Contents

Acknowledgments

1 Introduction 1
1.1 The pension fund challenge 1
1.2 The risk management revolution 3
1.3 Foundations and structure of this thesis 6

Part I: Embedded options in pension funds 11

2 Understanding and modelling embedded options in DB pension funds 13
2.1 The relevance of mastering embedded options in pension funds 13
2.2 Various embedded options in a DB pension fund 21
Intermezzo: Pension guarantee funds as embedded options? 33

3 Analysis of embedded options in corporate DB pension funds 39
3.1 Valuation techniques applied 39
3.2 The pension fund model 41
3.3 The impact of adding embedded options 51
3.4 Option values under various parameter sets 54
3.5 Sensitivity analysis around the initial funding ratio 56
3.6 Dominance in ownership 63
3.7 Moral hazard and the role of embedded options in pension funds 66
Appendix 3A: A brief history of the quest for option valuation 72

4 Valuing and hedging the conditional indexation option 75
4.1 Introduction 75
4.2 The CDC pension fund model 78
4.3 Value analysis of the indexation option 86
4.4 Hedging the indexation option 92
4.5 Suggestions for further analysis 100
Appendix 4A: Vega analysis for a single digital put option 103

5 Redesigning CDC pension funds 105
5.1 The concept of risk sharing without wealth redistribution 105
5.2 CDC analysis of a conditionally indexed pension fund in the case without upside entitlements 112
5.3 Redesigning conditionally indexed CDC pension funds 121
5.4 CDC analysis and design of a fund without conditional indexation 132
5.5 Debt versus equity holders: The classic case converted to a CDC pension fund 142
5.6 Extensions and practical considerations 150
5.6.1 Subordinated debt and other hybrid classes 150
5.6.2 Creating a going-concern CDC pension fund 151
5.6.3 Single versus multiple asset pool constructions 154
5.6.4 Considerations regarding optimisation 155
5.6.5 Transition from the current DB system to a fair risk sharing system 157

Part II: Optimal hedging strategies for DB pension funds 161

6 Interest rate hedging strategies in a fair value world 163
6.1 Introduction 163
6.2 The Asset & Liability Management model 167
6.3 Nominal interest rate hedges 172
6.4 Robustness analysis 179
6.5 Conclusions and suggestions for further research 182

7 Option based equity hedging strategies 185
7.1 Introduction 185
7.2 The Asset & Liability Management model 186
7.3 Introducing equity options in the portfolio 191
7.4 Robustness analysis 196
7.5 Conclusions 198

Epilogue: The future of the pension system 201

References 209
Notation 217
Summary 221
Samenvatting (Summary in Dutch) 231