Stochastic mortality modeling and securitization of mortality risk:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Ulm
IFA
2008
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| Series: | IFA-Schriftenreihe
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 242 S. graph. Darst. 21 cm |
| ISBN: | 9783931289843 |
Staff View
MARC
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| 100 | 1 | |a Bauer, Daniel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic mortality modeling and securitization of mortality risk |c Daniel Bauer. IFA, Institut für Finanz- und Aktuarwissenschaften |
| 264 | 1 | |a Ulm |b IFA |c 2008 | |
| 300 | |a XVI, 242 S. |b graph. Darst. |c 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a IFA-Schriftenreihe | |
| 502 | |a Zugl.: Ulm, Univ., Diss., 2007 | ||
| 650 | 4 | |a Dissertation / Thesis - 18 | |
| 650 | 4 | |a Sterblichkeit / Stochastischer Prozess / Lebensversicherung / Versicherungstechnisches Risiko / Securitization / Theorie | |
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Record in the Search Index
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| adam_text | Contents
Contents iii
List of Figures ix
List of Tables xi
List of Abbreviations xiii
1 Introduction 1
1.1 Historical Background and Motivation ............. 1
1.2 Scope and Aim.......................... 5
1.3 Organization and Contributions................. 6
2 Stochastic Mortality Modeling 13
2.1 An Arbitrage-Free Family of Longevity Bonds......... 14
2.1.1 Basic Definitions..................... 14
2.1.2 Survival Probabilities and Interest Rates........ 17
2.1.3 Existence of Equivalent Martingale Measures...... 29
2.1.4 Generalization Towards Multiple Inception Dates ... 32
2.2 Spot Force Modeling....................... 39
2.2.1 An Alternative Approach to Stochastic Mortality Mod-
eling ............................ 40
v
vi CONTENTS
2.2.2 Comparison of the Approaches.............. 44
2.2.3 Example: An Affine Spot Force Model with Jumps . . 46
2.3 Forward Force Modeling..................... 51
2.3.1 The Heath-Jarrow-Morton Drift Condition....... 53
2.3.2 What is the Age/Term-Structure of Mortality (1) . . 57
2.3.3 Consistent Forward Surface Factor Models....... 02
2.3.4 Reformulation of the Setup - the Musiela Parametrization 68
2.3.5 Finite Dimensional Realizations............. 73
2.3.6 Example: A Gaussian Gompertz Model......... 80
2.4 Summary and Remarks...................... 87
3 Stochastic Mortality and Life Insurance 91
3.1 Mortality Risk in Life Insurance................. 92
3.1.1 A Simple Life Insurance Model ............. 92
3.1.2 Decomposition of Mortality Risk ............ 94
3.1.3 Mortality Risk in Insurance Prices............ 95
3.2 Pricing Longevity Bonds..................... 99
3.2.1 The Approach of Milevsky et al. (2005)......... 100
3.2.2 The Approach of Lin and Cox (2005).......... 101
3.2.3 A No-Arbitrage Model for Longevity Bonds...... 107
3.2.4 What is the Age/Tenn-Structure of Mortality? (2) . . 112
3.3 Stochastic Mortality in Actuarial Practice ........... 116
3.3.1 Different Tables - Different Models........... 117
3.3.2 Inconsistencies of Classical Methods with Stochastic Mor-
tality ............................ 120
3.3.3 Valuation of Mortality Contingent Options....... 122
3.4 Summary and Remarks...................... 129
CONTENTS vii
4 Securitization of CAT Mortality Risk 133
4.1 The Market for Catastrophe Mortality Bonds ......... 135
1.1.1 Structure of Catastrophe Mortality Bonds....... 136
1.1.2 Market Development................... 139
¦1.1.3 Modeling Approaches in Practice............ 143
4.2 Calibration of our Model..................... 149
1.2.1 Backtesting the Model and Historical Parametrizations 150
4.2.2 Risk-Adjusted Calibration based on Insurance Prices . 160
4.2.3 Parameters Implied by Market Prices.......... 164
4.3 Results............................... 168
4.4 Summary and Outlook...................... 177
5 Securitization of Longevity Risk 181
5.1 Longevity Derivatives....................... 184
5.1.1 The EIB/BNP Longevity Bond............. 184
5.1.2 An Alternatively Designed Longevity Derivative .... 186
5.2 Forward Force Approach to Longevity Modeling........ 191
5.2.1 Modeling the Volatility of Mortality........... 191
5.2.2 Calibration of Gaussian Models............. 193
5.2.3 General Calibration.................... 196
5.2.4 Modeling and Pricing Longevity Derivatives...... 197
5.3 Specification and Application .................. 201
5.3.1 Specification Based on Epidemiological Insights .... 202
5.3.2 Data and Calibration Results.............. 203
5.3.3 Application of the Model................. 212
5.4 Summary, Remarks, and Outlook................ 220
viii CONTENTS
A Appendix to Chapter 4 225
Bibliography 229
List of Figures
3.1 Comparison between different K/r.o ............... 6
3.2 Market model........................... 108
3.3 Monthly time series of U.K. annuity rates (01/2001 - 12/2005) 100
3.4 Comparison between implied and Wans i /r.o.......... Ill
1.1 Tartan deal structure (Source: l.infoot (2007))......... 13(i
1.2 RMS Pandemic Influenza Model framework (Source: I.ogisch
(2007))............................... 115
1.3 Milliman model overview (Source: Logisch (2007))....... 1 Hi
4.4 Mortality intensities 1959..................... 152
4.5 Mortality intensities for years 36 and 43 ............ 152
4.6 Time series of /? ......................... 153
4.7 Distribution of the index value.................. Hi!)
1.8 Influence of the expected jump size on the tranche spreads . . 172
1.0 Discrctized tranche loss distributions.............. 173
5.1 Basic design............................ 187
5.2 An alternatively designed longevity derivative......... 190
5.3 Volatility structure for the Gaussian and the Square-root model 209
5.4 Relative volatility structure for the Gaussian and the Square-
root model............................. 211
ix
LIST OF FIGURES
5.5 Influence of a on the trigger probability for T = 20...... 213
5.6 Influence of a on C™ for T = 10 and T = 20 ........ 217
A.I Influence of the speed of mean reversion k on the expected
tranche loss............................ 227
A.2 Influence of the jump intensity A on the expected tranche loss 227
A.3 Influence of the expected jump size /u on the expected tranche
loss................................. 228
List of Tables
1.1 Gender and age weights for the Tartan transaction ...... 13N
1.2 Program summary of the notes issued by Tartan........ l- W
4.3 Deal comparison (Source: New Issue Reports from S^-F and
Moody s; Bloomberg data).................... 2
4.4 Parametrizations of Z1...................... ^
4.5 Parametrizations for the jump size distribution......... 159
4.6 Parameter calibration based on insurance prices........ 163
4.7 Cash flows for the Tartan bonds................. 166
4.8 Influence of the Baseline Component.............. 68
4.9 Influence of the Catastrophe Component............. 170
4.10 Summary of results for risk-adjusted parametrization based on
the Tartan tranche........................
4.11 Summary of results for risk-adjusted parametrization based on
insurance prices..........................
5.1 Gaussian model..........................
5.2 Square-root model ........................
5.3 Resulting parametrizations....................
5.4 Comparative statistics for the longevity security (o - 2.57c.
T = 20).............................. 212
5.5 Discounted expected values for x0 = 65, T = 20, and a = 2.5% 216
XI
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:29Z |
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| isbn | 9783931289843 |
| language | English |
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| physical | XVI, 242 S. graph. Darst. 21 cm |
| publishDate | 2008 |
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| spelling | Bauer, Daniel Verfasser aut Stochastic mortality modeling and securitization of mortality risk Daniel Bauer. IFA, Institut für Finanz- und Aktuarwissenschaften Ulm IFA 2008 XVI, 242 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier IFA-Schriftenreihe Zugl.: Ulm, Univ., Diss., 2007 Dissertation / Thesis - 18 Sterblichkeit / Stochastischer Prozess / Lebensversicherung / Versicherungstechnisches Risiko / Securitization / Theorie (DE-588)4113937-9 Hochschulschrift gnd-content HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017092543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bauer, Daniel Stochastic mortality modeling and securitization of mortality risk Dissertation / Thesis - 18 Sterblichkeit / Stochastischer Prozess / Lebensversicherung / Versicherungstechnisches Risiko / Securitization / Theorie |
| subject_GND | (DE-588)4113937-9 |
| title | Stochastic mortality modeling and securitization of mortality risk |
| title_auth | Stochastic mortality modeling and securitization of mortality risk |
| title_exact_search | Stochastic mortality modeling and securitization of mortality risk |
| title_full | Stochastic mortality modeling and securitization of mortality risk Daniel Bauer. IFA, Institut für Finanz- und Aktuarwissenschaften |
| title_fullStr | Stochastic mortality modeling and securitization of mortality risk Daniel Bauer. IFA, Institut für Finanz- und Aktuarwissenschaften |
| title_full_unstemmed | Stochastic mortality modeling and securitization of mortality risk Daniel Bauer. IFA, Institut für Finanz- und Aktuarwissenschaften |
| title_short | Stochastic mortality modeling and securitization of mortality risk |
| title_sort | stochastic mortality modeling and securitization of mortality risk |
| topic | Dissertation / Thesis - 18 Sterblichkeit / Stochastischer Prozess / Lebensversicherung / Versicherungstechnisches Risiko / Securitization / Theorie |
| topic_facet | Dissertation / Thesis - 18 Sterblichkeit / Stochastischer Prozess / Lebensversicherung / Versicherungstechnisches Risiko / Securitization / Theorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017092543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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