有隐含期权的银行资产负债表的利率风险控制

200288:100026788(2002)0820055206,(,710049):,,,,L,;,,;L:;;;;;:F830:AaControlOverInterestRateRiskofBank’AssetöLiabilitySheetwithEmbeddedOptionsLUODa2wei,WANDi2fang(SchoolofManagement,Xi’anJiaotongUniversity,710049,China)Abstract:ThebanksmustsetupthecontrolsystemsofinterestrateriskforthattheyshouldacceptinternationalregulatorystandardofriskafterenteringWTO,andinterestrateisbeingmarket2orientedgradually,buttheembeddedoptionsinbank’sassetöliabilitysheetenhancethecomplexityofinterestrateriskmanagement.Wemakeresearchesofcontroloverinterestrateriskofbank’assetöliabilitysheetwithembeddedoptions,andselectdurationgapandconvexitygapastheindicatorsofcontroloverinterestraterisk;andadvancethestrategiesofcontroloverinterestrateriskunderembeddedoptions,whichemphasizematchingoption-adjusteddurationandconstructingthepositiveconvexitygaptohedgethenegativeone;andanalysisthevaluationtechnologyofthesecuritywithembeddedoptionsonthebasisofscenegenerationofinterestrate,whichisessentialtoimplementingthestrategiesofcon2troloverinterestrateriskunderembeddedoptions.Keywords:embeddedoptions;assetöliability;interestraterisk;durationgap;convexitygap;scenegenerationofinterestrate1,L,L,,L,,L,L,,,La:2001203219:(79970013);(A2.92GL)©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.L,,L,,,,L,,L,,,,L,L:2,3,4,5L2didVZVi,V,dVDC:dV=-VD(di)+0.5VC(di)2(1)D=-dVdi1V,C=d2Vdi21V.ZA,LE,,,dE=dA-dL(2)DA,DLDE,CA,CLCE,(2)dE=-ADA-LADLdi+0.5ACA-LACL(di)2(3),(3),Z(3),,,ZDA=LDDL,CA=LACL(4)ZV0,V+V-i0,i+i-,D=-V+-V-i+-i-õ1V0(5)C=V+-V0i+-i0-V0-V-i0-i-0.5i+-0.5i-õ1V0(6)i+-i0=i0-i-ZV0,V+V-5(0.05)Z3(3),,DA(LöA)DL,[DA-(LöA)DL],[CA-(LöA)CL]2Z(5)(6),,6520028©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.ZZ,,ZZ,,Z,Z,,Z,Z,2,Z,Z(3),,,,,,Z,,Z,2,,,ZZ,Z,,,,,,Z,,,,Z,,,:1),,;2),,2,;3)2Z4,Z,,,Z,,Z,,,Z,,,,Z,,,,Z,Z4.14.1.1,Z,Z758©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.HullWhite:dr=[H(t)-ar]dt+Rdz(7)ARZR,dzWiner,H(t)ZtAH(t)öA,Z()Z,Z,Z4.1.2ZZ$t,$t,Z,,Z,,1ZööZ,öö,ööZZ4.1.3,,Zr3,r3rZ1)r3r3dr3=-ar3dt+Rdz(8)r3,r3r3=0Zr3t,,,$r$r=R3$t,$tZ(i,j)t=i$t,r3=j$rZZA0,j(jmax),öö,(jmin),ööZpu,pmpdZHullWhite,jmax0.184ö(A$t),jmax=-jmin,Z$r=R3$t,pu=16+a2j2$t2-aj$t2,pm=23-a2j2$t2pd=16+a2j2$t2+aj$t2(9)ööpu=16+a2j2$t2-aj$t2,pm=-13-a2j2$t2-2aj$tpd=76+a2j2$t2+3aj$t2(10)ööpu=76+a2j2$t2-3aj$t2,pm=-13-a2j2$t2+2aj$t8520028©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.pd=16+a2j2$t2-aj$t2(11)2)r,r3rZbiri$trr3i$tr3ZB(i,j)(i,j)(0,0)Zrr3,biZbi,(0,0),b0$tZ$tb0:b0=R($t),R($t)$tZB(1,1),B(1,0)B(1,-1)ZB(1,1)=pu(0,0)e-b0,B(1,0)=pm(0,0)e-b0,B(1,-1)=pd(0,0)e-b0(12)pu(0,0),pm(0,0)pd(0,0)(0,0)ZB(1,1),B(1,0)B(1,-1),b1ZB(1,1)e-(b1+$r)+B(1,0)e-b1+B(1,-1)e-(b1-$r)=e-R(2$t)õ2$t(13)R(2$t)2$tZB(2,2),B(2,1),B(2,0),B(2,-1)B(2,-2)ZB(1,1),B(1,0)B(1,-1),(1,1),(1,0)(1,-1)b1-$r,b1b1+$r,(12)Z3$tR(3$t),(13)b2Z,bi,rZ4.2,,ZVC,iC,CS(callablesecu2rity),Z,12VCiCVC(1+iC)ZNCS(noncallablesecurity)0NCS0=[E(NCS1)+VCiC)]ö(1+r(0,0))(14)r(0,0)(0,0),E(NCS1)NCS1E(NCS1)=NCS(1,1)pu(0,0)+NCS(1,0)pm(0,0)+NCS(1,-1)pd(0,0)(15)NCS(1,1),NCS(1,0)NCS(1,-1)NCS(1,1),(1,0)(1,-1)Z,CO(callableoption)0CO0=max[(NCS0-VC),E(CO1)ö(1+r(0,0)](16)E(CO1)CO1ZE(CO1)=CO(1,1)pu(0,0)+CO(1,0)pm(0,0)+CO(1,-1)pd(0,0)(17)CO(1,1),CO(1,0)CO(1,-1)(1,1),(1,0)(1,-1)Z,CS0CS0=NCS0-CO0(18),,NCS,COCSZ,,ZCO1CO(1,j)=max[NCS(1,j)-Vc,0],J=-1,0,1(19)NCSCS1NCS(1,j)=Vc(1+iC)ö(1+r(1,j)),,J=-1,0,1(20)CS(1,j)=NCS(1,j)-CO(1,j),,J=-1,0,1(21),,,958©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Z5Z,Z,,,,Z,Z:[1],.[J].,1998,(1):11-13.[2].[M].:,1999,614-618.[3]HullJ,WhiteA.Onefactorinterestratemodelsandthevaluationofinterestratederivativesecurities[J].JournalofFinancialandQuantitativeAnalysis,1993,28:235-254.[4]HullJ,WhiteA.Numericalprocedureforimplementingtermstructuremodels:single2factormodels[J].JournalofDerivatives,1994,Fall:7-16.(40),(15)LL:[1]BrennanMJ,SchwartzES.Convertiblebonds:valuationandoptimalstrategiesforcallandconversion[J].TheJournalofFinance,1977,27(5):1699-1715.[2]BrennanMJ,SchwartzES.Analyzingconvertiblebonds[J].JournalofFinancialandQuantitativeAnalysis,1980,15(4):907-929.[3]EvnineJJ.Threeessaysintheuseofoptionpricingtheory[D].Berkeley:UniversityofCalifornia,1983.[4]HarrisonJM,PliskaSR.Martingalesandstochasticintegralsinthetheoryofcontinuoustrading[J].StochasticProcessesandTheirApplications,1981,11:215-260.[5]HeathD,JarrowR,MortonA.Bondpricingandthetermstructureofinterestrates:anewmethodologyforcontin2gentclaimsvaluation[J].Econometrica,1992,60(1):77-105.[6]HoTSY,LeeSB.Termstructuremovementsandpricinginterestratecontingentclaims[J].TheJournalofFi2nance,1986,41(5):1011-1029.[7]Ingersoll,Jr,JE.AContingent2Claimsvaluationofconvertiblesecurities[J].JournalofFinancialEconomics,1977a,13(4):289-322.[8]JohnsonH.Optionsonthemaximumortheminimumofseveralassets[J].JournalofFinancialandQuantitativeAnalysis,1987,22(3):277-283.[9].[M].:,1999.[10].[N].,1998202221.0620028©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.