Fundamental aspects of operational risk and insurance analytics : a handbook of operational risk

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 of...

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Bibliographic Details
Main Authors Cruz, Marcelo G, Peters, Gareth W., Shevchenko, Pavel V
Format eBook Book
LanguageEnglish
Published Hoboken, N.J Wiley 2015
John Wiley & Sons, Incorporated
Wiley-Blackwell
John Wiley & Sons, Inc
Edition1
SeriesWiley handbooks in financial engineering and econometrics
Subjects
MATHEMATICS / Probability & Statistics / General
Operational risk
Operationelles Risiko
Risk management
Online AccessGet full text

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Table of Contents:
  • 7.9.3 Ignoring Data Truncation -- 7.9.4 Threshold Varying in Time -- 7.9.5 Unknown and Stochastic Truncation Level -- Chapter Eight Model Selection and Goodness-of-Fit Testing for Frequency and Severity Models -- 8.1 Qualitative Model Diagnostic Tools -- 8.2 Tail Diagnostics -- 8.3 Information Criterion for Model Selection -- 8.3.1 Akaike Information Criterion for LDA Model Selection -- 8.3.2 Deviance Information Criterion -- 8.4 Goodness-of-Fit Testing for Model Choice (How to Account for Heavy Tails!) -- 8.4.1 Convergence Results of the Empirical Process for GOF Testing -- 8.4.2 Overview of Generic GOF Tests-Omnibus Distributional Tests -- 8.4.3 Kolmogorov-Smirnov Goodness-of-Fit Test and Weighted Variants: Testing in the Presence of Heavy Tails -- 8.4.4 Cramer-von-Mises Goodness-of-Fit Tests and Weighted Variants: Testing in the Presence of Heavy Tails -- 8.5 Bayesian Model Selection -- 8.5.1 Reciprocal Importance Sampling Estimator -- 8.5.2 Chib Estimator for Model Evidence -- 8.6 SMC Sampler Estimators of Model Evidence -- 8.7 Multiple Risk Dependence Structure Model Selection: Copula Choice -- 8.7.1 Approaches to Goodness-of-Fit Testing for Dependence Structures -- 8.7.2 Double Parameteric Bootstrap for Copula GOF -- Chapter Nine Flexible Parametric Severity Models: Basics -- 9.1 Motivation for Flexible Parametric Severity Loss Models -- 9.2 Context of Flexible Heavy-Tailed Loss Models in OpRisk and Insurance LDA Models -- 9.3 Empirical Analysis Justifying Heavy-Tailed Loss Models in OpRisk -- 9.4 Quantile Function Heavy-Tailed Severity Models -- 9.4.1 g-and-h Severity Model Family in OpRisk -- 9.4.2 Tail Properties of the g-and-h, g, h, and h-h Severity in OpRisk -- 9.4.3 Parameter Estimation for the g-and-h Severity in OpRisk -- 9.4.4 Bayesian Models for the g-and-h Severity in OpRisk
  • 9.5 Generalized Beta Family of Heavy-Tailed Severity Models -- 9.5.1 Generalized Beta Family Type II Severity Models in OpRisk -- 9.5.2 Sub families of the Generalized Beta Family Type II Severity Models -- 9.5.3 Mixture Representations of the Generalized Beta Family Type II Severity Models -- 9.5.4 Estimation in the Generalized Beta Family Type II Severity Models -- 9.6 Generalized Hyperbolic Families of Heavy-Tailed Severity Models -- 9.6.1 Tail Properties and Infinite Divisibility of the Generalized Hyperbolic Severity Models -- 9.6.2 Subfamilies of the Generalized Hyperbolic Severity Models -- 9.6.3 Normal Inverse Gaussian Family of Heavy-Tailed Severity Models -- 9.7 Halphen Family of Flexible Severity Models: GIG and Hyperbolic -- 9.7.1 Halphen Type A: Generalized Inverse Gaussian Family of Flexible Severity Models -- 9.7.2 Halphen Type B and IB Families of Flexible Severity Models -- Chapter Ten Dependence Concepts -- 10.1 Introduction to Concepts in Dependence for OpRisk and Insurance -- 10.2 Dependence Modeling Within and Between LDA Model Structures -- 10.2.1 Where Can One Introduce Dependence Between LDA Model Structures? -- 10.2.2 Understanding Basic Impacts of Dependence Modeling Between LDA Components in Multiple Risks -- 10.3 General Notions of Dependence -- 10.4 Dependence Measures -- 10.4.1 Linear Correlation -- 10.4.2 Rank Correlation Measures -- 10.5 Tail Dependence Parameters, Functions, and Tail Order Functions -- 10.5.1 Tail Dependence Coefficients -- 10.5.2 Tail Dependence Functions and Orders -- 10.5.3 A Link Between Orthant Extreme Dependence and Spectral Measures: Tail Dependence -- Chapter Eleven Dependence Models -- 11.1 Introduction to Parametric Dependence Modeling Through a Copula -- 11.2 Copula Model Families for OpRisk -- 11.2.1 Gaussian Copula -- 11.2.2 t-Copula -- 11.2.3 Archimedean Copulas
  • Intro -- Title Page -- Copyright Page -- Contents -- Preface -- Acronyms -- List of Distributions -- Chapter One OpRisk in Perspective -- 1.1 Brief History -- 1.2 Risk-Based Capital Ratios for Banks -- 1.3 The Basic Indicator and Standardized Approaches for OpRisk -- 1.4 The Advanced Measurement Approach -- 1.4.1 Internal Measurement Approach -- 1.4.2 Score Card Approach -- 1.4.3 Loss Distribution Approach -- 1.4.4 Requirements for AMA -- 1.5 General Remarks and Book Structure -- Chapter Two OpRisk Data and Governance -- 2.1 Introduction -- 2.2 OpRisk Taxonomy -- 2.2.1 Execution, Delivery, and Process Management -- 2.2.2 Clients, Products, and Business Practices -- 2.2.3 Business Disruption and System Failures -- 2.2.4 External Frauds -- 2.2.5 Internal Fraud -- 2.2.6 Employment Practices and Workplace Safety -- 2.2.7 Damage to Physical Assets -- 2.3 The Elements of the OpRisk Framework -- 2.3.1 Internal Loss Data -- 2.3.2 Setting a Collection Threshold and Possible Impacts -- 2.3.3 Completeness of Database (Under-reporting Events) -- 2.3.4 Recoveries and Near Misses -- 2.3.5 Time Period for Resolution of Operational Losses -- 2.3.6 Adding Costs to Losses -- 2.3.7 Provisioning Treatment of Expected Operational Losses -- 2.4 Business Environment and Internal Control Environment Factors (BEICFs) -- 2.4.1 Risk Control Self-Assessment (RCSA) -- 2.4.2 Key Risk Indicators -- 2.5 External Databases -- 2.6 Scenario Analysis -- 2.7 OpRisk Profile in Different Financial Sectors -- 2.7.1 Trading and Sales -- 2.7.2 Corporate Finance -- 2.7.3 Retail Banking -- 2.7.4 Insurance -- 2.7.5 Asset Management -- 2.7.6 Retail Brokerage -- 2.8 Risk Organization and Governance -- 2.8.1 Organization of Risk Departments -- 2.8.2 Structuring a Firm Wide Policy: Example of an OpRisk Policy -- 2.8.3 Governance -- Chapter Three Using OpRisk Data for Business Analysis
  • 11.2.4 Archimedean Copula Generators and the Laplace Transform of a Non-Negative Random Variable
  • 6.3.7 Numerical Example -- Chapter Seven Estimation of Frequency and Severity Models -- 7.1 Frequentist Estimation -- 7.1.1 Parameteric Maximum Likelihood Method -- 7.1.2 Maximum Likelihood Method for Truncated and Censored Data -- 7.1.3 Expectation Maximization and Parameter Estimation -- 7.1.4 Bootstrap for Estimation of Parameter Accuracy -- 7.1.5 Indirect Inference-Based Likelihood Estimation -- 7.2 Bayesian Inference Approach -- 7.2.1 Conjugate Prior Distributions -- 7.2.2 Gaussian Approximation for Posterior (Laplace Type) -- 7.2.3 Posterior Point Estimators -- 7.2.4 Restricted Parameters -- 7.2.5 Noninformative Prior -- 7.3 Mean Square Error of Prediction -- 7.4 Standard Markov Chain Monte Carlo (MCMC) Methods -- 7.4.1 Motivation for Markov Chain Methods -- 7.4.2 Metropolis-Hastings Algorithm -- 7.4.3 Gibbs Sampler -- 7.4.4 Random Walk Metropolis-Hastings within Gibbs -- 7.5 Standard MCMC Guidelines for Implementation -- 7.5.1 Tuning, Burn-in, and Sampling Stages -- 7.5.2 Numerical Error -- 7.5.3 MCMC Extensions: Reducing Sample Autocorrelation -- 7.6 Advanced MCMC Methods -- 7.6.1 Auxiliary Variable MCMC Methods: Slice Sampling -- 7.6.2 Generic Univariate Auxiliary Variable Gibbs Sampler: Slice Sampler -- 7.6.3 Adaptive MCMC -- 7.6.4 Riemann-Manifold Hamiltonian Monte Carlo Sampler (Automated Local Adaption) -- 7.7 Sequential Monte Carlo (SMC) Samplers and Importance Sampling -- 7.7.1 Motivating OpRisk Applications for SMC Samplers -- 7.7.2 SMC Sampler Methodology and Components -- 7.7.3 Incorporating Partial Rejection Control into SMC Samplers -- 7.7.4 Finite Sample (Nonasymptotic) Accuracy for Particle Integration -- 7.8 Approximate Bayesian Computation (ABC) Methods -- 7.9 OpRisk Estimation and Modeling for Truncated Data -- 7.9.1 Constant Threshold - Poisson Process -- 7.9.2 Negative Binomial and Binomial Frequencies
  • 3.1 Cost Reduction Programs in Financial Firms -- 3.2 Using OpRisk Data to Perform Business Analysis -- 3.2.1 The Risk of Losing Key Talents: OpRisk in Human Resources -- 3.2.2 OpRisk in Systems Development and Transaction Processing -- 3.3 Conclusions -- Chapter Four Stress-Testing OpRisk Capital and the Comprehensive Capital Analysis and Review (CCAR) -- 4.1 The Need for Stressing OpRisk Capital Even Beyond 99.9% -- 4.2 Comprehensive Capital Review and Analysis (CCAR) -- 4.3 OpRisk and Stress Tests -- 4.4 OpRisk in CCAR in Practice -- 4.5 Reverse Stress Test -- 4.6 Stressing OpRisk Multivariate Models-Understanding the Relationship Among Internal Control Factors and Their Impact on Operation -- Chapter Five Basic Probability Concepts in Loss Distribution Approach -- 5.1 Loss Distribution Approach -- 5.2 Quantiles and Moments -- 5.3 Frequency Distributions -- 5.4 Severity Distributions -- 5.4.1 Simple Parametric Distributions -- 5.4.2 Truncated Distributions -- 5.4.3 Mixture and Spliced Distributions -- 5.5 Convolutions and Characteristic Functions -- 5.6 Extreme Value Theory -- 5.6.1 EVT-Block Maxima -- 5.6.2 EVT-Random Number of Losses -- 5.6.3 EVT-Threshold Exceedances -- Chapter Six Risk Measures and Capital Allocation -- 6.1 Development of Capital Accords Base I, II and III -- 6.2 Measures of Risk -- 6.2.1 Coherent and Convex Risk Measures -- 6.2.2 Comonotonic Additive Risk Measures -- 6.2.3 Value-at-Risk -- 6.2.4 Expected Shortfall -- 6.2.5 Spectral Risk Measure -- 6.2.6 Higher-Order Risk Measures -- 6.2.7 Distortion Risk Measures -- 6.2.8 Elicitable Risk Measures -- 6.2.9 Risk Measure Accounting for Parameter Uncertainty -- 6.3 Capital Allocation -- 6.3.1 Coherent Capital Allocation -- 6.3.2 Euler Allocation -- 6.3.3 Standard Deviation -- 6.3.4 Expected Shortfall -- 6.3.5 Value-at-Risk -- 6.3.6 Allocation by Marginal Contributions
  • 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 Levy 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 --
  • Sources 437 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.
  • Machine generated contents note: 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 --