基于指数效用函数的零息巨灾债券无差异定价
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摘要
巨灾经常对保险行业产生巨大冲击,也催生了巨灾债券市场。但巨灾债券的复杂性和非流动性特征,对巨灾债券定价带来了很大的困难,以至于目前还没有统一的定价方法,特别是由于巨灾债券市场还远不完备,不适合采用经典的无套利定价方法。本文应用无差异定价方法,假设买方(投资者)具有指数效用函数,给出了零息巨灾债券无差异价格的解析表达式。同时本文在股票价格与巨灾风险指数为正相依的情况下,对无差异价格进行了敏感性分析,得到了一些有意义的结果。
Catastrophes( CAT) occur more and more frequently in recent decades,which produces a huge impact on the development of the insurance industry. Along this trend,the CAT bond market has emerged and become sizable. In view of some characteristics such as complexity and illiquidity of this market,pricing CAT bonds is a challenging task. So far various approaches have been proposed,but they are very different and far from being unified.Due to the incompleteness of the CAT bond market,the prevailing non-arbitrage pricing theory does not work well.In this paper,we studied the undifferentiated pricing method for CAT bonds. Assuming a buyer( investor) having an exponential utility,we derived a formula for the undifferentiated price of a zero-coupon CAT bond,and conducted some sensitivity analyses on condition that share prices were positively correlated to CAT risk index. The results are of some reference value.
Catastrophes( CAT) occur more and more frequently in recent decades,which produces a huge impact on the development of the insurance industry. Along this trend,the CAT bond market has emerged and become sizable. In view of some characteristics such as complexity and illiquidity of this market,pricing CAT bonds is a challenging task. So far various approaches have been proposed,but they are very different and far from being unified.Due to the incompleteness of the CAT bond market,the prevailing non-arbitrage pricing theory does not work well.In this paper,we studied the undifferentiated pricing method for CAT bonds. Assuming a buyer( investor) having an exponential utility,we derived a formula for the undifferentiated price of a zero-coupon CAT bond,and conducted some sensitivity analyses on condition that share prices were positively correlated to CAT risk index. The results are of some reference value.
引文
[1]丁锋.中国首只巨灾债券境外成功发行[OL].财新.(2015-07-14)[2017-12-12].http://finance.caixin.com/2015-07-14/100828613.html.
[2]何江俊.基于政府参与情形的混合巨灾债券设计与实证分析[J].保险研究,2011,(06):69-74.
[3]康晗彬,邢天才.考虑多风险因素的我国巨灾债券定价研究[J].保险研究,2013,(08):94-106.
[4]田玲.巨灾风险债券运作模式与定价机理研究[M].武汉大学出版社,2009:76-102.
[5]韦勇凤,李勇,巴曙松.巨灾债券对投资组合分时期影响的实证分析[J].保险研究,2012,(08):121-127.
[6]邢天才,康晗彬.基于资产负债管理的我国巨灾再保险定价研究[J].保险研究,2013,(02):18-27.
[7]Barrieu P,Albertini L.The Handbook of Insurance-Linked Securities[M].John Wiley and Sons,2010:83-99.
[8]Barrieu P,LoubergéH.Hybrid CAT bonds[J].Journal of Risk and Insurance,2009,76(3):547-578.
[9]Bourdeau-Brien M,Kryzanowski L.The Impact of Natural Disasters on the Stock Returns and Volatilities of Local Firms[J].The Quarterly Review of Economics and Finance,2017,63:259-270.
[10]Cummins JD,Weiss MA.Convergence of Insurance and Financial Markets:Hybrid and Securitized Risktransfer Solutions[J].Journal of Risk and Insurance,2009,76(3):493-545.
[11]Egami M,Young VR.Indifference Prices of Structured Catastrophe(CAT)Bonds[J].Insurance:Mathematics and Economics,2008,42(2):771-778.
[12]Ferreira S,Karali B.Do Earthquakes Shake Stock Markets?[J].PLOS ONE,2015,10(7):e0133319.
[13]Hodges SD,Neuberger A.Optimal Replication of Contingent Claims Under Transaction costs[J].Review of Futures Markets,1989,8:223-238.
[14]Kaas R,Goovaerts M,Dhaene J,Denuit M.Modern Actuarial Risk Theory:Using R[M].Springer Science and Business Media,2008:115-122.
[15]Leobacher G,Ngare P.Utility indifference pricing of derivatives written on industrial loss indices[J].Journal of Computational and Applied Mathematics,2016,300:68-82.
[16]Mc Neil AJ,Frey R,Embrechts P.Quantitative Risk Management:Concepts,Techniques and Tools[M].Princeton University Press,2015:220-274.
[17]Swiss Re Institute.Natural catastrophes and man-made disasters in 2016:a year of widespread damages[J].Sigma,2017,(2).
[18]Tang Q,Vernic R.The impact on ruin probabilities of the association structure among financial risks[J].Statistics&Probability Letters,2007,77(14):1522-1525.
[19]Wang SS.A class of distortion operators for pricing financial and insurance risks[J].Journal of riskand insurance.2000,67(1):15-36.
[20]Young VR.Pricing in an incomplete market with an affine term structure[J].Mathematical Finance,2004,14(3):359-381.
[21]Valizadeh P,Karali B,Ferreira S.Ripple effects of the 2011 Japan earthquake on international stock markets[J]. Research in International Business and Finance,2017,41:556-576.
[2]何江俊.基于政府参与情形的混合巨灾债券设计与实证分析[J].保险研究,2011,(06):69-74.
[3]康晗彬,邢天才.考虑多风险因素的我国巨灾债券定价研究[J].保险研究,2013,(08):94-106.
[4]田玲.巨灾风险债券运作模式与定价机理研究[M].武汉大学出版社,2009:76-102.
[5]韦勇凤,李勇,巴曙松.巨灾债券对投资组合分时期影响的实证分析[J].保险研究,2012,(08):121-127.
[6]邢天才,康晗彬.基于资产负债管理的我国巨灾再保险定价研究[J].保险研究,2013,(02):18-27.
[7]Barrieu P,Albertini L.The Handbook of Insurance-Linked Securities[M].John Wiley and Sons,2010:83-99.
[8]Barrieu P,LoubergéH.Hybrid CAT bonds[J].Journal of Risk and Insurance,2009,76(3):547-578.
[9]Bourdeau-Brien M,Kryzanowski L.The Impact of Natural Disasters on the Stock Returns and Volatilities of Local Firms[J].The Quarterly Review of Economics and Finance,2017,63:259-270.
[10]Cummins JD,Weiss MA.Convergence of Insurance and Financial Markets:Hybrid and Securitized Risktransfer Solutions[J].Journal of Risk and Insurance,2009,76(3):493-545.
[11]Egami M,Young VR.Indifference Prices of Structured Catastrophe(CAT)Bonds[J].Insurance:Mathematics and Economics,2008,42(2):771-778.
[12]Ferreira S,Karali B.Do Earthquakes Shake Stock Markets?[J].PLOS ONE,2015,10(7):e0133319.
[13]Hodges SD,Neuberger A.Optimal Replication of Contingent Claims Under Transaction costs[J].Review of Futures Markets,1989,8:223-238.
[14]Kaas R,Goovaerts M,Dhaene J,Denuit M.Modern Actuarial Risk Theory:Using R[M].Springer Science and Business Media,2008:115-122.
[15]Leobacher G,Ngare P.Utility indifference pricing of derivatives written on industrial loss indices[J].Journal of Computational and Applied Mathematics,2016,300:68-82.
[16]Mc Neil AJ,Frey R,Embrechts P.Quantitative Risk Management:Concepts,Techniques and Tools[M].Princeton University Press,2015:220-274.
[17]Swiss Re Institute.Natural catastrophes and man-made disasters in 2016:a year of widespread damages[J].Sigma,2017,(2).
[18]Tang Q,Vernic R.The impact on ruin probabilities of the association structure among financial risks[J].Statistics&Probability Letters,2007,77(14):1522-1525.
[19]Wang SS.A class of distortion operators for pricing financial and insurance risks[J].Journal of riskand insurance.2000,67(1):15-36.
[20]Young VR.Pricing in an incomplete market with an affine term structure[J].Mathematical Finance,2004,14(3):359-381.
[21]Valizadeh P,Karali B,Ferreira S.Ripple effects of the 2011 Japan earthquake on international stock markets[J]. Research in International Business and Finance,2017,41:556-576.