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Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

by Pavel V. Shevchenko, Gareth W. Peters, Marcelo G. Cruz

February 2015

Beginner

928 pages

33h 17m

English

Wiley

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Cover
Title page
Copyright page
Dedication page
Preface
Acronyms
List of Distributions
Chapter One: OpRisk in Perspective
1.1 Brief History1.2 Risk-Based Capital Ratios for Banks1.3 The Basic Indicator and Standardized Approaches for OpRisk1.4 The Advanced Measurement Approach1.5 General Remarks and Book Structure
Chapter Two: OpRisk Data and Governance
2.1 Introduction2.2 OpRisk Taxonomy2.3 The Elements of the OpRisk Framework2.4 Business Environment and Internal Control Environment Factors (BEICFs)2.5 External Databases2.6 Scenario Analysis2.7 OpRisk Profile in Different Financial Sectors2.8 Risk Organization and Governance
Chapter Three: Using OpRisk Data for Business Analysis
3.1 Cost Reduction Programs in Financial Firms3.2 Using OpRisk Data to Perform Business Analysis3.3 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 Tests4.4 OpRisk in CCAR in Practice4.5 Reverse Stress Test4.6 Stressing OpRisk Multivariate Models—Understanding the Relationship Among Internal Control Factors and Their Impact on Operational Losses
Chapter Five: Basic Probability Concepts in Loss Distribution Approach
5.1 Loss Distribution Approach5.2 Quantiles and Moments5.3 Frequency Distributions5.4 Severity Distributions5.5 Convolutions and Characteristic Functions5.6 Extreme Value Theory
Chapter Six: Risk Measures and Capital Allocation
6.1 Development of Capital Accords Base I, II and III6.2 Measures of Risk6.3 Capital Allocation
Chapter Seven: Estimation of Frequency and Severity Models
7.1 Frequentist Estimation7.2 Bayesian Inference Approach7.3 Mean Square Error of Prediction7.4 Standard Markov Chain Monte Carlo (MCMC) Methods
7.5 Standard MCMC Guidelines for Implementation
7.6 Advanced MCMC Methods7.7 Sequential Monte Carlo (SMC) Samplers and Importance Sampling
7.8 Approximate Bayesian Computation (ABC) Methods
7.9 OpRisk Estimation and Modeling for Truncated Data
Chapter Eight: Model Selection and Goodness-of-Fit Testing for Frequency and Severity Models
8.1 Qualitative Model Diagnostic Tools8.2 Tail Diagnostics8.3 Information Criterion for Model Selection8.4 Goodness-of-Fit Testing for Model Choice (How to Account for Heavy Tails!)
8.5 Bayesian Model Selection
8.6 SMC Sampler Estimators of Model Evidence8.7 Multiple Risk Dependence Structure Model Selection: Copula Choice
Chapter Nine: Flexible Parametric Severity Models
9.1 Motivation for Flexible Parametric Severity Loss Models9.2 Context of Flexible Heavy-Tailed Loss Models in OpRisk and Insurance LDA Models9.3 Empirical Analysis Justifying Heavy-Tailed Loss Models in OpRisk9.4 Quantile Function Heavy-Tailed Severity Models
9.5 Generalized Beta Family of Heavy-Tailed Severity Models
9.6 Generalized Hyperbolic Families of Heavy-Tailed Severity Models
9.7 Halphen Family of Flexible Severity Models: GIG and Hyperbolic
Chapter Ten: Dependence Concepts
10.1 Introduction to Concepts in Dependence for OpRisk and Insurance10.2 Dependence Modeling Within and Between LDA Model Structures10.3 General Notions of Dependence10.4 Dependence Measures
10.5 Tail Dependence Parameters, Functions, and Tail Order Functions
Chapter Eleven: Dependence Models
11.1 Introduction to Parametric Dependence Modeling Through a Copula11.2 Copula Model Families for OpRisk
11.3 Copula Parameter Estimation in Two Stages: Inference for the Margins
Chapter Twelve: Examples of LDA Dependence Models
12.1 Multiple Risk LDA Compound Poisson Processes and Lévy Copula12.2 Multiple Risk LDA: Dependence Between Frequencies via Copula12.3 Multiple Risk LDA: Dependence Between the k-th Event Times/Losses12.4 Multiple Risk LDA: Dependence Between Aggregated Losses via Copula12.5 Multiple Risk LDA: Structural Model with Common Factors12.6 Multiple Risk LDA: Stochastic and Dependent Risk Profiles12.7 Multiple Risk LDA: Dependence and Combining Different Data Sources12.8 A Note on Negative Diversification and Dependence Modeling
Chapter Thirteen: Loss Aggregation
13.1 Analytic Solution13.2 Monte Carlo Method13.3 Panjer Recursion13.4 Panjer Extensions13.5 Fast Fourier Transform13.6 Closed-Form Approximation13.7 Capital Charge Under Parameter Uncertainty13.8 Special Advanced Topics on Loss Aggregation
Chapter Fourteen: Scenario Analysis
14.1 Introduction14.2 Examples of Expert Judgments14.3 Pure Bayesian Approach (Estimating Prior)14.4 Expert Distribution and Scenario Elicitation: Learning from Bayesian Methods14.5 Building Models for Elicited Opinions: Hierarchical Dirichlet Models14.6 Worst-Case Scenario Framework14.7 Stress Test Scenario Analysis14.8 Bow-Tie Diagram14.9 Bayesian Networks14.10 Discussion
Chapter Fifteen: Combining Different Data Sources
15.1 Minimum Variance Principle15.2 Bayesian Method to Combine Two Data Sources15.3 Estimation of the Prior Using Data15.4 Combining Expert Opinions with External and Internal Data
15.5 Combining Data Sources Using Credibility Theory
15.6 Nonparametric Bayesian Approach via Dirichlet Process15.7 Combining Using Dempster–Shafer Structures and p-Boxes15.8 General Remarks
Chapter Sixteen: Multifactor Modeling and Regression for Loss Processes
16.1 Generalized Linear Model Regressions and the Exponential Family16.2 Maximum Likelihood Estimation for Generalized Linear Models16.3 Bayesian Generalized Linear Model Regressions and Regularization Priors16.4 Bayesian Estimation and Model Selection via SMC Samplers16.5 Illustrations of SMC Samplers Model Estimation and Selection for Bayesian GLM Regressions16.6 Introduction to Quantile Regression Methods for OpRisk16.7 Factor Modeling for Industry Data16.8 Multifactor Modeling under EVT Approach
Chapter Seventeen: Insurance and Risk Transfer
17.1 Motivation for Insurance and Risk Transfer in OpRisk17.2 Fundamentals of Insurance Product Structures for OpRisk17.3 Single Peril Policy Products for OpRisk17.4 Generic Insurance Product Structures for OpRisk17.5 Closed-Form LDA Models with Insurance Mitigations
Chapter Eighteen: Insurance and Risk Transfer
18.1 Insurance-Linked Securities and CAT Bonds for OpRisk18.2 Basics of Valuation of ILS and CAT Bonds for OpRisk
18.3 Applications of Pricing ILS and CAT Bonds
18.4 Sidecars, Multiple Peril Baskets, and Umbrellas for OpRisk
18.5 Optimal Insurance Purchase Strategies for OpRisk Insurance via Multiple Optimal Stopping Times
Appendix A: Miscellaneous Definitions and List of Distributions
A.1 Indicator FunctionA.2 Gamma FunctionA.3 Discrete DistributionsA.4 Continuous Distributions
Bibliography
Index
Series Page
End User License Agreement

Content preview from Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

10.5 Tail Dependence Parameters, Functions, and Tail Order Functions

We begin this section with a discussion on tail dependence coefficients, introducing this concept and how to interpret the properties of models with this feature. Then we move to relaxing this definition to nonasymptotic cases by considering the case of tail dependence functions and the related tail order functions. The concept of tail dependence parameters, tail dependence functions, or tail order functions each play a crucial role in both copula modeling as well as extreme value theory.

10.5.1 TAIL DEPENDENCE COEFFICIENTS

Tail dependence provides one approach to quantification of the dependence in extremes of a multivariate distribution. Traditionally this notion of dependence was considered from a pairwise construction due to tractability of expressions for the pairwise construction when applied to copula models. However, there is no reason to restrict this notion to just pairwise analysis and later we consider first the pairwise definition and then the generalized definition for d-variate random vectors.

The importance of thinking about tail dependence was succinctly summarized in the questions posed in Charpentier (2003) as detailed later:

If one considers data that are is taken from a multivariate distribution anywhere in its support, then through the measures of dependence just discussed and dependence concepts previously detailed in this chapter, it is possible to obtain all the overall dependence structure ...

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Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

by Pavel V. Shevchenko, Gareth W. Peters, Marcelo G. Cruz