With the extension of life expectancy, the countries in the whole world must face the fact that aging population brings longevity risk. Longevity risk has put severe impacts on security departments, insurance companies and the governments in the world. Therefore how to manage it effectively has become the focus of study by the academic society. In view of the fact that the research model of longevity bonds has not considered the positive and negative asymmetry jump of population mortality, and in order to hedge the risk of longevity, based on Lee-Carter framework, a double exponential jump diffusion model is introduced to measure the positive and negative asymmetry jump of mortality rates, the interest rate is described with CIR. And in order to make the pricing of bonds closer to the real market, the risk neutral pricing is used to price the bond in the incomplete market. Empirical analysis with the population death data shows that the ability of this model is significantly better than the existing model when measuring longevity risk. Therefore, the use of this model for bond pricing, not only can provide a more reasonable pricing, but also can improve the life insurance companies to deal with the risk of longevity, then can promote the further development of life insurance industry in China.
CHAO Wen, ZOU Hui-wen
. Pricing Longevity Bonds based on Double Exponential Jump Diffusion Model[J]. Chinese Journal of Management Science, 2017
, 25(9)
: 46
-52
.
DOI: 10.16381/j.cnki.issn1003-207x.2017.09.006
[1] 曾燕, 曾庆邹, 康志林. 基于价格调整的长寿风险自然对冲策略[J]. 中国管理科学, 2015, 23(12):11-19.
[2] 汪伟, 刘玉飞. 城镇化进程中农民工融入城乡养老保险体系研究[J]. 中国行政管理, 2016,(6):87-93.
[3] Cairns A J G, Blake D, Dowd K. Pricing death:Frameworks for the valuation and securitization of mortality risk[J]. ASTIN Bulletin:The Journal of the IAA, 2006, 36(1):79-120.
[4] Wills S, Sherris M. Securitization, structuring and pricing of longevity risk[J]. Insurance Mathematics & Economics, 2010, 46(1):173-185.
[5] Wang C W, Yang S S. Pricing survivor derivatives with cohort mortality dependence under the Lee-Carter framework[J]. Journal of Risk and Insurance, 2013, 80(4):1027-1056.
[6] 尚勤, 秦学志, 周颖颖. 死亡强度服从Ornstein-Uhlenbeck跳过程的长寿债券定价模型[J].系统管理学报, 2008,17(3):297-302.
[7] Bauer D, Börger M, Russ J. On the pricing of longevity-linked securities[J]. Insurance Mathematics & Economics, 2010, 46(1):139-149.
[8] Cox S H, Lin Yijia, Pedersen H. Mortality risk modeling:Applications to insurance securitization[J]. Insurance Mathematics & Economics, 2010, 46(1):242-253.
[9] Deng Yinglu, Brockett P L, MacMinn R D. Longevity/Mortality risk modeling and securities pricing[J]. Journal of Risk and Insurance, 2012, 79(3):697-721.
[10] 田梦, 邓颖璐.我国随机死亡率的长寿风险建模和衍生品定价[J].保险研究,2013,(1):14-26.
[11] Kou S G, Wang Hui. Option pricing under a double exponential jump diffusion model[J]. Management Science, 2004, 50(9):1178-1192.
[12] Cox J, Ingersoll J, Ross S. A theory of the term-structure of interest rates[J]. Econometrica, 1985, 53(2):385-408.
[13] 尚勤, 张国忠, 胡友群, 等. 基于Cameron-Martin-Girsanov理论的长寿债券定价模型[J]. 系统管理学报, 2013, 22(4):472-477.
[14] 尚勤. 死亡率关联债券的定价模型与实证研究[D].大连:大连理工大学,2009.
[15] Shang Qin, Qin Xuezhi. Securitization of longevity risk in pension annuities[C]//Proceedings of the 2008 International Conference on Wireless Communications,Networking and Mobile Computing,Dalian,Qctober 12-14,2008.
