Implicit options in life insurance: valuation and risk assessment
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| Language: | English |
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2007
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 167 S. graph. Darst. |
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| 245 | 1 | 0 | |a Implicit options in life insurance |b valuation and risk assessment |c Nadine Verena Gatzert |
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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
|
| adam_txt |
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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| discipline_str_mv | Wirtschaftswissenschaften |
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| id | DE-604.BV022890721 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:53:35Z |
| indexdate | 2024-07-09T21:07:51Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016095567 |
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| physical | XVI, 167 S. graph. Darst. |
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| spelling | Gatzert, Nadine Verena Verfasser aut Implicit options in life insurance valuation and risk assessment Nadine Verena Gatzert 2007 XVI, 167 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier St. Gallen, Univ., Diss., 2007 Risiko (DE-588)4050129-2 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Wert (DE-588)4065654-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Lebensversicherung (DE-588)4034928-7 gnd rswk-swf Messung (DE-588)4038852-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Lebensversicherung (DE-588)4034928-7 s Mathematik (DE-588)4037944-9 s Risiko (DE-588)4050129-2 s Messung (DE-588)4038852-9 s Wert (DE-588)4065654-8 s DE-604 Versicherungsmathematik (DE-588)4063194-1 s DE-188 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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 |
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