巨灾风险债券定价

11CatastropheRiskBondGoshay&Sandor19731984SvenskExportkredit1992(CBOT)(CatastropheCAT)1993CAT(Callspreads)199612St.PaulRe1997303621(Hazard)(HazardModel)(Perils)2(Vulnerability)342CoxPedersen200133.11dT1dT1+dff1+dQ0{}Tkkd,2,1)(L=Q−+++∑=TkQkdnrrrE1)()]1(1[)]1(1)][0(1[1L1{}12,1:)(−=TkkrL),0(nP1n0−+++=)]1(1[)]1(1)][0(1[1),0(nrrrEnPQL2τT{}TL2,1∈τ=+++−=++===TkdfdTkdfdkdTTkk)()()()(1)1(1)1(1,2,11)1(1)(ττττL3fd3)1(df+T=τ=++−=+===TkfddTkfddkdTTkk)()()()(1111,2,111)(ττττL4QQ130∑∑===+++TkTkkQkPdfTQTPkQkPd11)(),0()1()(),0()(),0(τττ53)(kQτk3.2therepresentativeagenttherepresentativeutilityfunctiontheaggregateconsumptionprocess{}TkkcL,2,1,0)(=aggregateconsumptionprocess{}TkkCL,2,1,0)(=∗theaggregateconsumptionstochasticprocess()kC,ω∗kω()0∗Ck=0()kC∗1≥k()kC,ω∗ωωadditivelyseparable&differentiableTuuu,,,10L{}TkkcL,2,1,0)(=()()∑=ΡTkkkcuE0{}TkkddL,2,1,0)(==0()()()()()′′=∑∗∗)(00kdCukCuEdVkP7{}1,2,1,0)(−=TkkrL()()()()()[]1,,1,011111−=+′′=+∗+∗TkkCuEkCukrkkL8QΡRadon-NikodymderivativedPdQXdPdQ[]=dPdQXEXEPQdPdQ()()[]()[]()[]()()()()0,,1,11,1010ωωωωω∗∗′′−+++≡CuTCuTrrrdPdQTL94()()∏=−+kiirkc111Q-martingale{}TkkddL,2,1,0)(==07Q{}1,2,1,0)(−=TkkrL8()()[]()[]()[]()−+++=∑=TkQkdkrrrEdV11111011L1010()()[]()[]()[]()()[]()[]()[]()()[]()[]()[]()[]()[]()[]()[]()[]()[]kdEkPkdEkrrrEkdEkrrrEkdkrrrEkdkrrrEdVPTkPTkQQTkQTkQTkQ∑∑∑∑∑======−+++=−+++=−+++=−+++=11111),0(1111011111101111110111111011LLLL11()()()=++−=+===TkfddETkfddEkdETTPkkPP)()()()(1111,2,111)(ττττL123.3SwissReCSFirstBostonA$62million(40protected)B$60million(0protected)C$15million(0protected)5ALIBOR255bpsB10.5C12PCSA$18.5billion,$21billion,$24billionB$18.5billion,$21billion,$24billionC$12billionA1B1CNAMichaelS.Canter&JosephB.Cole,TheFoundationandEvolutionoftheCatastropheBondMarket,GLOABLEREINSURANCE,Sep.1997,at3-4.1997SwissReCL(t)M12()()()()[]()[][][]{}=+−===+−===++−=+==++−=+=≥≥==TkLMTLPdTkdTkdETkdETkddETkddETkfddETkfddEkdEMTLPPMYLMTLPMkLMkLPTTPkkPP)0()(1,,2,111,,2,11111,,2,1111111,,2,111)()()()()()()()()()(LLLLττττ13PL(t)()dNdZdtLdL1−Γ++=σµ14Γ()Γln()2,ΓΓσµNNλZσµ,()()()()()22200,2/ln~,lnΓΓ++−+=σσµσµititLNiNLLtt156[]()()()[]{}()()(){}()()()()∑∑+−−−−Φ•==•===ΓΓ−∞=222000002/lnln!,lnlnlnlnlnσσµσµλλititLMiteiNLMLPiNPLMLPLMLPitittttt16()()86.02,0,93.01,0,1.0,10,0,1,0,00========ΓΓPPLλσµσµM=120()()(){}[]()0152264.1930724.012.086.012.093.0120112.02,012.01,002=+×+×=×+•+•=LLPPPdV41.Cox,S.H.andPedersen,H.W.(2001).Catastropheriskbonds.NorthAmericanActuarialJournal.Toappear.2.Capitalmarketinnovationintheinsuranceindustry.SigmaNo.3,2001.3.Cox,S.H.,Fairchild,J.R.andPedersen,H.W.(2000).EconomicAspectsofsecuritizationofrisk.ASTINBulletin,Vol.30,No.1,157-193.4.2000.6PricingCatastropheRiskBondLuhengzhenChenWeizhongInstitutionofModernFinance,TongjiUniversityShanghai,200092,P.R.ChinaAbstract:CatastropheRiskBondtransferrisktocapitalmarketthroughsecuritization.Investorscangainhighyieldunaffectedbyfinancialmarketvariable7becauseofthecharacteristicofindependencebetweenCatastropheBondandeconomicvariable.ThispaperdeduceapricingCatastropheRiskBondmodelandexemplifyit.Keywords:CatastropheRiskBondPricing1239119200092e-mail:[e-mail]:021-65981246(h)13917304680(m)