Modelling in Life Insurance – A Management Perspective (eBook)

Foreword 6
Contents 8
Contributors 10
Introduction 11
Life Insurance Context 17
1 Paradigms in Life Insurance 18
Abstract 18
1.1 Introduction 18
1.1.1 Insurance on the Move 18
1.1.2 Insurance in the Recent Past 19
1.1.3 Insurance at Present 20
1.1.4 Outline of This Chapter 21
1.2 Preliminaries 22
1.2.1 Modern Financial Economics 1 22
1.2.2 The Casino 23
1.2.3 Competition and Costs 25
1.2.4 Modern Financial Economics 2 26
1.2.5 Galbraith & Co
1.3 Finance with a Single Asset: Banking 27
1.3.1 Asset Prices and Interest 27
1.3.2 Investments 28
1.3.3 Arbitrage 29
1.3.4 Financial Contracts 29
1.3.5 The Principle of Equivalence 30
1.3.6 The Prospective Reserve and Its Proxies 31
1.3.7 Information 31
1.4 Insurance 32
1.4.1 The Insurance Idea: Diversification in Large Portfolios 32
1.4.2 A Bank Savings Contract 34
1.4.3 Mortality 35
1.4.4 Life Annuities and Pensions 35
1.4.5 Life Insurance 36
1.4.6 Sensitivity of the Equivalence Premium to Changes in Interest and Mortality 37
1.5 Management of Economic-Demographic Risk 37
1.5.1 The Big Issue 37
1.5.2 With-Profit Insurance 38
1.5.3 † Derivation of (1.15) 41
1.5.4 Index-Linked Insurance 43
1.5.5 Guarantees 44
1.6 Finance in a Multi-asset Market 46
1.6.1 APT 46
1.6.2 A Market with Two Assets 47
1.6.3 Does This Market Admit Arbitrage? 48
1.6.4 Pricing 49
1.6.5 † The Risk Neutral Measure 50
1.6.6 Completeness 52
1.7 Some Bullet Points on the New Paradigm 53
1.7.1 The Crystal Ball 53
1.7.2 Securitization 53
1.7.3 Longevity Risk on the Market? 54
1.7.4 The Piggy Bank 55
1.7.5 Insurance in the Future 56
Acknowledgment 57
2 About Market Consistent Valuation in Insurance 58
Abstract 58
2.1 Introduction 58
2.2 A Business Structured by Regulations 59
2.2.1 An Illustration of Life Insurance in Euros: The French Case 60
2.2.2 Comparative Analysis: The German Situation 62
2.3 Fair Value and Its Criticism 64
2.3.1 One Fair Value Principle, Several Valuation Techniques 64
2.3.2 The Criticism 66
2.4 The Delicate Transposition to the Field of Insurance 68
2.4.1 The Implementation 70
2.4.2 Limits of the Approach 71
2.5 Annex 73
2.5.1 Market Consistent Embedded Value (MCEV) 73
2.5.2 Solvency II 73
2.5.3 IFRS Insurance Contracts (Phase 2) 74
Design and Implementation of Life Insurance Models 76
3 Cash Flow Projection Models 77
Abstract 77
3.1 Introduction 77
3.2 Discounting Issues 79
3.3 Probability Issues 79
3.4 Cash Flow Issues 80
3.4.1 Time Horizon 80
3.4.2 Modelling Cash Flows 80
3.4.3 Modelling the Liabilities’ Cash Flows 82
Structure of the Savings Model 82
Structure of the Protection Model 83
Structure of the Model and Its Impact on Data 84
Modelling Insurance Contracts’ Cash Flows 84
Overheads’ Cash Flow Modelling 86
3.4.4 Assets’ Cash Flow Modelling? 87
3.4.5 Assets and Liabilities Interactions Modelling 89
Assets and Savings Liabilities Interactions 89
The Financial Strategy 90
Policyholders’ Profit Sharing Modelling 91
Assets and Protection Liabilities Interactions 92
3.5 Conclusion 92
4 Economic Scenario Generators 94
Abstract 94
4.1 Introduction 94
4.2 Prices and Price Distributions 95
4.2.1 Asset/Liability Management 97
4.2.2 Calculating Reserves 97
4.2.3 Is There Any Coherence Between the Different Descriptions? 99
4.3 Calibration and Implementation 103
4.3.1 From Theory to Practice: Implementation of the Model 103
4.3.2 Some Remarks About the Calibration 106
4.3.3 An Example: ESG Packages 109
Illustration of the Calibration: BSHW Model 111
Validation of the Simulated Prices 113
4.4 Conclusion 117
5 From Internal to ORSA Models 118
Abstract 118
5.1 Introduction 118
5.2 What Is ORSA? 121
5.2.1 The Logic Behind the Three Evaluations 122
1st Evaluation: Overall Solvency Needs (OSN) 122
2nd Evaluation: Continual Respect for Statutory Solvency 123
3rd Evaluation: Analysis of the Variances Between the Risk Profile and the SCR Calculation Assumptions 124
5.2.2 Risk Appetite 124
5.2.3 Business Plan and Risk Profile 125
5.3 ORSA’S Quantitative Approaches 125
5.3.1 Scenario Approach 126
5.4 Structuring the Central Scenario 126
5.5 Building Stress Scenarios 127
5.5.1 Probabilistic Approaches 128
Choice of the Extreme Scenarios 128
The Weighted Monte Carlo Method 129
The Least-Squares Monte Carlo Method (LSMC) 129
Replicating Portfolios 129
Closed Formula Methods 130
5.6 ORSA, Pillar 1 and Internal Model: Need for Coordination? 130
5.6.1 Risks and Capital Requirements 130
5.6.2 Projections 131
5.6.3 ORSA and Internal Models 132
5.6.4 An Example of Economic Scenario Generators 132
Complexity of the Process in Play 133
Which Forecasting Dynamics for a Risk Neutral ESG? 134
5.6.5 Use of Proxies: An Illustration 134
5.7 Conclusion 136
6 Building a Model: Practical Implementation 138
Abstract 138
6.1 Introduction 138
6.2 Caveat Emptor 140
6.2.1 Inventory Tools 140
6.2.2 Financial Models 141
6.2.3 Embedded Value Calculation Tools 142
6.2.4 Asset-Liability Models 142
6.3 Structural Choices 143
6.3.1 Define an Application Scope 143
Regulatory Applications 144
Decision Support 145
6.3.2 Listing Features 145
Treating the Regulatory Applications 145
Treating the BI Applications 149
6.4 The Project Team 150
6.4.1 Professional Expertise 150
6.4.2 Separate Testing and Acceptation Process 151
6.4.3 Project Management 151
6.5 IT Development 152
6.5.1 Software Quality 152
6.5.2 Computer Engineering 153
Languages and Development Environments 153
Procedural Programming Versus Object Paradigm 154
6.5.3 Development Method 155
Waterfall Method 155
Agile Methods 156
6.5.4 Model Documentation 157
General Documentation of the Model 158
Documentation of Procedures 158
Application and Method Documentation 158
Model Logbook 159
6.6 Conclusions 159
Model Validation and Steering Processes 161
7 Ex-ante Model Validation and Back-Testing 162
Abstract 162
7.1 A Priori Formal Validation 162
7.2 Ex-post Validation: Back-Testing 167
8 The Threat of Model Risk for Insurance Companies 172
Abstract 172
8.1 Introduction 172
8.2 Understanding Model Risk 174
8.2.1 What Can We Learn from Quantitative Financial Analysts About Model Risk for Pricing Models? 175
8.2.2 What the Office of the Comptroller of the Currency of the U.S. Department of the Treasury Says 176
8.2.3 What the Casualty Actuarial Society, the Canadian Institute of Actuaries, and the Society of Actuaries Say 178
8.2.4 To Sum up 179
8.3 Is it Possible to Measure Model Risk in the Model Design Process? 179
8.3.1 Measures of Model Risk 179
8.3.2 Model Risk and Ambiguity 181
8.4 Model Risk Management or How to Mitigate Model Risk 182
8.4.1 Model Risk Management for Banks 182
8.4.2 Model Risk Management for Insurers 184
8.5 Model Risk and Solvency II 186
8.5.1 Model Risk and the Standard Formula 186
8.5.2 Model Risk and the ORSA 190
8.6 Conclusion 191
9 Meta-Models and Consistency Issues 192
Abstract 192
9.1 Life Insurance Models in a Nutshell 192
9.2 Models and Markets 194
9.3 Constraint-Driven Modelling 201
9.4 The Recalibration Puzzle 203
9.5 Fitting Models to Models 204
9.6 Model Parameters Set at Managerial Discretion 207
9.7 Approximation Issues for Pricing Models in the Finance and Insurance Contexts 207
9.8 Conclusion 212
Models and Business Processes 213
10 Model Feeding and Data Quality 214
Abstract 214
10.1 Introduction 215
10.2 Launching the Data Quality Project 215
10.2.1 The Reasons for Launching a Data Quality Project 215
10.2.2 The Sine Qua Non Involvements in the Data Quality Project 216
10.2.3 Definition of the Ambition of the Project 217
Modelled Lines of Business 217
Processes and Sub-processes 218
Categories of Input Data 219
Date of the Data 220
Framework of Use 220
Deployment in Entities 221
Setting Priorities 221
10.3 Data Quality: A Loop Approach 221
10.3.1 First Step: Define Data 222
Data Dictionary and Key Data 222
IT Systems and Data Sources 223
Key Controls 224
10.3.2 Second Step: Measure Data Quality 225
10.3.3 Third Step: Build Data Used by the Model 225
10.3.4 Fourth Step: Improve Data Quality 226
10.4 Data Governance 228
10.5 Conclusion 230
11 The Role of Models in Management Decision-Making 232
Abstract 232
11.1 Could an Insurance Undertaking Be Run Today Without Using Models? 233
11.2 Could Models’ Inputs in Decision-Making Become a Source of Mass Crisis? 234
11.3 Can Models Predict the Future and Can They Help the Company to Prepare for the Future? 236
11.4 How Consistent Are Different Decisions When They Are Made Based upon Different Models? 237
11.5 Is It Possible for a Decision-Maker to Understand Models? 238
11.6 Is the Decision What the Model Says? 239
11.7 How Far Could a Model Duplicate the Decision-Making Process? 242
11.8 Conclusion: The Model as the Fifth Solvency II Key Function? 243
12 Models and Behaviour of Stakeholders 245
Abstract 245
12.1 Endogenous Risk and Feedback Loops in Financial Markets 245
12.2 Endogenous Risk and Customer Behaviour in Insurance and Banking 247
12.3 Lapse, Sales, Fraud and Moral Hazard 248
12.4 Four Different Perspectives on Risk 249
12.5 Four Risk Strategies 250
12.6 Changing Risk Environments 251
12.7 Attitudes with Respect to Models 254
12.8 Surveying Attitudes with Respect to Risk and Models 254
12.9 Some Important Remarks 256
Bibliography 257