ꆡ뗚16뻭뗚6웚쾵춳맜샭톧놨ꆡꆡ2007쓪12퓂JournalofSystems&ꆡꆡꆡ컄헂뇠뫅:100522542(2007)0620698203샻싊럧쿕맜샭뗄죽틲쯘뻃웚쒣탍췵ퟚ뻼,ꆡ럫ꆡ뻪(뮪훐뿆벼듳톧맜샭톧풺,커몺430074)ꆾ햪튪ꆿ샻폃훷돉럖럖컶램릹붨쇋튻룶맜샭샻싊럧쿕뗄죽틲쯘뻃웚쒣탍,룃쒣탍뿉틔볆쯣쿠펦뗄훷돉럖뻃웚ꆣ춨맽쪵횤뇈뷏쇋룃랽램폫Fisher2Weil뻃웚뗄닮틬,랢쿖늻춬웚쿞뗄햮좯ퟩ뫏쯹쫜떽뗄훷튪펰쿬틲쯘늻쿠춬ꆣ틲듋,떥튻럧쿕틲쯘맜샭샻싊럧쿕늻쓜췪좫싺ퟣ튪쟳ꆣ맘볼듊:뻃웚;훷돉럖;샻싊럧쿕훐춼럖샠뫅:ꆡꆡꆡ컄쿗뇪쪶싫:AThree2FactorDurationModelforManagingInterestRateRiskWANGZong2jun,ꆡFENGJuan(SchoolofManagement,,Wuhan430074,China)ꆾAbstractꆿThisarticleconstructsathree2factordurationmodeltocontrolinterestrateriskusingprincipalcomponentanalysis(PCA).,ꆯ:duration;principalcomponentanalysis(PCA);interestrateriskꆡꆡ뷼쓪살,컒맺햮좯쫐뎡돊쿖돶뿬쯙랢햹뗄쟷쫆ꆣ좯뗄볛룱쫇웤캴살쿖뷰쇷뗄쿖횵뫍,틲듋,뻶뚨캴살튻랽쏦,짌튵틸탐뗄듦듻닮삩듳쯙뛈톸쏍,놣쿕릫쮾쿖뷰쇷쿖횵뗄벴웚샻싊웚쿞뷡릹쫇샻싊럧쿕맜샭뗄놣럑듳솿퓶볓,평폚헾닟쿞훆,듳솿퓶볓뗄뷰톡퓱훷튪쒿뇪ꆣ춶폚뿉컈뚨믱샻뗄햮쫐;쇭튻랽쏦,맺햮춶퓚믹쇮Vt뇭쪾t쪱뿌햮좯볛룱;rt(k)뇭쪾t쪱뿌뗚뷰닺엤훃훐뇈샽짏짽,늿럖짏쫐릫쮾튲샻폃쿐훃tk쓪벴웚샻싊;Ck뇭쪾캴살쎿웚뗄쿖뷰쇷,퓲폃떥뷰춶맺햮,풽살풽뛠뗄횤좯릫쮾뾪쪼짨솢떥뛀샻탎쪽뇭쪾뗄햮좯볛룱뗄만뚨쫕틦늿쏅ꆣ쿔좻,햮좯쫐뎡틑풽살풽뛠뗘컼N틽믺릹춶헟힢틢ꆣ쯦ퟅ컒맺샻싊쫐뎡뮯뷸돌뗄훰Vt=ꇆCkk=1[1+t-trt(k)]k늽췆뷸쿠펦뗘,햮좯볛룱뗄뇤뮯샻폃첩샕햹뾪뿉쟳뗃[1],붻틗믮풾돌뛈뗄쏷쿔퓶잿,햮좯쫐뎡늨뚯탔볓듳,샻싊럧쿕훰붥돉캪춶헟맘탄뗄맘볼쓚죝ꆣNꆡdVt=ꇆ5Vtdrt(k)+k=15r(k)1ꆡ샻싊럧쿕맜샭뒫춳쒣탍Nꆡꆡꆡ1햮좯뚨볛뗄믹놾릤뻟쫇쇣쾢쫕틦쟺쿟ꆣ평폚햮2ꇆ52Vt)drt(kꇤ)+ꛅ)5r(kꇤdrt(kk5r),kꇤt(kꆡꆡ뿉볻,펰쿬햮좯볛룱뗄럧쿕틲쯘쫇샻싊웚쿞뷡쫕룥죕웚릹짏뗄N룶쇣쾢샻싊ꆣ헢퇹,벴쪹뷶뷶뾼싇튻뷗:2007201222ퟷ헟볲뷩:췵ퟚ뻼(19642),쓐,뷌쫚ꆣ퇐뺿랽쿲캪뷰죚럧쿕맜샭ꆢ쿮,튲탨튪N룶닺닅쓜뛔햮좯ퟩ뫏뷸탐쳗웚놣웳튵움볛샭싛폫펦폃ꆢ춶움볛폫햽싔춶뻶닟ꆣ횵,퓚쪵볊훐헢퇹맽폚뢴퓓쟒쓑폚쪵쿖ꆣ틲듋,샻싊E2mail:wangzj@럧쿕맜샭뗄맘볼쫇뫏샭볲뮯럧쿕틲쯘ꆣ
ꆡ뗚6웚췵ퟚ뻼,뗈:샻싊럧쿕맜샭뗄죽틲쯘뻃웚쒣탍699튻룶뫏샭뗄볙짨쫇죏캪샻싊럧쿕룷틲쯘뗄뇤뮯릤뻟뷸탐PCAꆣ춨맽PCA랢쿖,헻룶샻싊웚쿞뷡솿쿠춬,벴dr(k)캪뎣쫽ꆣ퓚듋볙짨믹뒡짏,뿉뗃돶릹뿉틔평3룶틲쯘뷼쯆뿌뮭ꆣ뗚1룶틲쯘뛔펦뗚1쪵볊럧쿕맜샭훐맣랺쪹폃뗄뻃웚(횻뾼싇튻뷗틲쯘)듳쳘헷횵,웤쳘헷쿲솿e1뗄룷풪쯘뚼쫇헽횵,쯼듺춹뛈(뾼싇뛾뷗틲쯘)쒣탍ꆣFisher2Weil뻃웚뚨틥뇭샻싊뗄욽탐틆뚯돉럖;뗚2ꆢ3룶훷돉럖춨뎣뷢쫍캪[2]캪샻싊뇤뚯뗄킱싊틲쯘뫍쟺싊틲쯘ꆣ퓚쯼쏇뗄쳘헷NDCkk쿲솿룷풪쯘훐,뛔펦뛌웚ꆢ훐웚뫍뎤웚샻싊뗄쾵쫽퓲FW=1Pk0ꇆk=1ꇇ[1+r(k)]쫇헽ꆢ뢺쿠볤ꆣi=1ꆡꆡ샭싛짏,뻃웚쒣탍횻탨튪튻룶닺벴뿉뷸탐샻(3)릹붨탂뗄죽틲쯘뻃웚쒣탍ꆣ폃럻뫅뇭쪾싊럧쿕뗄쳗웚놣횵,틲듋,룃쒣탍ퟮ듳뗄폅뗣쫇랽뇣PCA뷡맻:잰3룶쳘헷횵ꛋ1ꆢꛋ2ꆢꛋ3,잰3룶헽붻쳘헷틗탐ꆣ좻뛸쿲솿e1ꆢe2ꆢe3,웤훐,ei=(e1i,e2i,ꆭT,eNi);훷돉럖,룃쒣탍볙짨쇋샻싊웚쿞뷡릹뗄욽탐틆뚯,헢훖볙뚨맽폚볲떥퇏룱,쪹폃짏뫜쓑듯떽쳗웚놣쿲솿pc퓲뿉뇭쪾캪횵뺫뛈튪쟳pc=ꚸT3x,ꆡx=ꚸ3pc,뛸퓚샻싊뻧쇒늨뚯뗄쪱웚,짵훁뿉쓜퓬돉춶헟뻞듳뗄쯰쪧ꆣ듓컒맺햮좯쫐뎡뷼2쓪뗄쪵샻싊뇤뮯ꚤr폫훷돉럖뗄맘쾵뷼쯆캪3볊쟩뿶뾴,샻싊뇤뚯췹췹볐퓓ퟅ뷏캪뢴퓓뗄탎쪽,뷶ꚤrkµN뷶샻폃뻃웚쒣탍쓑틔싺ퟣ럧쿕맜샭튪쟳ꆣꇆekipcii=1ꆡꆡ죴춶웚돵샻싊웚쿞뷡릹쫇r0(tk),k=1,2,2ꆡ샻싊럧쿕맜샭죽틲쯘뻃웚쒣탍붨솢ꆭ,N,쿠펦뗄쳹쿖틲ퟓ쫇B0(tk),ퟩ뫏볛횵쫇V0,쇭튻럧쿕틲쯘볲뮯랽램쫇볙짨떽웚웚쿞뷓뷼뗄캪볲뮯컊쳢,뾼싇솬탸뢴샻:N쇣쾢햮좯럧쿕틲쯘쿠춬,듓뛸붫샻싊웚쿞뷡릹럖돉B0(tk)=-tr(t)ekk,ꆡV0=ꇆCkB0(tk)벸뛎k=1,늢볙뚨쎿뛎뗄샻싊뇤뮯쿠춬ꆣ퓚듋볙짨믹뒡짏,뿉뗃맘볼샻싊뻃웚뛸ꚤrk=r(tk)-r0(tk)ꆣ틲듋,(KRD)쒣탍[3]ꆣ좻뛸,헢훖3볲뮯럧쿕틲쯘뗄랽램뇈뷏훷맛,좷뚨쓄킩샻싊ퟷ캪r(tk)=r0(tk)+Nꇆekipci맘볼럧쿕틲쯘췪좫욾뷨퇐뺿헟놾죋뗄뾴램ꆣ뷼쓪i=1살ꆡꆡ평폚샻싊뿉뾴돉룷훷돉럖뗄몯쫽,틲듋,ퟩ뫏볛,튻훖탂뗄퇐뺿샻싊럧쿕뗄랽램쫇샻폃훷돉럖럖컶(PCA)ꆣ룃랽램쓜춨맽춳볆럖컶,뷏캪뿍맛뗘뛔횵튲쫇룷훷돉럖뗄몯쫽:N3럧쿕틲쯘훘탂럖ퟩ,틲듋,쓜퓚ퟮ듳쿞뛈놣쇴풭쪼쫽V=ꇆCkꆤexp-tk[r0(tk)+Nꇆekipci]뻝탅쾢뗄믹뒡짏복짙럧쿕틲쯘ꆣk=1i=1룷훷돉럖쿠뮥뛀솢,ퟩ뫏ퟜ뗄쫕틦싊뇤뮯캪맺쓚췢뛔PCA뗄샭싛퇐뺿뫍쪵횤쿔쪾,잰3룶ꚤ3V0=15V0훷돉럖쓜릻뷢쫍뻸듳늿럖뗄샻싊뇤뚯,웤샛볆뷢쫍ꚤpci=V0V0ꇆ5pci=1i뇈샽(샛볆랽닮릱쿗싊)춨뎣퓚90%ꆫ99%[3,4]ꆣ틲3NN듋-,샻폃PCA뿉틔릹붨탂뗄죽틲쯘뻃웚쒣탍쳦듺뒫V0ꇆꇆ[CktkekiB0(tk)ꚤpci]i=1k=1춳뻃웚쒣탍뷸탐럧쿕맜샭ꆣ벴듓쫽톧뷇뛈뾴,PCA뻍쫇붫튻ퟩ뿉맛달떽뗄ꆢꚤV0쿠맘뗄샻싊럧쿕틲쯘뮯캪짙쫽벸룶늻뿉맛달떽=DTpc3(-ꚤpc)V0뗄ꆢ뛀솢뗄ퟛ뫏뇤솿ꆡꆡ뿉틔뾴돶,쿲솿Dpc뗄뗚i룶풪쯘뛈솿쇋떥캻,헢킩ퟛ뫏뇤솿쓜릻뢴훆풭쪼뇤솿뺡뿉쓜뛠뗄탅쾢ꆣ헢벸룶ퟛ뫏뇤솿뻍쫇풭쪼뇤솿쮮욽뗄뗚i룶훷돉럖뇤뚯틽웰뗄햮좯볛룱뇤뚯,틲뗄훷돉럖ꆣ릹붨훷돉럖쒣탍뗄돌탲죧쿂:듋,웤룅쓮샠쯆폚뻃웚,뚨틥쪽뿉킴캪N(1)샻폃햮좯쫐뎡쫽뻝뗃돶벴웚샻싊웚쿞뷡릹,늢뷸탐튻뷗닮럖뒦샭,뗃떽쿠펦퇹놾뇤솿쪱볤탲Di=NB0(tk)ekiV0ꇆCktkk=1쇐쫽뻝ꆣ캪쇋뇣폚춬DFW뇈뷏,뛔룷퇹놾뇤솿돋틔ꆡꆡ퓚룃쒣탍훐,죧맻쿲솿e1룷풪쯘폐쿠춬뗄횵,튻뎣쫽늢쟒늻춬웚쿞뗄샻싊뇤뮯쿠춬,퓲뗚1훷돉럖pc1,벴쇮1x=ꚤrꆣ탂뇤뮻늢늻룄뇤킭랽닮N=ꚤr,쿠펦뗘,D1=DFWꆣ틲듋,춨맽뇈뷏죽틲쯘뻃뻘헳,틲듋늻믡펰쿬PCA뷡맻ꆣ웚뫍Fisher2Weil뻃웚횵,뿉틔럖컶늻춬춶ퟩ뫏쯹(2)샻폃뇤솿뗄킭랽닮뻘헳S,쪹폃쿠펦죭볾쫜떽뗄맘볼펰쿬틲쯘ꆣ
700쾵ꆡ춳ꆡ맜ꆡ샭ꆡ톧ꆡ놨뗚16뻭ꆡꆡꆡꆡꆡ뗄샻싊쫽뻝뷸탐쪵샽럖컶ꆣ쒣탍볬퇩쪹폃쫽뻝살풴3ꆡ쪵샽럖컶폚훐맺믵뇒췸[5],퇹놾톡좡2004203211ꆫ2004209218캪쇋뇈뷏죽틲쯘뻃웚쒣탍뫍Fisher2Weil뻃웚맺햮벴웚샻싊쎿죕쫽뻝,뷸탐PCA뗃돶뗄잰3룶쳘퓚뷸탐샻싊럧쿕맜샭짏뗄닮틬,춨맽컒맺햮좯쫐뎡헷쿲솿죧뇭1쯹쪾ꆣ뇭1ꆡPCA뷡맻쓪ꆡꆡ쿞ꆡꆡ볙짨쒳짌튵틸탐퓚돵웚뷸탐튻쾵쇐햮좯춶,돵웚샻싊웚쿞뷡릹쇏쇐쪾폚뇭2ꆣ샻폃짏쫶룃춶뿉쪹틸탐퓚캴살3쓪믱뗃튻ퟩ만뚨쫕틦쿖뷰쇏,럖뇰볆쯣돶햮좯ퟩ뫏뗄쿖횵ꆢDFW;춬쪱,샻폃잰쇷ꆣ캪뷸탐뇈뷏,럖뇰볙짨쇋뛌웚ꆢ훐웚뫍뎤웚3훖쫶쒣탍뫍PCA뷡맻,볆쯣돶룃햮좯춶뗄죽틲쯘훷늻춬쿖뷰쇷웚쿞,캴살뿉믱뗃뗄쿖뷰쇷쟩뿶뫍춶돉럖뻃웚,뻟쳥볆쯣뷡맻볻뇭3ꆣ뇭2ꆡ춶돵웚늿럖쓪뛈벴웚샻싊벰ퟩ뫏쿖뷰쇷쫽뻝ퟩ뫏2ퟩ쓪쿞ퟩ뫏1뫏31Y2Y3Y12Y13Y14Y18Y19Y20Y벴웚샻싊쿖뷰쇷/췲풪102030102030102030뇭3ꆡ늻춬ퟩ뫏DFW뫍죽틲쯘뻃웚뛔뇈4ꆡ뷡ꆡ폯ퟩ뫏1ퟩ뫏2ퟩ뫏3놾컄샻폃PCA릹붨쇋튻룶맜샭샻싊럧쿕뗄죽쿖횵틲쯘뻃웚쒣탍ꆣ춬뒫춳Fisher2Weil뻃웚뇈뷏랢쿖,폃튻룶럧쿕틲쯘뷸탐샻싊럧쿕맜샭쫇풶풶늻릻뗄,훷돉럖뻃웚뛸탂쒣탍쓜룼좫쏦뗘랴펳샻싊럧쿕뗄뛠캬뇤뚯틲훷돉럖뻃웚쯘,틲듋,쓜룼ힼ좷뗘뿘훆뫍맜샭샻싊럧쿕ꆣ훷돉럖뻃웚닎뾼컄쿗:ꆡꆡ붫죽틲쯘뻃웚춬Fisher2Weil뻃웚쿠뇈뿉틔랢[1]ꆡ샮냂쓎뛻ꆤ쳘샯쓡,럆샻웕ꆤ웕샯냂삼뗂.만뚨쫕틦쿖,뛔폚뛌웚ퟩ뫏,D1쏷쿔킡폚DFW,D2ꆢD3뷏듳;횤좯-뛔샻싊럧쿕뷸탐뚨볛뫍쳗웚놣횵뗄뚯첬랽램뛔폚훐웚ퟩ뫏,D1럇뎣뷓뷼DFW,D2퓲뷏듳;뛸ퟮ[M].키뻼틫.놱뺩:믺킵릤튵돶냦짧,2002.뫳튻룶뎤웚ퟩ뫏[2]ꆡBarberJR,CopperML,Immunizationusingprinci2,D1쿔훸듳폚DFW,D2ꆢD3쿠뛔뷏킡ꆣ춨맽뛔뇈럖컶뾴돶,쯤좻욽탐틆뚯돉럖(듺뇭ퟅpalcomponentanalysis[J].TheJournalofPortfolio쯹폐웚쿞뗄샻싊춬쪱짏짽믲쿂붵)뛔쯹폐웚쿞뗄햮Management,1996:99-105.좯ퟩ뫏뚼폐뷏캪쿔훸펰쿬,떫쿠뛔룼펰쿬훐웚뫍뎤[3]ꆡLardicS,PriauletP,웚ퟩ뫏curvedynamics:Questionsofmethodologies[C]//;킱싊틲쯘ퟮ펰쿬뛌웚햮좯ퟩ뫏,뛸쟺싊틲쯘룼뛠펰쿬쇋훐웚ퟩ뫏ꆣ쿔좻,평폚웚쿞퓚HSBC2CCFGroupandProceedngsofthe2001French10ꆫ15쓪,2001.뗄훐웚ퟩ뫏뗚1훷돉럖뻃웚ퟮ뷓뷼Fisher2Weil뻃[4]ꆡ훬쫀커,돂붡뫣.붻틗쯹맺햮샻싊웚쿞뷡릹쪵횤퇐뺿웚,틲듋,떥튻럧쿕틲쯘뷸탐샻싊럧쿕맜샭뛔훐웚ퟩ[J].뷰죚퇐뺿,2003(10):63-73.뫏ퟮ캪폐킧ꆣ[5]ꆡ훐맺믵뇒췸..
