臺灣博碩士論文加值系統

保險公司以及退休基金面臨死亡率波動造成的風險，所以如何正確地衡量及控管此風險變成一個很重要的課題。本論文利用跳躍式的隨機方程來模型化死亡率，並以死亡率的歷史資料估計模型中的參數。本論文的實證結果發現，死亡率呈現跳躍的現象。此外，為了訂價死亡率的衍生性商品，本研究利用王氏轉換來轉換機率分配，以求得風險中立下的死亡率隨機過程，進一步對死亡率連動債/存活率連動債券以及存活交換等兩種商品做訂價分析。

The insurance and the pension fund providers face the mortality risks. How to accurately measure and manage the mortality risks becomes a main issue for them. In this study, we use a jump-diffusion process to model the mortality rate and show that the mortality rate exhibits the jump property in the mortality trend. Adopting to the multivariate exponential tilting and the Wang transform, we can neutralize the mortality rate distribution for pricing purposes. We show how to price two major types of the mortality derivatives in our method.

ABSTRACT ……………………………………………………………iv
LIST OF FIGURES ……………………………………………………………vi
LIST OF TABLES ……………………………………………………………vii
1 Introduction……………………………………………1
2 Literature Review…………………………………… 5
3 Model Assumption………………………………………8
3.1 Definition of the Mortality Rate and the Survivor Rate 8
3.2 Mortality Rate Data……………………………………9
3.3 The Mortality Rate Model 15
3.4 Maximum Likelihood Estimation 17
4 Incomplete Market Pricing Method…………………23
4.1 Methodology…………………………………………… 23
4.2 Risk-Neutralized Distribution…………………… 25
5 Pricing and Analysis…………………………………29
5.1 Mortality and Longevity Bond (MLB)…………………29
5.2 Vanilla Survivor Swap…………………………………43
6 Conclusion………………………………………………52
REFERENCES ……………………………………………………………55
Appendix A ……………………………………………………………56
Appendix B ………………………………………………………… 57

[1] Bauer, D., Ruß J., 2006, "Pricing Longevity Bonds using Implied Survival Probabilities", Working paper, April 2006.
[2] Blake, D., A.J.G. Cairns, and K. Dowd, "Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities", Discussed at the Faculty of Actuaries on 16 January, 2006 and at the Institute of Actuaries on 27 February, 2006.
[3] Cairns, A. J. G., D. Blake, and K. Dowd, "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk", ASTIN Bulletin, 36(1):79-120, 2006.
[4] Cox, S. H.,Y. Lin and S. Wang, "Multivariate Exponential Tilting and Pricing Implication for Mortality Securitization", Journal of Risk and Insurance, Vol 73, 4, pp. 719-736, Dec 2006.
[5] Dowd, K., "Survivor Bonds: A Comment on Blake and Burrows", Journal of Risk and Insurance, 70: 339-348, 2003.
[6] Dowd, K., Blake, D., Cairns, A. J. G. and Dawson, P., "Survivor Swaps", Journal of Risk and Insurance, Vol 73, 1, pp.1-17, 2006.
[7] Lin, Y. and Cox, S.H., "Securitization of Mortality Risks in Life Annuities", Journal of Risk and Insurance, Vol 72, 2, pp.227-252, 2005.
[8] Lin, Y. and Cox, S.H., "Securitization of Catastrophe Mortality Risks", Working paper, January 2006.
[9] Madan, D., and H. Unal, 2004, "Risk-Neutralizing Statistical Distributions: With an Application to Pricing Reinsurance Contracts on FDIC Losses". FDIC Center for Financial Research, Working paper no.2004-01, September 2004.
[10] Merton, R. C, "Option Pricing when Underlying Stock Returns Are Discontinuous". J. Financial Economic. 3 125-144, 1976.
[11] Wang, S.S, "A Class of Distribution Operators for Pricing Financial and Insurance Risks", Journal of Risk and Insurance, Vol. 67, 1, pp.15-36, 2000.
[12] Wang, S.S, "Normalized Exponential Tilting: Pricing and Measuring Multivariate Risks". Available at http://www.ermii.org/Research/Multivariate Exponential Tilting 01-08-2006.pdf.