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題名 厚尾分配在財務與精算領域之應用
Applications of Heavy-Tailed distributions in finance and actuarial science
作者 劉議謙
Liu, I Chien
貢獻者 黃泓智
Huang, Hong Chih
劉議謙
Liu, I Chien
關鍵詞 隨機死亡率模型
厚尾分配
長壽交換
百慕達選擇權
多元Lévy分配
低偏差網狀法
Stochastic Mortality Models
Heavy-Tailed Distributions
Longevity Swaps
Bermudan Options
Multivariate Lévy Distributions
Low Discrepancy Mesh
日期 2012
上傳時間 1-Nov-2012 13:51:16 (UTC+8)
摘要 本篇論文將厚尾分配（Heavy-Tailed Distribution）應用在財務及保險精算上。本研究主要有三個部分：第一部份是用厚尾分配來重新建構Lee-Carter模型（1992），發現改良後的Lee-Carter模型其配適與預測效果都較準確。第二部分是將厚尾分配建構於具有世代因子（Cohort Factor）的Renshaw and Haberman模型（2006）中，其配適及預測效果皆有顯著改善，此外，針對英格蘭及威爾斯（England and Wales）訂價長壽交換（Longevity Swaps），結果顯示此模型可以支付較少的長壽交換之保費以及避免低估損失準備金。第三部分是財務上的應用，利用Schmidt等人（2006）提出的多元仿射廣義雙曲線分配（Multivariate Affine Generalized Hyperbolic Distributions; MAGH）於Boyle等人（2003）提出的低偏差網狀法（Low Discrepancy Mesh; LDM）來定價多維度的百慕達選擇權。理論上，LDM法的數值會高於Longstaff and Schwartz（2001）提出的最小平方法（Least Square Method; LSM）的數值，而數值分析結果皆一致顯示此性質，藉由此特性，我們可知道多維度之百慕達選擇權的真值落於此範圍之間。
The thesis focus on the application of heavy-tailed distributions in finance and actuarial science. We provide three applications in this thesis. The first application is that we refine the Lee-Carter model (1992) with heavy-tailed distributions. The results show that the Lee-Carter model with heavy-tailed distributions provide better fitting and prediction. The second application is that we also model the error term of Renshaw and Haberman model (2006) using heavy-tailed distributions and provide an iterative fitting algorithm to generate maximum likelihood estimates under the Cox regression model. Using the RH model with non-Gaussian innovations can pay lower premiums of longevity swaps and avoid the underestimation of loss reserves for England and Wales. The third application is that we use multivariate affine generalized hyperbolic (MAGH) distributions introduced by Schmidt et al. (2006) and low discrepancy mesh (LDM) method introduced by Boyle et al. (2003), to show how to price multidimensional Bermudan derivatives. In addition, the LDM estimates are higher than the corresponding estimates from the Least Square Method (LSM) of Longstaff and Schwartz (2001). This is consistent with the property that the LDM estimate is high bias while the LSM estimate is low bias. This property also ensures that the true option value will lie between these two bounds.
參考文獻 Aas, K., Haff, I. H., 2006. The Generalized Hyperbolic Skew Student’s t-distribution. Journal of Financial Econometrics 4, 275-309.
Akaike, H, 1974. A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control AC-19, 716-723.
Amin, K., 1993. Jump Diffusion Option Valuation in Discrete Time. Journal of Finance 48, 1833-1863.
Anderson, T. W., 1962. On the Distribution of the Two-Sample Cramér-Von Mises Criterion. The Annals of Mathematical Statistics 33, 1148-1159.
Barbarin J., 2008. Heath-Jarrow-Morton Modelling of Longevity Bonds and the Risk Minimization of Life Insurance Portfolios. Insurance Mathematics and Economics 43, 41-55.
Barndorff-Nielsen, O. E., 1977. Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society of London 353, 409-419.
Barndorff-Nielsen, O. E., 1978. Hyperbolic distributions and distributions on hyperbolae. Scandinavian Journal of Statistics 5, 151-157.
Barndorff-Nielsen, O. E., 1995. Normal Inverse Gaussian Processes and the Modeling of Stock Returns. Technical Report 300, Department of Theoretical Statistics, Institute of Mathematics.
Barndorff-Nielsen , O. E, Pedersen, J., Sato, K. I., 2001. Multivariate Subordination Self-Decomposability and Stability. Advance Application Probability 33, 160-187.


Barndorff-Nielsen, O. E., Shephard, N., 2001. Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics. Journal of the Royal Statistical Society B 63, 167-241
Bauer, D., 2006. An Arbitrage-Free Family of Longevity Bonds, Discussion Paper, Ulm University.
Biffis, E., 2005. Affine Processes for Dynamic Mortality and Actuarial Valuations. Insurance: Mathematics and economics 37, 443-468.
Biffis, E., Blake, D., Pitotti, L., Sun, A., 2011. The Cost of Counterparty Risk and Collateralization in Longevity Swaps, Pensions Institute Discussion Paper PI-1107, June.
Biffis, E., Denuit, M., Devolder, P., 2010. Stochastic Mortality under Measure Changes. Scandinavian Actuarial Journal 4, 284-311.
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Blake, D., Burrows, W., 2001. Survivor Bonds: Helping to Hedge Mortality Risk. Journal of Risk and Insurance 68, 339-348.
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Blasild, P., Jensen, J. L., 1981. Multivariate Distributions of Hyperbolic Type. In Statistical Distributions in Scientific Work-Proceedings of theNATO Advanced Study Institute held at the Università degli studi di Trieste 4, 45-66.
Bølviken, E., Benth, F. E., 2000. Quantification of Risk in Norwegian Stocks via the Normal Inverse Gaussian Distribution. Proceedings of the AFIA 2000 Colloquium, Tromsø, Norway, 87-98.
Boyle, P. P., Kolkiewicz, A. W., Tan, K. S., 2003. Pricing American Style Options Using Low Discrepancy Mesh Method. Submitted for Publication.
Broadie, M., Glasserman, P., 2004. A Stochastic Mesh Method for Pricing High-Dimensional American Options. Journal of Computational Finance 7, 35-72.
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描述 博士
國立政治大學
風險管理與保險研究所
97358505
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097358505
資料類型 thesis
dc.contributor.advisor 黃泓智zh_TW
dc.contributor.advisor Huang, Hong Chihen_US
dc.contributor.author (Authors) 劉議謙zh_TW
dc.contributor.author (Authors) Liu, I Chienen_US
dc.creator (作者) 劉議謙zh_TW
dc.creator (作者) Liu, I Chienen_US
dc.date (日期) 2012en_US
dc.date.accessioned 1-Nov-2012 13:51:16 (UTC+8)-
dc.date.available 1-Nov-2012 13:51:16 (UTC+8)-
dc.date.issued (上傳時間) 1-Nov-2012 13:51:16 (UTC+8)-
dc.identifier (Other Identifiers) G0097358505en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/55113-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 97358505zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 本篇論文將厚尾分配（Heavy-Tailed Distribution）應用在財務及保險精算上。本研究主要有三個部分：第一部份是用厚尾分配來重新建構Lee-Carter模型（1992），發現改良後的Lee-Carter模型其配適與預測效果都較準確。第二部分是將厚尾分配建構於具有世代因子（Cohort Factor）的Renshaw and Haberman模型（2006）中，其配適及預測效果皆有顯著改善，此外，針對英格蘭及威爾斯（England and Wales）訂價長壽交換（Longevity Swaps），結果顯示此模型可以支付較少的長壽交換之保費以及避免低估損失準備金。第三部分是財務上的應用，利用Schmidt等人（2006）提出的多元仿射廣義雙曲線分配（Multivariate Affine Generalized Hyperbolic Distributions; MAGH）於Boyle等人（2003）提出的低偏差網狀法（Low Discrepancy Mesh; LDM）來定價多維度的百慕達選擇權。理論上，LDM法的數值會高於Longstaff and Schwartz（2001）提出的最小平方法（Least Square Method; LSM）的數值，而數值分析結果皆一致顯示此性質，藉由此特性，我們可知道多維度之百慕達選擇權的真值落於此範圍之間。zh_TW
dc.description.abstract (摘要) The thesis focus on the application of heavy-tailed distributions in finance and actuarial science. We provide three applications in this thesis. The first application is that we refine the Lee-Carter model (1992) with heavy-tailed distributions. The results show that the Lee-Carter model with heavy-tailed distributions provide better fitting and prediction. The second application is that we also model the error term of Renshaw and Haberman model (2006) using heavy-tailed distributions and provide an iterative fitting algorithm to generate maximum likelihood estimates under the Cox regression model. Using the RH model with non-Gaussian innovations can pay lower premiums of longevity swaps and avoid the underestimation of loss reserves for England and Wales. The third application is that we use multivariate affine generalized hyperbolic (MAGH) distributions introduced by Schmidt et al. (2006) and low discrepancy mesh (LDM) method introduced by Boyle et al. (2003), to show how to price multidimensional Bermudan derivatives. In addition, the LDM estimates are higher than the corresponding estimates from the Least Square Method (LSM) of Longstaff and Schwartz (2001). This is consistent with the property that the LDM estimate is high bias while the LSM estimate is low bias. This property also ensures that the true option value will lie between these two bounds.en_US
dc.description.tableofcontents Chapter 1. Introduction 1
Chapter 2. Heavy-Tailed Distributions 11
2.1. Introductions of Heavy-Tailed Distributions 11
2.2. The Standardization Approaches for Heavy-Tailed Distributions 17
2.3. Estimation Scheme with Standardization 20
Chapter 3. A Quantitative Comparison of the Lee-Carter Model under Different Types of Non-Gaussian Innovations 23
3.1. The Lee-Carter Model with Heavy-Tailed Innovations 23
3.2. Empirical Analysis 31
3.3. Conclusions 47
Chapter 4. Mortality Modeling with Non-Gaussian Innovations and Applications to the Valuation of Longevity Swaps 49
4.1. Stochastic Mortality Models with Cox Error Structures 49
4.2. Empirical Analysis 55
4.3. Application: The Valuation of Longevity Swaps 59
4.4. Conclusions and Suggestions 68
Chapter 5. Pricing High-Dimensional Bermudan Options with Lévy Processes Using Low Discrepancy Mesh Methods 71
5.1. Multivariate Affine Generalized Hyperbolic Distributions 71
5.2. Low Discrepancy Mesh (LDM) Method 75
5.3. Empirical and Numerical Analyses 79
5.4. Conclusions 91
Chapter 6. Conclusions 93
Appendix A 97
Appendix B 99
Appendix C 101
Appendix D 103
Appendix E 105
Appendix F 107
References 109		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097358505en_US
dc.subject (關鍵詞) 隨機死亡率模型zh_TW
dc.subject (關鍵詞) 厚尾分配zh_TW
dc.subject (關鍵詞) 長壽交換zh_TW
dc.subject (關鍵詞) 百慕達選擇權zh_TW
dc.subject (關鍵詞) 多元Lévy分配zh_TW
dc.subject (關鍵詞) 低偏差網狀法zh_TW
dc.subject (關鍵詞) Stochastic Mortality Modelsen_US
dc.subject (關鍵詞) Heavy-Tailed Distributionsen_US
dc.subject (關鍵詞) Longevity Swapsen_US
dc.subject (關鍵詞) Bermudan Optionsen_US
dc.subject (關鍵詞) Multivariate Lévy Distributionsen_US
dc.subject (關鍵詞) Low Discrepancy Meshen_US
dc.title (題名) 厚尾分配在財務與精算領域之應用zh_TW
dc.title (題名) Applications of Heavy-Tailed distributions in finance and actuarial scienceen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Aas, K., Haff, I. H., 2006. The Generalized Hyperbolic Skew Student’s t-distribution. Journal of Financial Econometrics 4, 275-309.
Akaike, H, 1974. A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control AC-19, 716-723.
Amin, K., 1993. Jump Diffusion Option Valuation in Discrete Time. Journal of Finance 48, 1833-1863.
Anderson, T. W., 1962. On the Distribution of the Two-Sample Cramér-Von Mises Criterion. The Annals of Mathematical Statistics 33, 1148-1159.
Barbarin J., 2008. Heath-Jarrow-Morton Modelling of Longevity Bonds and the Risk Minimization of Life Insurance Portfolios. Insurance Mathematics and Economics 43, 41-55.
Barndorff-Nielsen, O. E., 1977. Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society of London 353, 409-419.
Barndorff-Nielsen, O. E., 1978. Hyperbolic distributions and distributions on hyperbolae. Scandinavian Journal of Statistics 5, 151-157.
Barndorff-Nielsen, O. E., 1995. Normal Inverse Gaussian Processes and the Modeling of Stock Returns. Technical Report 300, Department of Theoretical Statistics, Institute of Mathematics.
Barndorff-Nielsen , O. E, Pedersen, J., Sato, K. I., 2001. Multivariate Subordination Self-Decomposability and Stability. Advance Application Probability 33, 160-187.


Barndorff-Nielsen, O. E., Shephard, N., 2001. Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics. Journal of the Royal Statistical Society B 63, 167-241
Bauer, D., 2006. An Arbitrage-Free Family of Longevity Bonds, Discussion Paper, Ulm University.
Biffis, E., 2005. Affine Processes for Dynamic Mortality and Actuarial Valuations. Insurance: Mathematics and economics 37, 443-468.
Biffis, E., Blake, D., Pitotti, L., Sun, A., 2011. The Cost of Counterparty Risk and Collateralization in Longevity Swaps, Pensions Institute Discussion Paper PI-1107, June.
Biffis, E., Denuit, M., Devolder, P., 2010. Stochastic Mortality under Measure Changes. Scandinavian Actuarial Journal 4, 284-311.
Bishop, C. M., 2006. Pattern Recognition and Machine Learning. Springer.
Blake, D., Burrows, W., 2001. Survivor Bonds: Helping to Hedge Mortality Risk. Journal of Risk and Insurance 68, 339-348.
Blake, D., Cairns, A. J. G., Coughlan, G., Dowd, K., MacMinn, R., 2012. The New Life Market, Discussion Paper.
Blasild, P., Jensen, J. L., 1981. Multivariate Distributions of Hyperbolic Type. In Statistical Distributions in Scientific Work-Proceedings of theNATO Advanced Study Institute held at the Università degli studi di Trieste 4, 45-66.
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