巨灾风险证券化下的再保险合同定价分析
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摘要
近年来全球范围内巨灾发生的频率不断上升,灾难损失越来越严重,传统的再保险业务越来越不能满足风险分散的需求。于是巨灾风险证券化应运而生,并逐渐被再保险公司视为未来解决巨灾风险的有效手段。目前,国内外对风险证券化的产物--巨灾衍生品如何影响再保险公司的再保险合同价值及其违约风险的研究还比较少,主要是停留在理论的定性研究上,很少建立具体的模型来计算再保险公司因发行巨灾衍生品而带来的再保险合同的价值、违约风险、基差风险、利率风险的变化。
本文选择巨灾风险证券化产品中交易最为活跃和最有发展潜力的产品--指数巨灾债券作为主要分析对象,建立了再保险合同定价的模型,并给出了在无风险测度下资产价值、负债、利率、巨灾损失的随机过程。本文并没有具体给出再保险合同价格的闭型表达式,而是通过蒙特卡罗模拟法模拟得到了再保险合同的无违约风险价格、违约风险贴水、基差风险贴水、利率风险贴水等,并讨论了指数型巨灾债券如何提高再保险公司合同价值并减小再保险公司的违约风险。最后,本文还给出了当市场有套利时指数型巨灾期权和巨灾债券的保险精算定价方法,该方法比传统的无套利定价法适用面更广
本研究能为巨灾债券需求动因的研究提供理论支持,能够科学指导再保险公司通过发行巨灾债券进行积极违约风险管理和利率风险管理,进而实现再保险公司再保险合同价值提高和偿付能力提高。同时本文研究结果还为再保险公司发行巨灾衍生品提供了定价保障,对于加深巨灾风险证券化认识,继而推动保险风险证券化的发展,具有较强的理论及实践指导意义。
Recent years, catastrophe disasters happen more and more frequent, which can cause substantial financial losses. However traditional reinsurance can't satisfy the basic need of reinsurance companies to diversify and transfer catastrophe risk. In this case, insurance-linked securities are invented as an important financial innovation to transfer risk from insurance markets to financial markets. Recently, little research has done to discuss the impact of the issue of CAT bonds on the reinsurance contract' valuation and default risk. Most of the former study is conducted qualitatively, and never build the models to compute the change of the values of reinsurance contract, default risk, basic risk, and interest risk after issuing the CAT bonds.
In this paper, we select the Indexed CAT bond which is the most active and promising in the insurance-linked securities markets as our major research object. We build the models to value the reinsurance contracts and get the asset, liability, interest, and catastrophe loss processes under the risk-neutral measure. We haven't get the closed form formula of the valuation, however we use the Monte Carlo simulation method to compute the value of the reinsurance contract with no default risk, default risk premium, basic risk premium, interest risk premium, and examine how a reinsurance company can increase the value of a reinsurance contract and reduce its default risk by issuing catastrophe bonds. At last, we use the actuarial approach to price the indexed option and bonds, this approach can be used in an arbitrage, none equilibrium or incomplete market.
The results of this paper can support the research "the requirement of the issuing of CAT bonds" in theory, and it can guide the reinsurance companies'default risk management and interest risk management through issuing CAT bonds, so as to increase the value of the reinsurance contracts. At the same time, it provides a reasonable basis for the valuation of catastrophe derivate products, and it has great meanings on intensify the knowledge of insurance-linked securities.
本文选择巨灾风险证券化产品中交易最为活跃和最有发展潜力的产品--指数巨灾债券作为主要分析对象,建立了再保险合同定价的模型,并给出了在无风险测度下资产价值、负债、利率、巨灾损失的随机过程。本文并没有具体给出再保险合同价格的闭型表达式,而是通过蒙特卡罗模拟法模拟得到了再保险合同的无违约风险价格、违约风险贴水、基差风险贴水、利率风险贴水等,并讨论了指数型巨灾债券如何提高再保险公司合同价值并减小再保险公司的违约风险。最后,本文还给出了当市场有套利时指数型巨灾期权和巨灾债券的保险精算定价方法,该方法比传统的无套利定价法适用面更广
本研究能为巨灾债券需求动因的研究提供理论支持,能够科学指导再保险公司通过发行巨灾债券进行积极违约风险管理和利率风险管理,进而实现再保险公司再保险合同价值提高和偿付能力提高。同时本文研究结果还为再保险公司发行巨灾衍生品提供了定价保障,对于加深巨灾风险证券化认识,继而推动保险风险证券化的发展,具有较强的理论及实践指导意义。
Recent years, catastrophe disasters happen more and more frequent, which can cause substantial financial losses. However traditional reinsurance can't satisfy the basic need of reinsurance companies to diversify and transfer catastrophe risk. In this case, insurance-linked securities are invented as an important financial innovation to transfer risk from insurance markets to financial markets. Recently, little research has done to discuss the impact of the issue of CAT bonds on the reinsurance contract' valuation and default risk. Most of the former study is conducted qualitatively, and never build the models to compute the change of the values of reinsurance contract, default risk, basic risk, and interest risk after issuing the CAT bonds.
In this paper, we select the Indexed CAT bond which is the most active and promising in the insurance-linked securities markets as our major research object. We build the models to value the reinsurance contracts and get the asset, liability, interest, and catastrophe loss processes under the risk-neutral measure. We haven't get the closed form formula of the valuation, however we use the Monte Carlo simulation method to compute the value of the reinsurance contract with no default risk, default risk premium, basic risk premium, interest risk premium, and examine how a reinsurance company can increase the value of a reinsurance contract and reduce its default risk by issuing catastrophe bonds. At last, we use the actuarial approach to price the indexed option and bonds, this approach can be used in an arbitrage, none equilibrium or incomplete market.
The results of this paper can support the research "the requirement of the issuing of CAT bonds" in theory, and it can guide the reinsurance companies'default risk management and interest risk management through issuing CAT bonds, so as to increase the value of the reinsurance contracts. At the same time, it provides a reasonable basis for the valuation of catastrophe derivate products, and it has great meanings on intensify the knowledge of insurance-linked securities.
引文
[1]寇锦玮、代佳、冯莉花、难庆举,“巨灾保险风险分散工具--指数巨灾债券和再保险”,2004年
[2]洪哲,“保险风险证券化初探”,现代财经,2004年第3期：15-18
[3]李勇权,《巨灾风险证券化研究》,中国财政经济出版社,2005年1月
[4]李勇权,“论保险风险证券化在我国的引入与发展”,保险研究,2003年第5期：41-43
[5]田玲、王萍,“巨灾风险债券的经济学分析”,数量经济技术经济研究,2003年第11期：45-49.
[6]奕存存：“巨灾风险的保险研究与应对策略综述”,经济学动态,2003年第8期：12-17
[7]亲存存：“保险证券化”,中国社会科学院经济研究所研究报告(2003年),
[8]滕帆,“巨灾债券及其在保险公司风险管理中的应用”,外国经济与管理,2002年第2期：33-37
[9]徐为山、谢跃：“保险风险证券化发展前景及对我国保险业启示”,保险研究,2004年第7期
[10]许丁元,“巨灾债券移转风险之研究”,国立中央大学土木研究所硕士论文,2005年7月
[11]韩天雄,陈建华,巨灾风险证券化产品的定价问题[J]。保险研究,2003,(12)：31-34.
[12]HELYETTE GEMAN, YOR M. Bessel Process, Asian Options, and Perpetuities [J].Mathematical Finance,1993,(4):349-375.
[13]CUMMINS J D, GEMANH. Pricing Catastrophe Insurance Futures and Call Spreads:An Arbitrage Approach [J] Journal of Fixed Income,1995, (1):46-57.
[14]CLAUS VORMCHRISTENSEN, HANSPETER SCHMIDLI. Pricing Catastrophe Insurance Products Based on Actually Reported Claims [J].Insurance:Mathematics and Economics,2000,27(2):189-200.
[15]KNUTAASE. An Equilibrium Model of Catastrophe Insurance Futures and Spreads [J].The GENEVA Papers on Risk and Insurance Theory,1999, 24(1):69-96.
[16]BLADTM, RDBERGTH. An Actuarial Approach to Option Pricing under the Physical Measure and Without Market Assumptions [J].Insurance:Mathematics and Economics,1998,22(1):65-73.
[17]VICTOR E VAUGIRARD. Pricing Catastrophe Bonds by an Arbitrage Approach [J].The Quarterly Review of Economics and Finance,2003,43(1):119-132.
[18]Bowers, N.L., Gerber, J.H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J., 1986.Actuarial Mathematics. Society of Actuaries, Itasca,Ⅲ.
[19]Chang, C, Chang, J.S., Yu, M.-T.,1996. Pricing catastrophe insurance futures call spreads:A randomized operational time approach. Journal of Risk and Insurance 63,599-617.
[20]Chang, J.S.K., Chueng, C.S., Krinsky, I.,1989. On the derivation of reinsurance premiums. Insurance:Mathematics and Economics 8 (2),137-144.
[21]Croson, D.C., Kunreuther, H.C.,2000. Customizing indemnity contracts and indexed cat bonds for natural hazard risks. Journal of Risk Finance 1,24-41.
[22]Cox, J., Ingersoll, J., Ross, S.,1985. The term structure of interest rates. Econometric 53,385-407.
[23]Cox, S.H., Pederson, H.W.,2000. Catastrophe risk bonds. North American Actuarial Journal 4,56-82.
[24]Cox, S.H., Schwebach, R.G.,1992. Insurance futures and hedging insurance price risk. Journal of Risk and Insurance 59,628-644.
[25]Cummins, J.D.,1988. Risk-based premiums for insurance guaranty funds. Journal of Finance 43,593-607.
[26]Cummins, J.D., Doherty, N., Lo, A.,2002. Can insurers pay for the "big one"? Measuring the capacity of insurance market to respond to catastrophic losses. Journal of Banking and Finance 26,557-583.
[27]Cummins, J.D., Lalonde, D., Phillips, R.D.,2004. The basis risk of catastrophic-loss index securities. Journal of Financial Economics 71,77-111.
[28]Cummins, J.D., Lewis, C.M., Phillips, R.D.,1999. Pricing excess of loss reinsurance contracts against catastrophic loss. In:Froot, K. (Ed.), The Financing of Catastrophe Risk. The University of Chicago Press, Chicago.
[29]Cummins, J.D., Geman, H.,1995. Pricing catastrophe futures and call spreads: An arbitrage approach. Journal of Fixed Income (March),46-57.
[30]Duan, J.-C., Moreau, A., Sealey, C.W.,1995. Deposit insurance and bank interest rate risk:Pricing and regulatory implications. Journal of Banking and Finance 19,1091-1108.
[31]Duan, J., Simonato, J.,1999. Estimating and testing exponential-affine term structure models by Kalman filter. Review of Quantitative Finance and Accounting 13,111-135.
[32]Duan, J.-C., Yu, M.-T.,2005. Fair insurance guaranty premium in the presence of risk-based capital regulations, stochastic interest rat and catastrophe risk. Journal of Banking and Finance 29 (10),2435-2454.
[33]Froot, K.A. (Ed.),1999. The Financing of Catastrophe Risk. University of Chicago Press, Chicago.
[34]Froot, K.A.,2001. The market for catastrophe risk:A clinical examination. Journal of Financial Economics 60 (2),529-571.
[35]Harrington, S.E., Niehaus, G,1999. Basis risk with PCS catastrophe insurance derivative contracts. Journal of Risk and Insurance 66,49-82.
[36]Harrington, S.E., Niehaus, G.,2003. Capital, corporate income taxes, and catastrophe insurance. Journal of Financial Intermediation 12 (4),365-389.
[37]Lee, J.-P., Yu, M.-T.,2002. Pricing default-risky CAT bonds with moral hazard and basis risk. Journal of Risk and Insurance 69 (1),25-44.
[38]Lewis, C.M.. Murdock, K.C.,1996. The role of government contracts in discretionary reinsurance market for natural disasters. Journal of Risk and Insurance 63,567-597.
[39]Merton, R.,1976. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3,125-144.
[40]Merton, R.,1977. An analytic derivation of the cost of deposit insurance and loan guarantee. Journal of Banking and Finance 1,3-11.
[41]Naik, V., Lee, M.,1990. General equilibrium pricing of options on the market portfolio with discontinuous returns. Review of Financial Studies 3(4),493-521.
[2]洪哲,“保险风险证券化初探”,现代财经,2004年第3期：15-18
[3]李勇权,《巨灾风险证券化研究》,中国财政经济出版社,2005年1月
[4]李勇权,“论保险风险证券化在我国的引入与发展”,保险研究,2003年第5期：41-43
[5]田玲、王萍,“巨灾风险债券的经济学分析”,数量经济技术经济研究,2003年第11期：45-49.
[6]奕存存：“巨灾风险的保险研究与应对策略综述”,经济学动态,2003年第8期：12-17
[7]亲存存：“保险证券化”,中国社会科学院经济研究所研究报告(2003年),
[8]滕帆,“巨灾债券及其在保险公司风险管理中的应用”,外国经济与管理,2002年第2期：33-37
[9]徐为山、谢跃：“保险风险证券化发展前景及对我国保险业启示”,保险研究,2004年第7期
[10]许丁元,“巨灾债券移转风险之研究”,国立中央大学土木研究所硕士论文,2005年7月
[11]韩天雄,陈建华,巨灾风险证券化产品的定价问题[J]。保险研究,2003,(12)：31-34.
[12]HELYETTE GEMAN, YOR M. Bessel Process, Asian Options, and Perpetuities [J].Mathematical Finance,1993,(4):349-375.
[13]CUMMINS J D, GEMANH. Pricing Catastrophe Insurance Futures and Call Spreads:An Arbitrage Approach [J] Journal of Fixed Income,1995, (1):46-57.
[14]CLAUS VORMCHRISTENSEN, HANSPETER SCHMIDLI. Pricing Catastrophe Insurance Products Based on Actually Reported Claims [J].Insurance:Mathematics and Economics,2000,27(2):189-200.
[15]KNUTAASE. An Equilibrium Model of Catastrophe Insurance Futures and Spreads [J].The GENEVA Papers on Risk and Insurance Theory,1999, 24(1):69-96.
[16]BLADTM, RDBERGTH. An Actuarial Approach to Option Pricing under the Physical Measure and Without Market Assumptions [J].Insurance:Mathematics and Economics,1998,22(1):65-73.
[17]VICTOR E VAUGIRARD. Pricing Catastrophe Bonds by an Arbitrage Approach [J].The Quarterly Review of Economics and Finance,2003,43(1):119-132.
[18]Bowers, N.L., Gerber, J.H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J., 1986.Actuarial Mathematics. Society of Actuaries, Itasca,Ⅲ.
[19]Chang, C, Chang, J.S., Yu, M.-T.,1996. Pricing catastrophe insurance futures call spreads:A randomized operational time approach. Journal of Risk and Insurance 63,599-617.
[20]Chang, J.S.K., Chueng, C.S., Krinsky, I.,1989. On the derivation of reinsurance premiums. Insurance:Mathematics and Economics 8 (2),137-144.
[21]Croson, D.C., Kunreuther, H.C.,2000. Customizing indemnity contracts and indexed cat bonds for natural hazard risks. Journal of Risk Finance 1,24-41.
[22]Cox, J., Ingersoll, J., Ross, S.,1985. The term structure of interest rates. Econometric 53,385-407.
[23]Cox, S.H., Pederson, H.W.,2000. Catastrophe risk bonds. North American Actuarial Journal 4,56-82.
[24]Cox, S.H., Schwebach, R.G.,1992. Insurance futures and hedging insurance price risk. Journal of Risk and Insurance 59,628-644.
[25]Cummins, J.D.,1988. Risk-based premiums for insurance guaranty funds. Journal of Finance 43,593-607.
[26]Cummins, J.D., Doherty, N., Lo, A.,2002. Can insurers pay for the "big one"? Measuring the capacity of insurance market to respond to catastrophic losses. Journal of Banking and Finance 26,557-583.
[27]Cummins, J.D., Lalonde, D., Phillips, R.D.,2004. The basis risk of catastrophic-loss index securities. Journal of Financial Economics 71,77-111.
[28]Cummins, J.D., Lewis, C.M., Phillips, R.D.,1999. Pricing excess of loss reinsurance contracts against catastrophic loss. In:Froot, K. (Ed.), The Financing of Catastrophe Risk. The University of Chicago Press, Chicago.
[29]Cummins, J.D., Geman, H.,1995. Pricing catastrophe futures and call spreads: An arbitrage approach. Journal of Fixed Income (March),46-57.
[30]Duan, J.-C., Moreau, A., Sealey, C.W.,1995. Deposit insurance and bank interest rate risk:Pricing and regulatory implications. Journal of Banking and Finance 19,1091-1108.
[31]Duan, J., Simonato, J.,1999. Estimating and testing exponential-affine term structure models by Kalman filter. Review of Quantitative Finance and Accounting 13,111-135.
[32]Duan, J.-C., Yu, M.-T.,2005. Fair insurance guaranty premium in the presence of risk-based capital regulations, stochastic interest rat and catastrophe risk. Journal of Banking and Finance 29 (10),2435-2454.
[33]Froot, K.A. (Ed.),1999. The Financing of Catastrophe Risk. University of Chicago Press, Chicago.
[34]Froot, K.A.,2001. The market for catastrophe risk:A clinical examination. Journal of Financial Economics 60 (2),529-571.
[35]Harrington, S.E., Niehaus, G,1999. Basis risk with PCS catastrophe insurance derivative contracts. Journal of Risk and Insurance 66,49-82.
[36]Harrington, S.E., Niehaus, G.,2003. Capital, corporate income taxes, and catastrophe insurance. Journal of Financial Intermediation 12 (4),365-389.
[37]Lee, J.-P., Yu, M.-T.,2002. Pricing default-risky CAT bonds with moral hazard and basis risk. Journal of Risk and Insurance 69 (1),25-44.
[38]Lewis, C.M.. Murdock, K.C.,1996. The role of government contracts in discretionary reinsurance market for natural disasters. Journal of Risk and Insurance 63,567-597.
[39]Merton, R.,1976. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3,125-144.
[40]Merton, R.,1977. An analytic derivation of the cost of deposit insurance and loan guarantee. Journal of Banking and Finance 1,3-11.
[41]Naik, V., Lee, M.,1990. General equilibrium pricing of options on the market portfolio with discontinuous returns. Review of Financial Studies 3(4),493-521.