Operational Risk Modeling Analytics

This book provides a highly detailed development of the many probabilistic and statistical methods that are used in operational risk. These methods have traditionally been developed in the insurance/actuarial field, but they are now applicable to operational risk measurement and management. The book is premised on the availability of data for analysis. In the past few years, there have been several initiatives to gather such data in individual organizations; it is intended that this volume present such data for more detailed analysis than what is currently being done in the literature. The book is written by one of the foremost authorities in the world on risk modelling and its effects in the business environment.

HARRY H. PANJER, PHD, FSA, FCIA, HonFIA, is Professor in the Department of Statistics and Actuarial Science at the University of Waterloo, Ontario, Canada. He is past president of both the Canadian Institute of Actuaries and the Society of Actuaries, and he has published numerous articles and books on the subject of risk modeling over the years in the fields of finance and actuarial science.

Preface

xiii

Acknowledgments

xv

Part I Introduction to operational risk modeling

Operational risk

3

(16)

Introduction

3

(8)

Basel II - General

6

(2)

Basel II - Operational risk

8

(3)

Operational risk in insurance

11

(1)

The analysis of operational risk

12

(2)

The model-based approach

14

(2)

The modeling process

15

(1)

Organization of this book

16

(3)

Basic probability concepts

19

(26)

Introduction

19

(1)

Distribution functions and related concepts

20

(10)

Moments

30

(8)

Quantiles of a distribution

38

(1)

Generating functions

38

(3)

Exercises

41

(4)

Measures of risk

45

(12)

Introduction

45

(1)

Risk measures

46

(4)

Tail- Value-at-Risk

50

(7)

Part II Probabilistic tools for operational risk modeling

Models for the size of losses: Continuous distributions

57

(50)

Introduction

57

(1)

An inventory of continuous distributions

58

(10)

One-parameter distributions

58

(1)

Two-parameter distributions

59

(5)

Three-parameter distributions

64

(3)

Four-parameter distributions

67

(1)

Distributions with finite support

68

(1)

Selected distributions and their relationships

68

(2)

Introduction

68

(1)

Two important parametric families

69

(1)

Limiting distributions

70

(3)

The role of parameters

73

(7)

Parametric and scale distributions

74

(1)

Finite mixture distributions

75

(3)

Data-dependent distributions

78

(2)

Tails of distributions

80

(4)

Classification based on moments

80

(1)

Classification based on tail behavior

81

(1)

Classification based on hazard rate function

82

(2)

Creating new distributions

84

(9)

Introduction

84

(1)

Multiplication by a constant

84

(1)

Transformation by raising to a power

85

(2)

Transformation by exponentiation

87

(1)

Continuous mixture of distributions

88

(2)

Frailty models

90

(2)

Splicing pieces of distributions

92

(1)

TVaR for continuous distributions

93

(9)

Continuous elliptical distributions

94

(3)

Continuous exponential dispersion distributions

97

(5)

Exercises

102

(5)

Models for the number of losses: Counting distributions

107

(54)

Introduction

107

(1)

The Poisson distribution

108

(2)

The negative binomial distribution

110

(4)

The binomial distribution

114

(1)

The (a, b, 0) class

114

(4)

The (a, b, 1) class

118

(4)

Compound frequency models

122

(4)

Recursive calculation of compound probabilities

126

(4)

An inventory of discrete distributions

130

(6)

The (a, b, 0) class

130

(2)

The (a, b, 1) class

132

(1)

The zero-truncated subclass

132

(2)

The zero-modified subclass

134

(1)

The compound class

135

(1)

A hierarchy of discrete distributions

136

(1)

Further properties of the compound Poisson class

137

(5)

Mixed frequency models

142

(2)

Poisson mixtures

144

(5)

Effect of exposure on loss counts

149

(1)

TVaR for discrete distributions

150

(6)

TVaR for discrete exponential dispersion distributions

151

(5)

Exercises

156

(5)

Aggregate loss models

161

(44)

Introduction

161

(1)

Model choices

162

(1)

The compound model for aggregate losses

163

(5)

Some analytic results

168

(3)

Evaluation of the aggregate loss distribution

171

(3)

The recursive method

174

(9)

Compound frequency models

175

(3)

Underflow/overflow problems

178

(1)

Numerical stability

179

(1)

Continuous severity

179

(1)

Constructing arithmetic distributions

180

(3)

Fast Fourier transform methods

183

(4)

Using approximating severity distributions

187

(3)

Arithmetic distributions

187

(3)

Comparison of methods

190

(1)

TVaR for aggregate losses

191

(7)

TVaR for discrete aggregate loss distributions

191

(1)

TVaR for some frequency distributions

192

(2)

TVaR for some severity distributions

194

(4)

Summary

198

(1)

Exercises

198

(7)

Extreme value theory: The study of jumbo losses

205

(28)

Introduction

205

(2)

Extreme value distributions

207

(1)

Distribution of the maximum

208

(5)

From a fixed number of losses

208

(2)

From a random number of losses

210

(3)

Stability of the maximum of the extreme value distribution

213

(1)

The Fisher- Tippett theorem

214

(3)

Maximum domain of attraction

217

(2)

Generalized Pareto distributions

219

(2)

The frequency of exceedences

221

(5)

From a fixed number of losses

221

(1)

From a random number of losses

222

(4)

Stability of excesses of the generalized Pareto

226

(1)

Mean excess function

227

(1)

Limiting distributions of excesses

228

(1)

TVaR for extreme value distributions

229

(1)

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Operational Risk Modeling Analytics

Summary

Author Biography

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Operational Risk Modeling Analytics

Summary

Author Biography

Table of Contents

Supplemental Materials

Digital License