Risk Quantification
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Content
Foreword xi
Introduction xiii
1 Foundations 1
Risk management: principles and practice 1
Definitions 3
Systematic and unsystematic risk 4
Insurable risks 4
Exposure 7
Management 7
Risk management 7
Risk management objectives 8
Organizational objectives 8
Other significant objectives 10
Risk management decision process 11
Step 1-Diagnosis of exposures 11
Step 2-Risk treatment 16
Step 3-Audit and corrective actions 19
State of the art and the trends in risk management 20
Risk profile, risk map or risk matrix 20
Frequency × Severity 20
Risk financing and strategic financing 23
From risk management to strategic risk management 23
From managing physical assets to managing reputation 25
From risk manager to chief risk officer 26
Why is risk quantification needed? 27
Risk quantification - a knowledge-based approach 28
Introduction 28
Causal structure of risk 28
Building a quantitative causal model of risk 31
Exposure, frequency, and probability 33
Exposure, occurrence, and impact drivers 34
Controlling exposure, occurrence, and impact 35
Controllable, predictable, observable, and hidden drivers 35
Cost of decisions 36
Risk financing 37
Risk management programme as an influence diagram 38
Modelling an individual risk or the risk management programme 39
Summary 41
2 Tool Box 43
Probability basics 43
Introduction to probability theory 43
Conditional probabilities 45
Independence 49
Bayes' theorem 50
Random variables 54
Moments of a random variable 57
Continuous random variables 58
Main probability distributions 62
Introduction-the binomial distribution 62
Overview of usual distributions 64
Fundamental theorems of probability theory 67
Empirical estimation 68
Estimating probabilities from data 68
Fitting a distribution from data 69
Expert estimation 71
From data to knowledge 71
Estimating probabilities from expert knowledge 73
Estimating a distribution from expert knowledge 74
Identifying the causal structure of a domain 74
Conclusion 75
Bayesian networks and influence diagrams 76
Introduction to the case 77
Introduction to Bayesian networks 78
Nodes and variables 79
Probabilities 79
Dependencies 81
Inference 83
Learning 85
Extension to influence diagrams 87
Introduction to Monte Carlo simulation 90
Introduction 90
Introductory example: structured funds 90
Risk management example 1 - hedging weather risk 96
Description 96
Collecting information 98
Model 99
Manual scenario 101
Monte Carlo simulation 101
Summary 104
Risk management example 2- potential earthquake in cement industry 104
Analysis 104
Model 106
Monte Carlo simulation 107
Conclusion 109
A bit of theory 109
Introduction 109
Definition 110
Estimation according to Monte Carlo simulation 111
Random variable generation 112
Variance reduction 113
Software tools 117
3 Quantitative Risk Assessment: A Knowledge Modelling Process 119
Introduction 119
Increasing awareness of exposures and stakes 119
Objectives of risk assessment 120
Issues in risk quantification 121
Risk quantification: a knowledge management process 122
The basel II framework for operational risk 122
Introduction 123
The three pillars 123
Operational risk 124
The basic indicator approach 124
The sound practices paper 125
The standardized approach 125
The alternative standardized approach 127
The advanced measurement approaches (AMA) 127
Risk mitigation 130
Partial use 130
Conclusion 131
Identification and mapping of loss exposures 131
Quantification of loss exposures 134
The candidate scenarios for quantitative risk assessment 134
The exposure, occurrence, impact (XOI) model 135
Modelling and conditioning exposure at peril 135
Summary 136
Modelling and conditioning occurrence 137
Consistency of exposure and occurrence 137
Evaluating the probability of occurrence 140
Conditioning the probability of occurrence 143
Summary 144
Modelling and conditioning impact 145
Defining the impact equation 145
Defining the distributions of variables involved 146
Identifying drivers 147
Summary 148
Quantifying a single scenario 148
An example - "fat fingers" scenario 150
Modelling the exposure 150
Modelling the occurrence 151
Modelling the impact 152
Quantitative simulation 154
Merging scenarios 157
Modelling the global distribution of losses 158
Conclusion 159
4 Identifying Risk Control Drivers 161
Introduction 161
Loss control - a qualitative view 163
Loss prevention (action on the causes) 164
Eliminating the exposure 164
Reducing the probability of occurrence 166
Loss reduction (action on the consequences) 166
Pre-event or passive reduction 166
Post-event or active reduction 167
An introduction to cindynics 169
Basic concepts 170
Dysfunctions 172
General principles and axioms 174
Perspectives 174
Quantitative example 1 - pandemic influenza 176
Introduction 176
The influenza pandemic risk model 177
Exposure 177
Occurrence 177
Impact 178
The Bayesian network 180
Risk control 181
Pre-exposition treatment (vaccination) 182
Post-exposition treatment (antiviral drug) 182
Implementation within a Bayesian network 183
Strategy comparison 185
Cumulated point of view 185
Discussion 188
Quantitative example 2 - basel II operational risk 189
The individual loss model 189
Analysing the potential severe losses 189
Identifying the loss control actions 189
Analysing the cumulated impact of loss control actions 191
Discussion 192
Quantitative example 3 - enterprise-wide risk management 194
Context and objectives 195
Risk analysis and complex systems 195
An alternative definition of risk 196
Representation using Bayesian networks 196
Selection of a time horizon 197
Identification of objectives 197
Identification of risks (events) and risk factors (context) 198
Structuring the network 199
Identification of relationships (causal links or influences) 200
Quantification of the network 200
Example of global enterprise risk representation 200
Usage of the model for loss control 201
Risk mapping 201
Importance factors 202
Scenario analysis 202
Application to the risk management of an industrial plant 203
Description of the system 203
Assessment of the external risks 204
Integration of external risks in the global risk assessment 207
Usage of the model for risk management 210
Summary - using quantitative models for risk control 210
5 Risk Financing: The Right Cost of Risks 211
Introduction 211
Risk financing instruments 212
Retention techniques 214
Current treatment 214
Reserves 215
Captives (insurance or reinsurance) 215
Transfer techniques 219
Contractual transfer (for risk financing - to a noninsurer) 219
Purchase of insurance cover 219
Hybrid techniques 220
Pools and closed mutual 220
Claims history-based premiums 222
Choice of retention levels 222
Financial reinsurance and finite risks 223
Prospective aggregate cover 225
Capital markets products for risk financing 225
Securitization 226
Insurance derivatives 227
Contingent capital arrangements 228
Risk financing and risk quantifying 230
Using quantitative models 231
Example 1: Satellite launcher 231
Example 2: Defining a property insurance programme 243
A tentative general representation of financing methods 252
Introduction 252
Risk financing building blocks 254
Usual financing tools revisited 257
Combining a risk model and a financing model 261
Conclusion 263
Index 267
