巨灾风险债券的分析策略及模型构建
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摘要
传统意义上,巨灾风险通常将风险转移给再保险公司来达到避险的目的,巨灾风险债券(Catastrophe Risk Bond)作为一种新型方式,直接将风险转移到资本市场,债券持有人的现金流来源于与某种特别灾害事件(地震、飓风或洪水)相联系的债券。对于巨灾债券这种特殊的债券来说,对其价格的确定相比普通债券要复杂的多,在巨灾债券市场中,市场是不完全的,因此简单运用复制组合的方法是不适用的。论文针对巨灾债券的定价问题,从相关理论出发,发展新方法对巨灾债券进行定价,利用非寿险精算技术分析我国地震损失分布和次数,并在此基础上利用CAPM和债券定价原理计算地震灾害债券的收益率和价格,从而对地震灾害债券作了初步设计。
首先,分析了当前巨灾风险的特点及其不断扩大趋势,论述了传统再保险应对巨灾风险的不足以及巨灾风险证券化的发展动因,并对巨灾风险证券运作方式进行了综述研究。
其次,在Cox & Pedersen均衡定价模型理论基础上,推导出巨灾风险债券定价模型,即用两个模拟现金流对巨灾风险债券的定价机制作一个二叉树的精算分析:单一时期现金流和两时期现金流。
再次,通过对地震样本数据的分析,建立相关的经验分布函数并拟合损失分布,同时对地震发生次数进行拟合,最后根据CAPM来确定巨灾债券不同类型的地震债券的票面利率及债券价格。
最后,在地震次数符合泊松分布的基础上,引入风险模型与复合泊松模型两者之间距离的概念,利用复合泊松分布来拟合巨灾风险模型。
In the traditional sense, the risk of catastrophic risk is usually transferred to the reinsurance company to achieve the purpose of hedging. As a new way, catastrophe risk bond directly transfers the risk to the capital market, the cash of bondholders’flows from the bonds, which associates with particular hazard events, such as earthquakes, hurricanes or floods. To make sure the price of catastrophe risk bond, this particular bond is much more complex than the regular bonds. In the catastrophe bond market, the market is incomplete; therefore, it is not applicable to simply use the method of replication and portfolio. In this paper, for the pricing of catastrophe bonds we developed a new method to the pricing of catastrophe bonds from the relevant theory, used the non-life insurance actuarial technical to analyze the distribution and frequency of earthquake losses in China, and used the CAPM and bond pricing principles to calculate the earthquake bond profit and price on this basis. So we made a preliminary design for bonds earthquake.
Firstly, we analyzed the current characteristics of catastrophic risk and the rapidly increasing trend, discussed the traditional reinsurance dealing with the lack of catastrophic risk and the development of motivation of Catastrophe Risk Securitization, and made a reviewed research for the mode of operation theory of catastrophic risk bonds.
Secondly, based on the theory of the Cox & Pedersen equilibrium pricing model, we deduced the bond pricing model of catastrophic risk. That is, we made a binary tree of actuarial analysis with two simulated cash flow for the pricing mechanism of catastrophic risk bonds: single-period cash flow, and two times cash flow.
Again, through the sample data of the seismic analysis, we established the distribution function of relevant experience, fitted loss distributions, then fitted the number of occurrences of earthquakes, and lastly determined the different types of earthquake catastrophe bond coupon rate bond according to CAPM.
Finally, on the basis of tremors conforming to the Poisson distribution, we introduced the concept of the distance between the of risk models and the compound Poisson model and used the compound Poisson distribution to fit the catastrophe risk model.
首先,分析了当前巨灾风险的特点及其不断扩大趋势,论述了传统再保险应对巨灾风险的不足以及巨灾风险证券化的发展动因,并对巨灾风险证券运作方式进行了综述研究。
其次,在Cox & Pedersen均衡定价模型理论基础上,推导出巨灾风险债券定价模型,即用两个模拟现金流对巨灾风险债券的定价机制作一个二叉树的精算分析:单一时期现金流和两时期现金流。
再次,通过对地震样本数据的分析,建立相关的经验分布函数并拟合损失分布,同时对地震发生次数进行拟合,最后根据CAPM来确定巨灾债券不同类型的地震债券的票面利率及债券价格。
最后,在地震次数符合泊松分布的基础上,引入风险模型与复合泊松模型两者之间距离的概念,利用复合泊松分布来拟合巨灾风险模型。
In the traditional sense, the risk of catastrophic risk is usually transferred to the reinsurance company to achieve the purpose of hedging. As a new way, catastrophe risk bond directly transfers the risk to the capital market, the cash of bondholders’flows from the bonds, which associates with particular hazard events, such as earthquakes, hurricanes or floods. To make sure the price of catastrophe risk bond, this particular bond is much more complex than the regular bonds. In the catastrophe bond market, the market is incomplete; therefore, it is not applicable to simply use the method of replication and portfolio. In this paper, for the pricing of catastrophe bonds we developed a new method to the pricing of catastrophe bonds from the relevant theory, used the non-life insurance actuarial technical to analyze the distribution and frequency of earthquake losses in China, and used the CAPM and bond pricing principles to calculate the earthquake bond profit and price on this basis. So we made a preliminary design for bonds earthquake.
Firstly, we analyzed the current characteristics of catastrophic risk and the rapidly increasing trend, discussed the traditional reinsurance dealing with the lack of catastrophic risk and the development of motivation of Catastrophe Risk Securitization, and made a reviewed research for the mode of operation theory of catastrophic risk bonds.
Secondly, based on the theory of the Cox & Pedersen equilibrium pricing model, we deduced the bond pricing model of catastrophic risk. That is, we made a binary tree of actuarial analysis with two simulated cash flow for the pricing mechanism of catastrophic risk bonds: single-period cash flow, and two times cash flow.
Again, through the sample data of the seismic analysis, we established the distribution function of relevant experience, fitted loss distributions, then fitted the number of occurrences of earthquakes, and lastly determined the different types of earthquake catastrophe bond coupon rate bond according to CAPM.
Finally, on the basis of tremors conforming to the Poisson distribution, we introduced the concept of the distance between the of risk models and the compound Poisson model and used the compound Poisson distribution to fit the catastrophe risk model.
引文
1 J. D. Cummins. An Asian option Approach to the valuation of Insurance Futures Contracts. The Review of Futures Markets, 1993,3(1): 518-521
2 S. J. Johnson. Catastrophe Risk Securitization. Journal of insurance Regulation, 2000 (19): 3-25
3 A. D. Neil. The Limited Financing of Catastrophe Risk. An Overview. Nber Working Paper, 2004,23(3): 23-28
4徐爱荣.论保险业的证券化发展趋势.上海保险, 2002(1):13-15
5 J. D. Cummins. Pricing Catastrophe Insurance Futures and Call Spread. An Arbitrage Approach, Journal of Fixed Income, 1995(2): 66-85
6 S. Cox. The Evolving Market for Catastrophic Event Risk. NBER Working Paper, 1999(3): 72-87
7 E .P .Briys. Catastrophe Risk Bonds. Astin/afir Colloquia, Cairns, Australia. 1997: 117-140
8 E. V. Vict. From Genoa to Kobe. Natural Hazards. Insurance Risks and the Pricing of Insurance-Linked Bonds, London, Lehman Brothers International, 1997(3): 56-66
9魏敏杰,纪昌明.洪水保险债券的运作机制与发展思路.水科学进展, 2004(1)
10 Insurance Industry Catastrophe Management Practices. work Paper,http:// www. actuary.org
11李永平.美国巨灾风险证券化创新及其对我国的启示.万方数据库,2000(1): 7-18
12中国地震信息网,官方网站地址:www.csi.ac.cn
13 R. Swiss Sigma. 2003. www.csi.ac.cn
14 R. Swiss Sigma .2004. www.csi.ac.cn
15 R. Swiss. Too Little Reinsurance of Natural Disasters In Many Markets,Sigma. 1997 (7): 13-9
16 C. Sam, H.Pedersen. Catastrophe Risk Bonds. North American Actuarial Journal, 2001(5): 52-61
17国务院新闻办公室6月30日下午根据国务院抗震救灾总指挥部授权发布数字.新华网, 2008年6月30日. http: //news. xinhuanet . com
18汤白露.汶川大地震损失估计达5000亿元. 21世纪经济报道. 2008(5):1-21
19国务院关于抗击低温雨雪冰冻灾害及灾后重建工作情况的报告, 2008(4): 2-16 http: //npc. people. com. cn
20国务院新闻办公室6月30日下午根据国务院抗震救灾总指挥部授权发布数字.新华网, 2008,6,30. http: //news. xinhuanet. com
21张潇.地震灾害损失已超500亿,凸现巨灾保险缺失.金羊网, 2008(5). www.ycwb. com
22杨元明.财产保险业的发展及营销模式探讨. www. hiia. com. cn/upload/yym. doc, 2007(12)
23栾存存.巨灾风险的保险研究与应对策略综述http://www1.cei.gov.cn/union/ doc/ lhcasrep/200305292403.htm
24裴光.中国保险业竞争力研究.中国金融出版社. 2002
25施方,俞自由.巨灾保险的资本市场选择.中国保险. 2003(6): 42-43
26韩天雄,陈建华.巨灾风险证券化产品的定价问题.保险研究. 2003(12): 31-33
27魏敏杰,田玲.巨灾风险证券化及在中国保险市场的应用.科技进步策. 2003(10): 173-175
28小哈罗德,斯凯博.国际风险与保险:环境管理分析.机械工业出版社, 1999: 245-316
29李扬,王国刚,何德旭.中国金融理论前沿.社会科学文献出版社, 2001(2): 176-198
30张超英,翟祥辉.资产证券化.经济科学出版社, 1998
31陆晰镇,陈伟忠.保险风险证券化—巨灾风险债券.华东经济管理, 2003(8): 111-113
32陶正如,陶夏新.地震巨灾风险债券雏议.自然灾害学报, 2004(6):138-143
33周伏平.巨灾风险证券研究.财经研究, 2002(28):36-41.
34杨大楷.资产定价理论.上海财经大学出版社, 2004(2): 23-30
35张洪涛.非寿险精算.中国人民大学出版社, 2004(3):14-35
36王新军.财产保险中损失分布建模的方法性研究.统计研究,2002(19):40-43
37田玲,向飞.基于风险定价框架的巨灾债券定价模型比较研究.武汉大学学报, 2006(2):2-11
38周志刚.世界巨灾再保险市场的最新动态.上海保险, 2005(5): 21-36
39朱军勇,迟晓英.巨灾债券基于比较优势和运行原理的分析.保险研究, 2005 (2): 9-32
40李勇权.巨灾风险证券化的需求与发展分析.保险研究, 2005(8): 1-9
41肖文,孙明波.西方保险风险证券化的运作方式.保险研究, 2004(3): 9-21
42施方.巨灾保险证券化的探讨.上海大学学报, 2004(1):2-10
43王晓炜.巨灾基金及相关会计的建立初探.现代财经, 2007, 27(5): 48-52.
44李永.巨灾给我国造成的经济损失与补偿机制研究.华北地震科学, 2007(1): 6-10
45徐为山,谢跃.保险风险证券化的发展前景.保险研究, 2004 (7): 52-54.
46翟慎刚.我国保险风险证券化可行性研究.江苏广播电视大学学报, 2008(1):1-20
47闫石.农业巨灾风险证券化.济南金融, 2005(6) : 50-51
48俞自由.保险风险证券化的障碍.中国保险, 2003 (3): 1-9
49赵圆媛.化零为整地震呼唤巨灾风险证券化.四川日报, 2008(7): 9-12
50胡小晖,范改潮.陕西省灾害保险赔案分析及防灾减灾.灾害学, 2000(3): 85-89
51谢家智.我国自然灾害损失补偿机制研究.自然灾害学报, 2004(4): 28-32
52 V. J. Bnatwal , H. C. Kunreuther. A Cat Bond Premium Puzzle.wharton School, 1999 (4): 155-160
53 M. A. Boose , A. S. Graham. An Examiniation of the Futures Market of Catastrophe Insurance. The Journal of Insurance Issues, 1996(2):23-45
54 E. Briys. From Genoa to Kobe: Natural Hazards,Insurance Risk and the Pricing of Insurance-Linked Bonds. London Lehman Brother International, 1997(4): 96-113
55 D. C. Croson ,H. C. Kunreuther . Customizing indemnity contracts and indexed cat bonds for natural hazard risks. Journal of Risk Finance, 2000(3) :24-42
56 P. Poncet, V. E. Vaugirard. The pricing of insurance - linked securities under interest rate uncertainty. Journal of Risk Finance, 2002(3): 48-59
57 V. E.Vaugirard. Pricing catastrophe bonds by an arbitrage approach. The QuarterlyReview of Economics and Finance, 2003(4): 119-132
58 S. Simon, M. J. Goovaerts, J. Dhaene. An easy computable upper bound for the price of an arithmetic Asian option. Insurance:Mathematics&Economics, 2000:175-184
59 J. Vecer. A new PDE approach for pricing arithmetic average Asian options. Journal of Computational Finance, 2001(4): 105-113
60 V. R. Young. Pricing in an incomplete market with an affine term structure. Journal of Finance, 2004(3): 359-381
61 J. Lee , M. Yu. Variation of catastrophe reinsurance with catastrophe bonds Insurance Mathematics and Economics, 2007(2): 160-110
62 C. M. Ghee. The catastrophe bond market at year-end 2003. Guy Carpenter and Com- pany, Inc, MMC Security Corporation, 2004(6): 35-47
63 S. Cox, H.Pedersen. Catastrophe risk bonds. North American Actuarial Journal, 2000 (48): 56-82
64 A. M. Murmann. Pricing Catastrophe Insurance Derivatives. The Wharton School, 2001(6): 264-269
65 R. Swiss. Economic Research & Consulting, sigma,2005(3)
66 R. Swiss. Economic Research & Consulting, sigma,2002(3)
67 R. Swiss. Economic Research & Consulting, sigma,2001(8)
68 H. Louberge, E. Kellezi, M. Gilli. Using Catastrophe-linked Securities to Diversity Insurance Risk. A Financial Analysis of Cat Bonds. Journal of Insurance Issues, 1999 (22): 125-146
69 P. Carayannopoulos, P. Kovace. Insurance Securitization-Catastrophic event exposure and the role of insurance linked securities in addressing risk. ICLR Research ,2003(1) 89-97
70 N. A. Doherty. Insurance Contracts and Securitization. Journal of Risk and Insurance. 2002(69): 45-62
71 E. Briys, Y. Kahane, Y. Kroll. Voluntary insurance coverage compulsory insuranceand risk less Portfolio opportunities. Journal of Risk and Insurance. 1988(4): 713-722
2 S. J. Johnson. Catastrophe Risk Securitization. Journal of insurance Regulation, 2000 (19): 3-25
3 A. D. Neil. The Limited Financing of Catastrophe Risk. An Overview. Nber Working Paper, 2004,23(3): 23-28
4徐爱荣.论保险业的证券化发展趋势.上海保险, 2002(1):13-15
5 J. D. Cummins. Pricing Catastrophe Insurance Futures and Call Spread. An Arbitrage Approach, Journal of Fixed Income, 1995(2): 66-85
6 S. Cox. The Evolving Market for Catastrophic Event Risk. NBER Working Paper, 1999(3): 72-87
7 E .P .Briys. Catastrophe Risk Bonds. Astin/afir Colloquia, Cairns, Australia. 1997: 117-140
8 E. V. Vict. From Genoa to Kobe. Natural Hazards. Insurance Risks and the Pricing of Insurance-Linked Bonds, London, Lehman Brothers International, 1997(3): 56-66
9魏敏杰,纪昌明.洪水保险债券的运作机制与发展思路.水科学进展, 2004(1)
10 Insurance Industry Catastrophe Management Practices. work Paper,http:// www. actuary.org
11李永平.美国巨灾风险证券化创新及其对我国的启示.万方数据库,2000(1): 7-18
12中国地震信息网,官方网站地址:www.csi.ac.cn
13 R. Swiss Sigma. 2003. www.csi.ac.cn
14 R. Swiss Sigma .2004. www.csi.ac.cn
15 R. Swiss. Too Little Reinsurance of Natural Disasters In Many Markets,Sigma. 1997 (7): 13-9
16 C. Sam, H.Pedersen. Catastrophe Risk Bonds. North American Actuarial Journal, 2001(5): 52-61
17国务院新闻办公室6月30日下午根据国务院抗震救灾总指挥部授权发布数字.新华网, 2008年6月30日. http: //news. xinhuanet . com
18汤白露.汶川大地震损失估计达5000亿元. 21世纪经济报道. 2008(5):1-21
19国务院关于抗击低温雨雪冰冻灾害及灾后重建工作情况的报告, 2008(4): 2-16 http: //npc. people. com. cn
20国务院新闻办公室6月30日下午根据国务院抗震救灾总指挥部授权发布数字.新华网, 2008,6,30. http: //news. xinhuanet. com
21张潇.地震灾害损失已超500亿,凸现巨灾保险缺失.金羊网, 2008(5). www.ycwb. com
22杨元明.财产保险业的发展及营销模式探讨. www. hiia. com. cn/upload/yym. doc, 2007(12)
23栾存存.巨灾风险的保险研究与应对策略综述http://www1.cei.gov.cn/union/ doc/ lhcasrep/200305292403.htm
24裴光.中国保险业竞争力研究.中国金融出版社. 2002
25施方,俞自由.巨灾保险的资本市场选择.中国保险. 2003(6): 42-43
26韩天雄,陈建华.巨灾风险证券化产品的定价问题.保险研究. 2003(12): 31-33
27魏敏杰,田玲.巨灾风险证券化及在中国保险市场的应用.科技进步策. 2003(10): 173-175
28小哈罗德,斯凯博.国际风险与保险:环境管理分析.机械工业出版社, 1999: 245-316
29李扬,王国刚,何德旭.中国金融理论前沿.社会科学文献出版社, 2001(2): 176-198
30张超英,翟祥辉.资产证券化.经济科学出版社, 1998
31陆晰镇,陈伟忠.保险风险证券化—巨灾风险债券.华东经济管理, 2003(8): 111-113
32陶正如,陶夏新.地震巨灾风险债券雏议.自然灾害学报, 2004(6):138-143
33周伏平.巨灾风险证券研究.财经研究, 2002(28):36-41.
34杨大楷.资产定价理论.上海财经大学出版社, 2004(2): 23-30
35张洪涛.非寿险精算.中国人民大学出版社, 2004(3):14-35
36王新军.财产保险中损失分布建模的方法性研究.统计研究,2002(19):40-43
37田玲,向飞.基于风险定价框架的巨灾债券定价模型比较研究.武汉大学学报, 2006(2):2-11
38周志刚.世界巨灾再保险市场的最新动态.上海保险, 2005(5): 21-36
39朱军勇,迟晓英.巨灾债券基于比较优势和运行原理的分析.保险研究, 2005 (2): 9-32
40李勇权.巨灾风险证券化的需求与发展分析.保险研究, 2005(8): 1-9
41肖文,孙明波.西方保险风险证券化的运作方式.保险研究, 2004(3): 9-21
42施方.巨灾保险证券化的探讨.上海大学学报, 2004(1):2-10
43王晓炜.巨灾基金及相关会计的建立初探.现代财经, 2007, 27(5): 48-52.
44李永.巨灾给我国造成的经济损失与补偿机制研究.华北地震科学, 2007(1): 6-10
45徐为山,谢跃.保险风险证券化的发展前景.保险研究, 2004 (7): 52-54.
46翟慎刚.我国保险风险证券化可行性研究.江苏广播电视大学学报, 2008(1):1-20
47闫石.农业巨灾风险证券化.济南金融, 2005(6) : 50-51
48俞自由.保险风险证券化的障碍.中国保险, 2003 (3): 1-9
49赵圆媛.化零为整地震呼唤巨灾风险证券化.四川日报, 2008(7): 9-12
50胡小晖,范改潮.陕西省灾害保险赔案分析及防灾减灾.灾害学, 2000(3): 85-89
51谢家智.我国自然灾害损失补偿机制研究.自然灾害学报, 2004(4): 28-32
52 V. J. Bnatwal , H. C. Kunreuther. A Cat Bond Premium Puzzle.wharton School, 1999 (4): 155-160
53 M. A. Boose , A. S. Graham. An Examiniation of the Futures Market of Catastrophe Insurance. The Journal of Insurance Issues, 1996(2):23-45
54 E. Briys. From Genoa to Kobe: Natural Hazards,Insurance Risk and the Pricing of Insurance-Linked Bonds. London Lehman Brother International, 1997(4): 96-113
55 D. C. Croson ,H. C. Kunreuther . Customizing indemnity contracts and indexed cat bonds for natural hazard risks. Journal of Risk Finance, 2000(3) :24-42
56 P. Poncet, V. E. Vaugirard. The pricing of insurance - linked securities under interest rate uncertainty. Journal of Risk Finance, 2002(3): 48-59
57 V. E.Vaugirard. Pricing catastrophe bonds by an arbitrage approach. The QuarterlyReview of Economics and Finance, 2003(4): 119-132
58 S. Simon, M. J. Goovaerts, J. Dhaene. An easy computable upper bound for the price of an arithmetic Asian option. Insurance:Mathematics&Economics, 2000:175-184
59 J. Vecer. A new PDE approach for pricing arithmetic average Asian options. Journal of Computational Finance, 2001(4): 105-113
60 V. R. Young. Pricing in an incomplete market with an affine term structure. Journal of Finance, 2004(3): 359-381
61 J. Lee , M. Yu. Variation of catastrophe reinsurance with catastrophe bonds Insurance Mathematics and Economics, 2007(2): 160-110
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63 S. Cox, H.Pedersen. Catastrophe risk bonds. North American Actuarial Journal, 2000 (48): 56-82
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