 Multiple Risk LDA: Dependence and Combining
Different Data Sources437 10.14 A Note on Negative Diversification and
Dependence Modelling 445 11 Loss Aggregation 447 11.1 Introduction 447 11.2
Analytic Solution 448 11.3 Monte Carlo Method 454 11.4 Panjer Recursion 457
11.5 Panjer Extensions 462 11.6 Fast Fourier Transform 463 11.7 Closed-Form
Approximation 466 11.8 Capital Charge Under Parameter Uncertainty 471 12
Scenario Analysis 477 12.1 Introduction 477 12.2 Examples of Expert
Judgements 480 12.3 Pure Bayesian Approach (Estimating Prior) 482 12.4
Expert Distribution and Scenario Elicitation: learning from Bayesian
methods 484 12.5 Building Models for Elicited Opinions: Heirarchical
Dirichlet Models 487 12.6 Worst Case Scenario Framework 489 12.7 Stress
Test Scenario Analysis 492 12.8 Bow-Tie Diagram 495 12.9 Bayesian Networks
497 12.10 Discussion 504 13 Combining Different Data Sources 507 13.1
Minimum variance principle 508 13.2 Bayesian Method to Combine Two Data
Sources 510 13.3 Estimation of the Prior Using Data 528 13.4 Combining
Expert Opinions with External and Internal Data 530 13.5 Combining Data
Sources Using Credibility Theory 546 13.6 Nonparametric Bayesian approach
via Dirichlet process 556 13.7 Combining using Dempster-Shafer structures
and p-boxes 558 13.8 General Remarks 567 14 Multifactor Modelling and
Regression for Loss Processes 571 14.1 Generalized Linear Model Regressions
and the Exponential Family 571 14.2 Maximum Likelihood Estimation for
Generalized Linear Models 573 14.3 Bayesian Generalized Linear Model
Regressions and Regularization Priors 576 14.4 Bayesian Estimation and
Model Selection via SMC Samplers 583 14.5 Illustrations of SMC Samplers
Model Estimation and Selection for Bayesian GLM Regressions 585 14.6
Introduction to Quantile Regression Methods for OpRisk 590 14.7 Factor
Modelling for Industry Data 597 14.8 Multifactor Modelling under EVT
Approach 599 15 Insurance and Risk Transfer: Products and Modelling 601
15.1 Motivation for Insurance and Risk Transfer in OpRisk 602 15.2
Fundamentals on Insurance Product Structures for OpRisk 604 15.3 Single
Peril Policy Products for OpRisk 609 15.4 Generic Insurance Product
Structures for OpRisk 611 15.5 Closed Form LDA Models with Insurance
Mitigations 621 16 Insurance and Risk Transfer: Pricing 663 16.1 Insurance
Linked Securities and Catastrophe Bonds for OpRisk 664 16.2 Basics of
Valuation of Insurance Linked Securities and Catastrophe Bonds for OpRisk
679 16.3 Applications of Pricing Insurance Linked Securities and
Catastrophe Bonds 709 16.4 Sidecars, Multiple Peril Baskets and Umbrellas
for OpRisk 726 16.5 Optimal Insurance Purchase Strategies for OpRisk
Insurance via Multiple Optimal Stopping Times 733 A. Miscellaneous
Definitions and List of Distributions 751 A.1 Indicator Function 751 A.2
Gamma Function 751 A.3 Discrete Distributions 752 A.4 Continuous
Distributions 753 Index 811
Risk-Based Capital Ratios for Banks 5 1.3 The Basic Indicator and
Standardized Approaches for OpRisk 9 1.4 The Advanced Measurement Approach
11 1.5 General Remarks and Book Structure 16 2 OpRisk Data and Governance
17 2.1 Introduction 17 2.2 OpRisk Taxonomy 18 2.3 The Elements of the
OpRisk Framework 25 2.4 Business Environment and Internal Control
Environment Factors (BEICFs) 29 2.5 External Databases 32 2.6 Scenario
Analysis 33 2.7 OpRisk Profile in Different Financial Sectors 36 2.8 Risk
Organization and Governance 43 3 Using OpRisk Data for Business Analysis 49
3.1 Cost Reduction Programs at Financial Firms 50 3.2 Using OpRisk Data to
Perform Business Analysis 54 3.3 The Risk of Losing Key Talents: OpRisk in
Human Resources 55 3.4 Systems Risks: OpRisk in Systems Development and
Transaction Processing 56 3.5 Conclusions 59 4 Stress Testing OpRisk
Capital and CCAR 61 4.1 The Need for Stressing OpRisk Capital Even Beyond
the 99.9% 61 4.2 Comprehensive Capital Review and Analysis (CCAR) 62 4.3
OpRisk and Stress Tests 68 4.4 OpRisk in CCAR in Practice 69 4.5 Reverse
Stress Test 75 4.6 Stressing OpRisk Multivariate Models 75 5 Basic
Probability Concepts in Loss Distribution Approach 79 5.1 Loss Distribution
Approach 79 5.2 Quantiles and Moments 84 5.3 Frequency Distributions 87 5.4
Severity Distributions 88 5.5 Convolutions and Characteristic Functions 93
5.6 Extreme Value Theory 95 6 Risk Measures and Capital Allocation 101 6.1
Development of Capital Accords Base I, II and III 102 6.2 Measures of Risk
105 6.3 Capital Allocation 130 7 Estimation of Frequency and Severity
Models 143 7.1 Frequentist Estimation 143 7.2 Bayesian Inference Approach
155 7.3 Mean Square Error of Prediction 160 7.4 Standard Markov Chain Monte
Carlo Methods. 161 7.5 Standard MCMC Guidelines for Implementation 174 7.6
Advanced Markov chain Monte Carlo Methods 182 7.7 Sequential Monte Carlo
Samplers and Importance Sampling 194 7.8 Approximate Bayesian Computation
(ABC) Methods 212 7.9 Modelling Truncated Data 215 8 Model Selection and
Goodness of Fit Testing 231 8.1 Qualitative Model Diagnostic Tools 231 8.2
Information Criterion for Model Selection 235 8.3 Goodness of Fit Testing
for Model Choice (How to Account for Heavy Tails!) 239 8.4 Bayesian Model
Selection 274 8.5 SMC Samplers Estimators of Model Evidence 276 8.6
Multiple Risk Dependence Structure Model Selection: Copula Choice 277 9
Flexible Parametric Severity Models: Basics 289 9.1 Motivation for Flexible
Parametric Severity Loss Models 289 9.2 Context of Flexible Heavy Tailed
Loss Models in OpRisk and Insurance LDA Models 290 9.3 Empirical Analysis
Justifying Heavy Tailed Loss Models in OpRisk 292 9.4 Flexible
Distributions for Severity Models in OpRisk 294 9.5 Quantile Function Heavy
Tailed Severity Models 294 9.6 Generalized Beta Family of Heavy Tailed
Severity Models 321 9.7 Generalized Hyperbolic Families of Heavy Tailed
Severity Models 328 9.8 Halphen Family of Flexible Severity Models: GIG and
Hyperbolic 338 10 Modelling Dependence 353 10.1 Dependence Modelling Within
and Between LDA Model Structures 353 10.2 General Notions of Dependence 358
10.3 Dependence Measures and Tail Dependence 364 10.4 Introduction to
Parametric Dependence Modeling Through a Copula 380 10.5 Copula Model
Families for OpRisk 387 10.6 Copula Parameter Estimation in Two Stages:
Inference For the Margins 416 10.7 Multiple Risk LDA Compound Poisson
Processes and Lévy Copula 420 10.8 Multiple Risk LDA: Dependence Between
Frequencies via Copula 425 10.9 Multiple Risk LDA: Dependence Between the
k-th Event Times/Losses 425 10.10 Multiple Risk LDA: Dependence Between
Aggregated Losses via Copula 430 10.11 Multiple Risk LDA: Structural Model
with Common Factors 432 10.12 Multiple Risk LDA: Stochastic and Dependent
Risk Profiles 434 10.13 Multiple Risk LDA: Dependence and Combining
Different Data Sources437 10.14 A Note on Negative Diversification and
Dependence Modelling 445 11 Loss Aggregation 447 11.1 Introduction 447 11.2
Analytic Solution 448 11.3 Monte Carlo Method 454 11.4 Panjer Recursion 457
11.5 Panjer Extensions 462 11.6 Fast Fourier Transform 463 11.7 Closed-Form
Approximation 466 11.8 Capital Charge Under Parameter Uncertainty 471 12
Scenario Analysis 477 12.1 Introduction 477 12.2 Examples of Expert
Judgements 480 12.3 Pure Bayesian Approach (Estimating Prior) 482 12.4
Expert Distribution and Scenario Elicitation: learning from Bayesian
methods 484 12.5 Building Models for Elicited Opinions: Heirarchical
Dirichlet Models 487 12.6 Worst Case Scenario Framework 489 12.7 Stress
Test Scenario Analysis 492 12.8 Bow-Tie Diagram 495 12.9 Bayesian Networks
497 12.10 Discussion 504 13 Combining Different Data Sources 507 13.1
Minimum variance principle 508 13.2 Bayesian Method to Combine Two Data
Sources 510 13.3 Estimation of the Prior Using Data 528 13.4 Combining
Expert Opinions with External and Internal Data 530 13.5 Combining Data
Sources Using Credibility Theory 546 13.6 Nonparametric Bayesian approach
via Dirichlet process 556 13.7 Combining using Dempster-Shafer structures
and p-boxes 558 13.8 General Remarks 567 14 Multifactor Modelling and
Regression for Loss Processes 571 14.1 Generalized Linear Model Regressions
and the Exponential Family 571 14.2 Maximum Likelihood Estimation for
Generalized Linear Models 573 14.3 Bayesian Generalized Linear Model
Regressions and Regularization Priors 576 14.4 Bayesian Estimation and
Model Selection via SMC Samplers 583 14.5 Illustrations of SMC Samplers
Model Estimation and Selection for Bayesian GLM Regressions 585 14.6
Introduction to Quantile Regression Methods for OpRisk 590 14.7 Factor
Modelling for Industry Data 597 14.8 Multifactor Modelling under EVT
Approach 599 15 Insurance and Risk Transfer: Products and Modelling 601
15.1 Motivation for Insurance and Risk Transfer in OpRisk 602 15.2
Fundamentals on Insurance Product Structures for OpRisk 604 15.3 Single
Peril Policy Products for OpRisk 609 15.4 Generic Insurance Product
Structures for OpRisk 611 15.5 Closed Form LDA Models with Insurance
Mitigations 621 16 Insurance and Risk Transfer: Pricing 663 16.1 Insurance
Linked Securities and Catastrophe Bonds for OpRisk 664 16.2 Basics of
Valuation of Insurance Linked Securities and Catastrophe Bonds for OpRisk
679 16.3 Applications of Pricing Insurance Linked Securities and
Catastrophe Bonds 709 16.4 Sidecars, Multiple Peril Baskets and Umbrellas
for OpRisk 726 16.5 Optimal Insurance Purchase Strategies for OpRisk
Insurance via Multiple Optimal Stopping Times 733 A. Miscellaneous
Definitions and List of Distributions 751 A.1 Indicator Function 751 A.2
Gamma Function 751 A.3 Discrete Distributions 752 A.4 Continuous
Distributions 753 Index 811
Preface xxi Acronyms xxv 1 OpRisk in Perspective 1 1.1 Brief History 1 1.2
Risk-Based Capital Ratios for Banks 5 1.3 The Basic Indicator and
Standardized Approaches for OpRisk 9 1.4 The Advanced Measurement Approach
11 1.5 General Remarks and Book Structure 16 2 OpRisk Data and Governance
17 2.1 Introduction 17 2.2 OpRisk Taxonomy 18 2.3 The Elements of the
OpRisk Framework 25 2.4 Business Environment and Internal Control
Environment Factors (BEICFs) 29 2.5 External Databases 32 2.6 Scenario
Analysis 33 2.7 OpRisk Profile in Different Financial Sectors 36 2.8 Risk
Organization and Governance 43 3 Using OpRisk Data for Business Analysis 49
3.1 Cost Reduction Programs at Financial Firms 50 3.2 Using OpRisk Data to
Perform Business Analysis 54 3.3 The Risk of Losing Key Talents: OpRisk in
Human Resources 55 3.4 Systems Risks: OpRisk in Systems Development and
Transaction Processing 56 3.5 Conclusions 59 4 Stress Testing OpRisk
Capital and CCAR 61 4.1 The Need for Stressing OpRisk Capital Even Beyond
the 99.9% 61 4.2 Comprehensive Capital Review and Analysis (CCAR) 62 4.3
OpRisk and Stress Tests 68 4.4 OpRisk in CCAR in Practice 69 4.5 Reverse
Stress Test 75 4.6 Stressing OpRisk Multivariate Models 75 5 Basic
Probability Concepts in Loss Distribution Approach 79 5.1 Loss Distribution
Approach 79 5.2 Quantiles and Moments 84 5.3 Frequency Distributions 87 5.4
Severity Distributions 88 5.5 Convolutions and Characteristic Functions 93
5.6 Extreme Value Theory 95 6 Risk Measures and Capital Allocation 101 6.1
Development of Capital Accords Base I, II and III 102 6.2 Measures of Risk
105 6.3 Capital Allocation 130 7 Estimation of Frequency and Severity
Models 143 7.1 Frequentist Estimation 143 7.2 Bayesian Inference Approach
155 7.3 Mean Square Error of Prediction 160 7.4 Standard Markov Chain Monte
Carlo Methods. 161 7.5 Standard MCMC Guidelines for Implementation 174 7.6
Advanced Markov chain Monte Carlo Methods 182 7.7 Sequential Monte Carlo
Samplers and Importance Sampling 194 7.8 Approximate Bayesian Computation
(ABC) Methods 212 7.9 Modelling Truncated Data 215 8 Model Selection and
Goodness of Fit Testing 231 8.1 Qualitative Model Diagnostic Tools 231 8.2
Information Criterion for Model Selection 235 8.3 Goodness of Fit Testing
for Model Choice (How to Account for Heavy Tails!) 239 8.4 Bayesian Model
Selection 274 8.5 SMC Samplers Estimators of Model Evidence 276 8.6
Multiple Risk Dependence Structure Model Selection: Copula Choice 277 9
Flexible Parametric Severity Models: Basics 289 9.1 Motivation for Flexible
Parametric Severity Loss Models 289 9.2 Context of Flexible Heavy Tailed
Loss Models in OpRisk and Insurance LDA Models 290 9.3 Empirical Analysis
Justifying Heavy Tailed Loss Models in OpRisk 292 9.4 Flexible
Distributions for Severity Models in OpRisk 294 9.5 Quantile Function Heavy
Tailed Severity Models 294 9.6 Generalized Beta Family of Heavy Tailed
Severity Models 321 9.7 Generalized Hyperbolic Families of Heavy Tailed
Severity Models 328 9.8 Halphen Family of Flexible Severity Models: GIG and
Hyperbolic 338 10 Modelling Dependence 353 10.1 Dependence Modelling Within
and Between LDA Model Structures 353 10.2 General Notions of Dependence 358
10.3 Dependence Measures and Tail Dependence 364 10.4 Introduction to
Parametric Dependence Modeling Through a Copula 380 10.5 Copula Model
Families for OpRisk 387 10.6 Copula Parameter Estimation in Two Stages:
Inference For the Margins 416 10.7 Multiple Risk LDA Compound Poisson
Processes and Lévy Copula 420 10.8 Multiple Risk LDA: Dependence Between
Frequencies via Copula 425 10.9 Multiple Risk LDA: Dependence Between the
k-th Event Times/Losses 425 10.10 Multiple Risk LDA: Dependence Between
Aggregated Losses via Copula 430 10.11 Multiple Risk LDA: Structural Model
with Common Factors 432 10.12 Multiple Risk LDA: Stochastic and Dependent
Risk Profiles 434 10.13 Multiple Risk LDA: Dependence and Combining
Different Data Sources437 10.14 A Note on Negative Diversification and
Dependence Modelling 445 11 Loss Aggregation 447 11.1 Introduction 447 11.2
Analytic Solution 448 11.3 Monte Carlo Method 454 11.4 Panjer Recursion 457
11.5 Panjer Extensions 462 11.6 Fast Fourier Transform 463 11.7 Closed-Form
Approximation 466 11.8 Capital Charge Under Parameter Uncertainty 471 12
Scenario Analysis 477 12.1 Introduction 477 12.2 Examples of Expert
Judgements 480 12.3 Pure Bayesian Approach (Estimating Prior) 482 12.4
Expert Distribution and Scenario Elicitation: learning from Bayesian
methods 484 12.5 Building Models for Elicited Opinions: Heirarchical
Dirichlet Models 487 12.6 Worst Case Scenario Framework 489 12.7 Stress
Test Scenario Analysis 492 12.8 Bow-Tie Diagram 495 12.9 Bayesian Networks
497 12.10 Discussion 504 13 Combining Different Data Sources 507 13.1
Minimum variance principle 508 13.2 Bayesian Method to Combine Two Data
Sources 510 13.3 Estimation of the Prior Using Data 528 13.4 Combining
Expert Opinions with External and Internal Data 530 13.5 Combining Data
Sources Using Credibility Theory 546 13.6 Nonparametric Bayesian approach
via Dirichlet process 556 13.7 Combining using Dempster-Shafer structures
and p-boxes 558 13.8 General Remarks 567 14 Multifactor Modelling and
Regression for Loss Processes 571 14.1 Generalized Linear Model Regressions
and the Exponential Family 571 14.2 Maximum Likelihood Estimation for
Generalized Linear Models 573 14.3 Bayesian Generalized Linear Model
Regressions and Regularization Priors 576 14.4 Bayesian Estimation and
Model Selection via SMC Samplers 583 14.5 Illustrations of SMC Samplers
Model Estimation and Selection for Bayesian GLM Regressions 585 14.6
Introduction to Quantile Regression Methods for OpRisk 590 14.7 Factor
Modelling for Industry Data 597 14.8 Multifactor Modelling under EVT
Approach 599 15 Insurance and Risk Transfer: Products and Modelling 601
15.1 Motivation for Insurance and Risk Transfer in OpRisk 602 15.2
Fundamentals on Insurance Product Structures for OpRisk 604 15.3 Single
Peril Policy Products for OpRisk 609 15.4 Generic Insurance Product
Structures for OpRisk 611 15.5 Closed Form LDA Models with Insurance
Mitigations 621 16 Insurance and Risk Transfer: Pricing 663 16.1 Insurance
Linked Securities and Catastrophe Bonds for OpRisk 664 16.2 Basics of
Valuation of Insurance Linked Securities and Catastrophe Bonds for OpRisk
679 16.3 Applications of Pricing Insurance Linked Securities and
Catastrophe Bonds 709 16.4 Sidecars, Multiple Peril Baskets and Umbrellas
for OpRisk 726 16.5 Optimal Insurance Purchase Strategies for OpRisk
Insurance via Multiple Optimal Stopping Times 733 A. Miscellaneous
Definitions and List of Distributions 751 A.1 Indicator Function 751 A.2
Gamma Function 751 A.3 Discrete Distributions 752 A.4 Continuous
Distributions 753 Index 811
Risk-Based Capital Ratios for Banks 5 1.3 The Basic Indicator and
Standardized Approaches for OpRisk 9 1.4 The Advanced Measurement Approach
11 1.5 General Remarks and Book Structure 16 2 OpRisk Data and Governance
17 2.1 Introduction 17 2.2 OpRisk Taxonomy 18 2.3 The Elements of the
OpRisk Framework 25 2.4 Business Environment and Internal Control
Environment Factors (BEICFs) 29 2.5 External Databases 32 2.6 Scenario
Analysis 33 2.7 OpRisk Profile in Different Financial Sectors 36 2.8 Risk
Organization and Governance 43 3 Using OpRisk Data for Business Analysis 49
3.1 Cost Reduction Programs at Financial Firms 50 3.2 Using OpRisk Data to
Perform Business Analysis 54 3.3 The Risk of Losing Key Talents: OpRisk in
Human Resources 55 3.4 Systems Risks: OpRisk in Systems Development and
Transaction Processing 56 3.5 Conclusions 59 4 Stress Testing OpRisk
Capital and CCAR 61 4.1 The Need for Stressing OpRisk Capital Even Beyond
the 99.9% 61 4.2 Comprehensive Capital Review and Analysis (CCAR) 62 4.3
OpRisk and Stress Tests 68 4.4 OpRisk in CCAR in Practice 69 4.5 Reverse
Stress Test 75 4.6 Stressing OpRisk Multivariate Models 75 5 Basic
Probability Concepts in Loss Distribution Approach 79 5.1 Loss Distribution
Approach 79 5.2 Quantiles and Moments 84 5.3 Frequency Distributions 87 5.4
Severity Distributions 88 5.5 Convolutions and Characteristic Functions 93
5.6 Extreme Value Theory 95 6 Risk Measures and Capital Allocation 101 6.1
Development of Capital Accords Base I, II and III 102 6.2 Measures of Risk
105 6.3 Capital Allocation 130 7 Estimation of Frequency and Severity
Models 143 7.1 Frequentist Estimation 143 7.2 Bayesian Inference Approach
155 7.3 Mean Square Error of Prediction 160 7.4 Standard Markov Chain Monte
Carlo Methods. 161 7.5 Standard MCMC Guidelines for Implementation 174 7.6
Advanced Markov chain Monte Carlo Methods 182 7.7 Sequential Monte Carlo
Samplers and Importance Sampling 194 7.8 Approximate Bayesian Computation
(ABC) Methods 212 7.9 Modelling Truncated Data 215 8 Model Selection and
Goodness of Fit Testing 231 8.1 Qualitative Model Diagnostic Tools 231 8.2
Information Criterion for Model Selection 235 8.3 Goodness of Fit Testing
for Model Choice (How to Account for Heavy Tails!) 239 8.4 Bayesian Model
Selection 274 8.5 SMC Samplers Estimators of Model Evidence 276 8.6
Multiple Risk Dependence Structure Model Selection: Copula Choice 277 9
Flexible Parametric Severity Models: Basics 289 9.1 Motivation for Flexible
Parametric Severity Loss Models 289 9.2 Context of Flexible Heavy Tailed
Loss Models in OpRisk and Insurance LDA Models 290 9.3 Empirical Analysis
Justifying Heavy Tailed Loss Models in OpRisk 292 9.4 Flexible
Distributions for Severity Models in OpRisk 294 9.5 Quantile Function Heavy
Tailed Severity Models 294 9.6 Generalized Beta Family of Heavy Tailed
Severity Models 321 9.7 Generalized Hyperbolic Families of Heavy Tailed
Severity Models 328 9.8 Halphen Family of Flexible Severity Models: GIG and
Hyperbolic 338 10 Modelling Dependence 353 10.1 Dependence Modelling Within
and Between LDA Model Structures 353 10.2 General Notions of Dependence 358
10.3 Dependence Measures and Tail Dependence 364 10.4 Introduction to
Parametric Dependence Modeling Through a Copula 380 10.5 Copula Model
Families for OpRisk 387 10.6 Copula Parameter Estimation in Two Stages:
Inference For the Margins 416 10.7 Multiple Risk LDA Compound Poisson
Processes and Lévy Copula 420 10.8 Multiple Risk LDA: Dependence Between
Frequencies via Copula 425 10.9 Multiple Risk LDA: Dependence Between the
k-th Event Times/Losses 425 10.10 Multiple Risk LDA: Dependence Between
Aggregated Losses via Copula 430 10.11 Multiple Risk LDA: Structural Model
with Common Factors 432 10.12 Multiple Risk LDA: Stochastic and Dependent
Risk Profiles 434 10.13 Multiple Risk LDA: Dependence and Combining
Different Data Sources437 10.14 A Note on Negative Diversification and
Dependence Modelling 445 11 Loss Aggregation 447 11.1 Introduction 447 11.2
Analytic Solution 448 11.3 Monte Carlo Method 454 11.4 Panjer Recursion 457
11.5 Panjer Extensions 462 11.6 Fast Fourier Transform 463 11.7 Closed-Form
Approximation 466 11.8 Capital Charge Under Parameter Uncertainty 471 12
Scenario Analysis 477 12.1 Introduction 477 12.2 Examples of Expert
Judgements 480 12.3 Pure Bayesian Approach (Estimating Prior) 482 12.4
Expert Distribution and Scenario Elicitation: learning from Bayesian
methods 484 12.5 Building Models for Elicited Opinions: Heirarchical
Dirichlet Models 487 12.6 Worst Case Scenario Framework 489 12.7 Stress
Test Scenario Analysis 492 12.8 Bow-Tie Diagram 495 12.9 Bayesian Networks
497 12.10 Discussion 504 13 Combining Different Data Sources 507 13.1
Minimum variance principle 508 13.2 Bayesian Method to Combine Two Data
Sources 510 13.3 Estimation of the Prior Using Data 528 13.4 Combining
Expert Opinions with External and Internal Data 530 13.5 Combining Data
Sources Using Credibility Theory 546 13.6 Nonparametric Bayesian approach
via Dirichlet process 556 13.7 Combining using Dempster-Shafer structures
and p-boxes 558 13.8 General Remarks 567 14 Multifactor Modelling and
Regression for Loss Processes 571 14.1 Generalized Linear Model Regressions
and the Exponential Family 571 14.2 Maximum Likelihood Estimation for
Generalized Linear Models 573 14.3 Bayesian Generalized Linear Model
Regressions and Regularization Priors 576 14.4 Bayesian Estimation and
Model Selection via SMC Samplers 583 14.5 Illustrations of SMC Samplers
Model Estimation and Selection for Bayesian GLM Regressions 585 14.6
Introduction to Quantile Regression Methods for OpRisk 590 14.7 Factor
Modelling for Industry Data 597 14.8 Multifactor Modelling under EVT
Approach 599 15 Insurance and Risk Transfer: Products and Modelling 601
15.1 Motivation for Insurance and Risk Transfer in OpRisk 602 15.2
Fundamentals on Insurance Product Structures for OpRisk 604 15.3 Single
Peril Policy Products for OpRisk 609 15.4 Generic Insurance Product
Structures for OpRisk 611 15.5 Closed Form LDA Models with Insurance
Mitigations 621 16 Insurance and Risk Transfer: Pricing 663 16.1 Insurance
Linked Securities and Catastrophe Bonds for OpRisk 664 16.2 Basics of
Valuation of Insurance Linked Securities and Catastrophe Bonds for OpRisk
679 16.3 Applications of Pricing Insurance Linked Securities and
Catastrophe Bonds 709 16.4 Sidecars, Multiple Peril Baskets and Umbrellas
for OpRisk 726 16.5 Optimal Insurance Purchase Strategies for OpRisk
Insurance via Multiple Optimal Stopping Times 733 A. Miscellaneous
Definitions and List of Distributions 751 A.1 Indicator Function 751 A.2
Gamma Function 751 A.3 Discrete Distributions 752 A.4 Continuous
Distributions 753 Index 811