Implicit options in life insurance: valuation and risk assessment
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Hochschulschrift/Dissertation Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
2007
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| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016095567&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVI, 167 S. graph. Darst. |
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Datensatz im Suchindex
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| adam_text | Outline
1 Introduction..........................................................................................................1
2 The Impact of Implicit Options in Life Insurance Contracts:
Systematization and Overview............................................................................8
3 Life Insurance Liabilities at the Corporate Level...........................................33
3.1 Analysis of Participating Life Insurance Contracts: A Unification
Approach......................................................................................................33
3.2 Management Strategies in Life Insurance: An Examination with
Respect to Risk Pricing and Risk Measurement..........................................62
3.3 Risk Assessment of Life Insurance Contracts: A Comparative Study
in a Levy Framework...................................................................................83
4 Evaluation of Individual Life Insurance Contracts......................................108
4.1 Assessing the Risk Potential of Premium Payment Options in
Participating Life Insurance Contracts......................................................108
4.2 Pricing Premium Payment Options: The Impact of Stochastic
Interest Rates..............................................................................................132
5 Summary...........................................................................................................149
Contents
Outline..........................................................................................................................i
Contents......................................................................................................................ii
List of Figures...........................................................................................................vii
List of Tables..............................................................................................................ix
List of Symbols and Abbreviations............................................................................xi
Abstract.....................................................................................................................xvi
1 Introduction..........................................................................................................1
1.1 Motivation......................................................................................................1
1.2 Research Objective and Organization of the Thesis......................................3
2 The Impact of Implicit Options in Life Insurance Contracts:
Systematization and Overview............................................................................8
2.1 Introduction....................................................................................................8
2.2 Comparison of Life Insurance Products in the United States and
Europe............................................................................................................9
2.2.1 Life Insurance Contracts in Europe..................................................10
2.2.2 Life Insurance Contracts in the United States..................................12
2.3 Implicit Options in Life Insurance...............................................................13
2.3.1 Dividend Options..............................................................................15
2.3.2 Premium Payment Options...............................................................16
2.3.3 Surrender Option..............................................................................17
2.3.4 Flexible Expiration Option...............................................................17
2.3.5 Settlement Options............................................................................18
2.3.6 Right of Objection............................................................................19
2.3.7 Policy Loan.......................................................................................19
2.3.8 Policy Backdating.............................................................................20
2.3.9 Conversion Option............................................................................20
2.3.10 Extended Term Insurance.................................................................20
2.3.11 Lump Sum Settlement Option During Annuity...............................21
2.3.12 Additional Payments.........................................................................21
2.3.13 Reinstatement...................................................................................21
2.3.14 Coverage Extension Option..............................................................22
2.3.15 Contract Term Extension Option......................................................22
2.4 The Impact of Implicit Options: Literature Survey for Participating
Endowment Policies....................................................................................25
2.4.1 Dividend Options with Accumulation at Interest.............................25
2.4.2 Point to Point Dividends..................................................................26
2.4.3 Cliquet Style Dividends....................................................................27
2.4.4 Surrender Option..............................................................................27
2.4.5 Premium Payment Options...............................................................28
2.4.6 Flexible Expiration Option...............................................................29
2.4.7 Settlement Option: Guaranteed Annuity Option..............................29
2.5 Outlook........................................................................................................30
Life Insurance Liabilities at the Corporate Level...........................................33
3.1 Analysis of Participating Life Insurance Contracts: A Unification
Approach......................................................................................................33
3.1.1 Introduction.......................................................................................33
3.1.2 Model Framework............................................................................37
3.1.2.1 Model overview..................................................................37
3.1.2.2 Dynamics............................................................................38
3.1.2.3 Customer payoff..................................................................39
3.1.2.4 Fair contracts.......................................................................39
3.1.2.5 Shortfall and risk measurement..........................................40
3.1.3 A Point To Point Model...................................................................42
3.1.3.1 Dynamics of the liabilities and customer payoff................42
3.1.3.2 Fair contracts.......................................................................43
3.1.3.3 Shortfall...............................................................................44
3.1.3.4 Isoquants.............................................................................45
3.1.3.5 Risk of fair contracts...........................................................46
3.1.4 A Cliquet Style Model......................................................................48
3.
3.
3.
3.
3.
3.1.5 A
3.
3.
3.
3.
3.
.4.1 Dynamics of the liabilities and customer payoff................48
.4.2 Fair contracts.......................................................................49
.4.3 Shortfall...............................................................................51
.4.4 Isoquants.............................................................................51
.4.5 Risk of fair contract............................................................52
Danish Cliquet Style Model.........................................................55
.5.1 Dynamics of the liabilities and customer payoff................55
.5.2 Fair contracts.......................................................................56
.5.3 Shortfall...............................................................................57
.5.4 Isoquants.............................................................................57
.5.5 Risk of fair contracts...........................................................59
3.1.6 Summary...........................................................................................60
3.2 Management Strategies in Life Insurance: An Examination with
Respect to Risk Pricing and Risk Measurement..........................................62
3.2.1 Introduction.......................................................................................62
3.2.2 Model Framework and Fair Valuation of Insurance Company s
Liabilities..........................................................................................64
3.2.2.1 The life insurance contract..................................................64
3.2.2.2 Fair valuation......................................................................66
3.2.3 Fair Valuation of Liabilities Given a Fixed Safety Level................67
3.2.3.1 Fair contracts.......................................................................67
3.2.3.2 Fixing the insurer s safety level..........................................67
3.2.3.3 Risk measurement...............................................................69
3.2.3.4 Numerical results................................................................69
3.2.4 The Influence of Management Strategies on Pricing and Risk
Measurement.....................................................................................71
3.2.4.1 Management strategies in life insurance.............................71
3.2.4.2 Strategy (A).........................................................................72
3.2.4.3 Strategy (B).........................................................................73
3.2.4.4 Strategy (C).........................................................................73
3.2.4.5 Numerical results................................................................74
3.2.5 The Influence of Management Strategies on Risk Measurement
Given a Fixed Safety Level..............................................................78
3.2.5.1 Numerical results for Strategy (A)......................................78
3.2.5.2 Numerical results for Strategy (B)......................................79
3.2.5.3 Numerical results for Strategy (C)......................................81
3.2.6 Summary...........................................................................................81
3.3 Risk Assessment of Life Insurance Contracts: A Comparative Study
in a Levy Framework...................................................................................83
3.3.1 Introduction.......................................................................................83
3.3.2 Model Framework............................................................................85
3.3.2.1 The life insurance contract..................................................85
3.3.2.2 The Black Scholes model for asset prices..........................86
3.3.2.3 A Levy model for asset prices............................................87
3.3.2.4 Option pricing in general Levy models..............................90
3.3.2.5 The Esscher transform........................................................90
3.3.2.6 Calibration to option prices.................................................91
3.3.3 Fair Valuation of Life Insurance Liabilities.....................................93
3.3.3.1 Fair contracts.......................................................................94
3.3.3.2 Decomposition of policyholder claims into building
blocks..................................................................................96
3.3.4 Risk of Fair Contracts under Black Scholes and Levy Process
Specifications..................................................................................100
3.3.5 Sensitivity Analysis and Parameter Risk........................................103
3.3.5.1 Varying the asset volatility...............................................103
3.3.5.2 Varying the initial equity capital......................................105
3.3.6 Summary.........................................................................................106
4 Evaluation of Individual Life Insurance Contracts......................................108
4.1 Assessing the Risk Potential of Premium Payment Options in
Participating Life Insurance Contracts......................................................108
4.1.1 Introduction.....................................................................................108
4.1.2 Model Framework..........................................................................111
4.1.2.1 The basic contract.............................................................111
4.1.2.2 Exercising the paid up option once without
resumption option.............................................................113
4.1.2.3 The resumption option......................................................115
4.1.2.4 Valuation and exercise behavior.......................................117
4.1.3 Numerical Results...........................................................................119
4.1.3.1 Input data..........................................................................119
4.1.3.2 Further procedure and table description...........................120
4.1.3.3 Numerical results given a contract term of 15 years........120
4.1.3.4 Numerical results given a contract term of 30 years........124
4.1.4 Sensitivity of Option Values...........................................................126
4.1.4.1 Figure description.............................................................126
4.1.4.2 Varying the guaranteed interest rate.................................127
4.1.4.3 Varying the annual surplus participation rate...................128
4.1.4.4 Varying the asset volatility...............................................128
4.1.4.5 Varying the risk free interest rate and the contract
term...................................................................................129
4.1.5 Summary.........................................................................................129
4.2 Pricing Premium Payment Options: The Impact of Stochastic
Interest Rates..............................................................................................132
4.2.1 Introduction.....................................................................................132
4.2.2 Model Framework..........................................................................133
4.2.2.1 Modeling the basic contract..............................................133
4.2.2.2 Modeling asset and short rate processes...........................134
4.2.2.3 Valuation...........................................................................135
4.2.3 The Paid up Option.........................................................................137
4.2.3.1 The basic contract with paid up option.............................137
4.2.3.2 Valuation...........................................................................139
4.2.4 Numerical Analysis........................................................................141
4.2.4.1 Simulation procedure........................................................141
4.2.4.2 Numerical results..............................................................142
4.2.4.3 Implications for insurance companies..............................146
4.2.5 Summary.........................................................................................147
5 Summary...........................................................................................................149
Appendix.................................................................................................................152
Bibliography............................................................................................................157
Curriculum Vitae........................................................ ................167
List of Figures
Chapter 1
Figure 1: Motivation of the thesis...........................................................................2
Figure 2: Research objectives and aims of the thesis..............................................4
Chapter 3
Chapter 3.1
Figure 1: PTP Model. Isoquants for a = 10%......................................................46
Figure 2: PTP Model. Risk of fair contracts in Table 2 as a function ofg...........47
Figure 3: CS Model. Isoquants for a = 10%, A,, = 100, En = 10, y = 10%,
T= 10.....................................................................................................51
Figure 4: CS Model. Risk of fair contracts in Table 3 as a function of g for
£0=10withy= 10%.............................................................................53
Figure 5: CS Model. Risk of fair contracts in Table 3 as a function of g for
£0= 0 with y = 10%...............................................................................54
Figure 6: Danish Model. Isoquants for a = 10%, a = 20%, y = 10%.................58
Figure 7: Danish Model. Risk of fair contracts in Table 4 as a function of g
with£,,= 0.............................................................................................59
Chapter 3.3
Figure 1: Empirical log returns of EuroStoxx 50 (green curve) and maximum
likelihood fits of NIG (red) and normal (blue) distributions.................88
Figure 2: Fair contracts under Brownian motion and NIG specifications............96
Figure 3: Decomposition of fair contract value in building blocks under
Brownian motion and NIG specifications for 8 = 40%.........................99
Figure 4: Shortfall probability and expected shortfall of fair contracts in
Figure 2................................................................................................102
Figure 5: Fair contracts and corresponding shortfall probability for 50/50
portfolio (Table 4) and 6 = 40%..........................................................104
Figure 6: Fair contracts and corresponding shortfall probability for £0 = 15
and S = 40%.........................................................................................105
Chapter 4
Chapter 4.1
Figure 1: Additional option values in $ at / = 0 given exercise at maximum
value with respect to the guaranteed interest rate g, annual surplus
participation rate a, asset volatility a, and risk free interest rate r
for a 30 year old male policyholder with contract term of 15
years.....................................................................................................127
Appendix
Figure A. 1: Additional option values at t 0 with respect to the guaranteed
interest rate g, annual surplus participation rate a, and contract term
Tfor a 30 year old male policyholder with contract term of
15 years................................................................................................155
List of Tables
Chapter 2
Table 1: Main individual life insurance policies sold in Europe and the
United States..........................................................................................10
Table 2: Overview of implicit options in life insurance......................................14
Table 3: Main implicit options in life insurance contracts from Table 1............23
Chapter 3
Chapter 3.1
Table 1: Insurance company s balance sheet at time /........................................37
Table 2: PTP Model. Values of £for fair contracts with Aa = 100, k= 80%.....44
Table 3: CS Model. Values of a for fair contracts with y = 10%, T= 10............50
Table 4: Danish Model. Values of £ for fair contracts.........................................57
Chapter 3.2
Table 1: Shortfall risk of fair contracts with fixed safety level d = 9%.............70
Table 2: Influence of Strategies (A), (B), and (C) on fair valuation and
shortfall risk; values at time / = 0..........................................................75
Table 3: Fair valuation given Strategy (A), fixed safety level d* = 9%,
and shortfall risk....................................................................................78
Table 4: Fair valuation given Strategy (B), fixed safety level d = 9%,
and shortfall risk....................................................................................80
Table 5: Fair valuation given Strategy (C), fixed safety level d = 9%,
and shortfall risk...................................................................................80
Chapter 3.3
Table 1: Risk neutral parameters according to Schoutens (2003) and
corresponding risk neutral moments for S P 500 index......................92
Table 2: Risk neutral and real world parameters and moments for a
portfolio with 25% stocks and 75% bonds............................................93
Table 3: Decomposition of fair contract value in building blocks under
Brownian motion and NIG specifications for S = 40%.........................98
Table 4: Risk neutral and real world parameters and moments for a
portfolio with 50% stocks and 50% bonds..........................................104
X
Chapter 4
Chapter 4.1
Table 1: Results for a 30 year old male policyholder with contract term
of 15 years...........................................................................................121
Table 2: Results for a 50 year old male policyholder with contract term
of 15 years...........................................................................................123
Table 3: Results for a 30 year old male policyholder with contract term
of 30 years...........................................................................................125
Chapter 4.2
Table I: Parameters of the reference contract.......................................143
Table 2: Option values in $ and as relative percentages of the present value of
the expected premium payments for a fair basic contract;
modifications with respect to Table 1.................................................144
Appendix
Table A. 1: Results for a 30 year old male policyholder with contract term
of 10 years...........................................................................................152
Table A.2: Results for a 50 year old male policyholder with contract term
of 10 years...........................................................................................153
Table A.3: Results for a 30 year old female policyholder with contract term
of 30 years...........................................................................................154
|
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| spellingShingle | Gatzert, Nadine Verena Implicit options in life insurance valuation and risk assessment Risiko (DE-588)4050129-2 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Wert (DE-588)4065654-8 gnd Mathematik (DE-588)4037944-9 gnd Lebensversicherung (DE-588)4034928-7 gnd Messung (DE-588)4038852-9 gnd |
| subject_GND | (DE-588)4050129-2 (DE-588)4063194-1 (DE-588)4065654-8 (DE-588)4037944-9 (DE-588)4034928-7 (DE-588)4038852-9 (DE-588)4113937-9 |
| title | Implicit options in life insurance valuation and risk assessment |
| title_auth | Implicit options in life insurance valuation and risk assessment |
| title_exact_search | Implicit options in life insurance valuation and risk assessment |
| title_full | Implicit options in life insurance valuation and risk assessment Nadine Verena Gatzert |
| title_fullStr | Implicit options in life insurance valuation and risk assessment Nadine Verena Gatzert |
| title_full_unstemmed | Implicit options in life insurance valuation and risk assessment Nadine Verena Gatzert |
| title_short | Implicit options in life insurance |
| title_sort | implicit options in life insurance valuation and risk assessment |
| title_sub | valuation and risk assessment |
| topic | Risiko (DE-588)4050129-2 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Wert (DE-588)4065654-8 gnd Mathematik (DE-588)4037944-9 gnd Lebensversicherung (DE-588)4034928-7 gnd Messung (DE-588)4038852-9 gnd |
| topic_facet | Risiko Versicherungsmathematik Wert Mathematik Lebensversicherung Messung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016095567&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gatzertnadineverena implicitoptionsinlifeinsurancevaluationandriskassessment |