훐맺얩튵듳톧톧놨ꆡ2003,8(4):81ꆫ85JournalofChinaAgriculturalUniversity햮좯볛룱ꆢ떽웚웚쿞틔벰떽웚쫕틦싊뗄쫽톧럖컶랽램뎣쟥펢1ꆡ쇖쟥좪2(11훐맺얩튵듳톧샭톧풺,놱뺩100083;21훐맺죋쏱듳톧닆헾뷰죚톧풺,놱뺩)햪ꆡ튪ꆡ뛔햮좯쫐뎡볛룱폫욱쾢싊ꆢ떽웚쫕틦싊틔벰떽웚웚쿞뗈닎쫽횮볤맘쾵뗄퇐뺿춨뎣닉폃쪵횤랽램,헢훖폃룶뇰췆돶튻냣뗄랽램늻짵퇏쏜ꆣ놾컄훐닉폃쫽톧럖컶뗄랽램,샻폃볆쯣믺뷸탐쫽뻝뒦샭,뛔틔짏룷닎쫽횮볤뗄맘쾵뷸탐쇋퇏룱뗄싛횤ꆣ춨맽뛔솿뮯뷡맻뗄쳖싛,쳡돶쇋럖컶룷닎쫽뛔햮좯볛룱펰쿬뗄폐킧랽램,뗃돶쇋튻킩폐틢틥뗄뷡맻ꆣ맘볼듊ꆡ햮좯볛룱;욱쾢싊;떽웚쫕틦싊훐춼럖샠뫅ꆡF224111;O21116ꆡꆡꆡꆡ컄헂뇠뫅ꆡ100724333(2003)0420081205ꆡꆡꆡꆡ컄쿗뇪쪶싫ꆡAAnalysisonsecurityprice,time,incomerateChangQingying1ꆡLinQingquan2(11CollegeofScience,ChinaAgriculturalUniversity,Beijing100083,China;21SchoolofFinance,RenminUniversityofChina)AbstractꆡUsuallywestudiedtherelationshipoftheseparameters,suchassecurityprice,couponrate,ꆡsecurityprice;couponrate;incomerateꆡꆡ햮좯볛룱컊쳢쫇햮좯랢탐헟퓚랢탐햮좯횮잰뇘폚떽웚쫕틦싊쫇좡횵폚(0,1)쟸볤쓚뗄죎튻쫽,맊퓚탫튪뷢뻶뗄쫗튪컊쳢ꆣ죧맻랢탐볛룱맽룟,뿉쓜돶폐쿞듎뗄쫔듭훐뺭뎣뗃늻떽뷡맻ꆣ놾컄훐퓋폃쫽톧쿖훍쿺쿖쿳;랴횮,퓲믡룸햮좯랢탐헟듸살쯰쪧ꆣ좷럖컶랽램뫍솬탸몯쫽뗄탔훊,틔볆쯣믺캪볆쯣릤뻟,뚨햮좯볛룱뗄랽램쫇:볆쯣햮좯욱쾢싊뛔떽웚쫕틦럖컶햮좯욱쾢ꆢ햮좯떽웚쫕틦싊틔벰햮좯떽웚웚쿞싊헛쿖뛸뗃떽뗄쿖횵,룃쏦횵헛쿖뗄ퟜ뫍벴캪햮좯뗈닎쫽뛔햮좯볛룱뗄펰쿬,룹뻝뇈샽램(쿒캻램)뫍볛룱[1,2]ꆣ햮좯볛룱폫햮좯떽웚웚쿞ꆢ욱쾢싊틔벰얣뛙램(쟐쿟램),닉폃뇆뷼뗄랽램,퓚튻뚨뗄컳닮쳵떽웚쫕틦싊횮볤폐ퟅ쏜쟐뗄솪쾵,퇐뺿쯼쏇횮볤뗄볾쿂쟳돶햮좯떽웚쫕틦싊ꆣ쿠뮥맘쾵뛔럖컶햮좯쫐뎡뻟폐쪮럖훘튪뗄틢틥ꆣ뒫춳뗄랽램쫇춨맽뛔벸룶쪵샽뗄럖컶뛸뗃떽쿠1ꆡ햮좯볛룱ꆢ햮좯떽웚쫕틦싊폫햮좯떽웚웚펦뗄맦싉[3,4]ꆣ헢훖랽램쯤좻뇈뷏랽뇣,떫쫇듓퇏쿞횮볤뗄맘쾵룱틢틥짏붲,헢훖폃룶뇰(뺡맜폐벸ퟩ쫽뻝)췆돶튻111ꆡ햮좯볛룱뗄좷뚨냣뗄랽램쫇뫜늻퇏쏜뗄ꆣ뛔폚죧뫎퓚룸뚨햮좯볛룱짨쒳튻훖햮좯뗄쏦횵캪m,욱쾢싊캪r,떽웚웚뫍햮좯욱쾢뗄쳵볾쿂,좷뚨햮좯떽웚쫕틦싊헢룶컊쿞캪n,퓲쎿튻룶쪱웚뗄욱쾢C=rm;폖짨떽웚쫕쳢짏,춨뎣닉폃쫔듭램,룃랽램뗄좱쿝럇뎣쏷쿔:1)틦싊캪3]y,퓲햮좯볛룱[2,떱햮좯떽웚쫕틦싊늻쫇솽캻킡쫽뗄쳘쫢횵(죧mq=0126,01ꇆnC+i11,뗈뗈)쪱,뻍뫜쓑쫔돶헽좷뗄횵살;2)평i=1(1+y)(1+n(1)y)쫕룥죕웚:2002203228ퟷ헟볲뷩:뎣쟥펢,뢱뷌쫚,훷튪퇐뺿랽쿲캪쫽톧ꆢ컯샭랽램퓚뺭볃톧훐뗄펦폃' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
ꆡ82훐맺얩튵듳톧톧놨2003쓪샻폃볆쯣믺쯦믺닺짺Cꆢnꆢy뫍m뗄늻춬횵,뇠돌뇭3ꆡ욱쾢ꆢ쏦횵ꆢ떽웚쫕틦싊튻뚨쪱떽웚웚쿞볆쯣돶햮좯볛룱q,뷡맻볻뇭1ꆣ뛔볛룱뗄펰쿬뇭Table3ꆡTheeffectontheb1ꆡ늻춬욱쾢ꆢ떽웚웚쿞ꆢ떽웚쫕틦싊뫍ondpriceofterm,whencoupon,쏦횵쿂뗄햮좯볛룱facevalueandincomeratehavebeengivenTable1ꆡThebondpriceatdifferentcoupon,term,쳵볾탲욱쾢떽웚웚쏦횵떽웚쫕틦싊햮좯볛룱incomerate&facevalue뫅C/풪쿞n/am/풪yq/풪탲욱쾢떽웚웚쿞쏦횵떽웚쫕틦싊햮좯볛룱12523100001050662179뫅22525100001050647165C/풪n/am/풪yq/풪32527100001050633192121394000103485601194252810000105062715521838240001046750103y>r5252910000105062114731324500010823868190625321000010506041934184759000101831211177253210000105060419351329200010578254178825351000010505901656118300010033791849253910000105057415772413180001061103917810ꆡ25421000010505641428112584000106817361541406710000103012871339837560001040144113824065100001030128415310ꆡ18540001052388114340631000010301281156440621000010301280100112ꆡ욱쾢ꆢ쏦횵뫍떽웚웚쿞튻뚨쪱,떽웚쫕틦싊뛔햮좯볛룱뗄펰쿬y<r540611000010301278140640581000010301273131샻폃볆쯣믺뇠돌볆쯣,뷡맻볻뇭2ꆣ평뇭2뿉740581000010301273131횪떱떽웚쫕틦싊y짽룟쪱,햮좯볛룱q쿂붵;y붵840551000010301267174뗍쪱,q짏짽ꆣ940511000010301259151뇭10ꆡ404810000103012521672ꆡ욱쾢ꆢ쏦횵벰떽웚웚쿞튻뚨쪱떽웚쫕틦싊뛔햮좯볛룱뗄펰쿬114ꆡ룸뚨욱쾢ꆢ쏦횵ꆢ햮좯볛룱뫍떽웚웚쿞,떽웚쫕Table2ꆡTheeffectonthebondpriceofincomerate,when틦싊쟳뷢랽램coupon,facevalueandtermhavebeengiven룹뻝쪽(1),쇮탲욱쾢떽웚웚쏦횵떽웚쫕틦싊햮좯볛룱Cm뫅Cf(y)=q-ꇆn-/풪쿞n/am/풪yq/풪(i=11+iy)(1+ny)125501000010241043104평듋뿉횪f(y)떥뗷짏짽ꆣ평폚y>0,맊듦퓚y1쪹22550100001026966193뗃f(y1)<0(쫂쪵짏y=0쪱f(0)<0),튲듦퓚y232550100001029892190쪹뗃f(y425501000010318581952)>0ꆣ룹뻝몯쫽뗄솬탸탔뿉횪뇘듦퓚튻뗣y0쪹뗃f(y0)=0[5]52550100001032825152ꆣ쟳뷢y0뗄랽램폐2훖:625501000010367481061)뇈샽램(쿒캻램)ꆣ72550100001036746176죴몯쫽f(x)폚뇕쟸볤[a,b]짏솬탸,쟒f(a)ꆤ82550100001040681108f(b)<0,떱a<x<b쪱,fꇤ(x)ꇙ0,퓲랽돌9255010000104462012010ꆡ2550100001047573195f(x)=0(2)폚쟸볤(a,b)쓚폐,뛸쟒뷶폐튻룶쪵룹ꆣ톰헒룃쪵113ꆡ욱쾢ꆢ쏦횵ꆢ떽웚쫕틦싊뫍욱쾢싊튻뚨쪱,떽웚룹뗄볆쯣랽램죧쿂ꆣ쫗쿈좡웚쿞뛔햮좯볛룱뗄펰쿬x1=a+ꛄ1볆쯣뷡맻볻뇭3ꆣ뿉볻:1)떱y>r쪱,쯦ퟅ햮뗄횵ퟷ캪듋룹뗄뗚튻룶뷼쯆횵,웤훐좯떽웚웚쿞n뗄퓶볓,햮좯볛룱q쿂붵ꆣ2)떱y<ꛄf(a)1=-(b-a)r쪱,쯦ퟅn뗄복짙,q쿂붵ꆣf(b)-f(a)' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
ꆡꆡ뗚4웚뎣쟥펢뗈:햮좯볛룱ꆢ떽웚웚쿞틔벰떽웚쫕틦싊뗄쫽톧럖컶랽램83뷸뛸퓚쟸볤(a,x1)믲(x1,b)쓚,럖뇰볆쯣몯쫽퓚2죴퓚쟸볤(a,b)쓚fꇥ(x)ꇙ0,쟒f(a)fꇥ(a)>룶뛋뗣뗄횵,뛔몯쫽f(x)퓚웤솽뛋틬뫅뗄쓇룶쟸볤퓋폃헢훖랽램,뗃떽ꛄ뗄뗚뛾뷼쯆횵0,퓲뿉좡쫽횵ꛄf(a)1=a-xfꇤퟷ캪랽돌f(x)=0뗄(a)2ꆣ평듋샠췆,뛔폚뗚n룶뷼쯆횵xn릫쪽(3)헽좷ꆣ쪽(3)죧룹ꛄ뗄뗚튻룶뇆뷼횵ꛄ1ꆣ훘뢴룃랽램,뫜뿬뻍뗃떽쿂쟷뷼폚쪽(2)뗄룹ꛄ뗄튻쾵쇐뷼쯆횵ꛄn(n=1,2,3ꆭ)ꆣ헢킩뷼쯆횵뿉룹뻝릫쪽(3)살맀볆|xn-ꛄ|ꇜ|f(xn)|(3)d3)ퟛ뫏램ꆣ웤훐춬쪱펦폃쿒캻램폫쟐쿟램듓x0뗄솽닠뷓뷼폚:d=inf|fꇤ(x)|,늢쟒limbxꇺꇞxn=ꛄꆣa<x<x0,듓뛸뿉틔볓쯙볆쯣뷼쯆룹뗄맽돌(춼1)ꆣ2)얣뛙램(쟐쿟램)ꆣ(a)fꇥ>0,fꇤ>0(b)fꇥ>0,fꇤ<0(c)fꇥ<0,fꇤ>0(d)fꇥ<0,fꇤ<0춼1ꆡퟛ뫏램춼쪾ꆡGraphsofsyntheticmethodꆡꆡ룹뻝ퟛ뫏램샭싛,뛔늻춬뗄qꆢnꆢC뫍m,뇠돌ELSE볆쯣쿠펦뗄y,늿럖돌탲죧쿂,볆쯣뷡맻볻뇭4ꆣENDIFRANDOMIZETIMERNEXTxCLSFORx=0TO9PRINTꇥq1110ꇥy=g+x/100PRINTꇥcꇥ,ꇥnꇥ,ꇥmꇥ,ꇥqꇥ,ꇥyꇥIFy=0FORk=1TO20STEP1THENc=10+FIX(RND340)d=c3n+mn=10+FIX(RND340)ELSEm=1000+FIX(RND3100)310d=c/y3(1-1/(1+yꇄ)n)+m/(1+yꇄ)nq=1000+FIX(RND3100)310ENDIFf=10000000IFd-q>=0ANDd-q<=fi=-10000000THENFORx=0TO9o=yy=x/10f=d-qIFy=0ELSETHENENDIFd=c3n+mENXTxELSEFORx=0TO9d=ꇄc/y3(1-1/(1+yꇄ)n)+m/(1+y)ny=o+x/1000ENDIFIFy=0IFd-q>=0ANDd-q<=fTHENTHENd=c3n+mg=yELSEf=d-qd=c/y3(1ꇄ-1/(1+y)n)+m/(1+yꇄ)n' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
ꆡ84훐맺얩튵듳톧톧놨2003쓪ENDIFELSEIFd-q>=0ANDd-q<=fd=c/y3(1-1/(1+yꇄ)n)+m/(1+yꇄ)nTHENENDIFg=yIFd-q>=0ANDd-q<=ff=d-qTHENELSEo=yENDIFf=d-qNEXTxELSEENDIFFORx=0TO9NEXTxy=g+x/10000FORx=0TO9IFy=0y=o+x/10000000THENIFy=0d=c3n+mTHENELSEd=c3n+md=c/y3ꇄ(1-1/(1+y)n)+m/(1+yꇄ)nELSEENDIFd=c/y3(1-1ꇄ/(1+y)n)+m/ꇄ(1+y)nIFd-q>=0ANDd-q<=fENDIFTHENIFd-q>=0ANDd-q<=fo=yTHENf=d-qg=yELSEf=d-qENDIFELSENEXTxENDIFFORx=0TO9NEXTxy=o+x/100000FORx=0TO9IFy=0y=g+x/100000000THENIFy=0d=c3n+mTHENELSEd=c3n+md=c/y3(1-1/(1+yꇄ)n)+m/(1+yꇄ)nELSEENDIFd=c/y3(1-1/(1+yꇄ)n)+m/(1+yꇄ)nIFd-q>=0ANDd-q<=fENDIFTHENIFd-q>=0g=yTHENf=d-qIFd-q<=fELSETHENENDIFo=yNEXTxf=d-qFORx=0TO9ELSEy=g+x/1000000ENDIFIFy=0ELSETHENIFd-q>=id=c3n+mTHEN' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
ꆡꆡ뗚4웚뎣쟥펢뗈:햮좯볛룱ꆢ떽웚웚쿞틔벰떽웚쫕틦싊뗄쫽톧럖컶랽램85p=y2)햮좯볛룱ꆢ욱쾢싊뫍떽웚쫕틦싊횮볤뗄맘쾵ꆣi=d-qa.떱햮좯쫕틦싊y룸뚨쪱,평폚qꇤr>0,틲듋떱ELSE욱쾢싊짏짽쪱햮좯볛룱튲짏짽,랴횮퓲쿂붵;ENDIFb.떱욱쾢싊r룸뚨쪱,평폚qꇤy<0,틲듋떱떽웚ENDIF쫕틦싊짏짽쪱햮좯볛룱쿂붵,뛸떱떽웚쫕틦싊쿂붵NEXTx쪱햮좯볛룱짏짽ꆣPRINTc,n,m,q,o+p/23)욱쾢싊폫햮좯볛룱뗄맘쾵ꆣNEXTk1a.평폚1-n>0,틲듋떱떽웚쫕틦싊yEND(1+y)튻뚨쪱,욱쾢싊쯦햮좯볛룱뗄짏짽뛸짏짽,쯦햮좯볛뇭4ꆡ늻춬햮좯볛룱ꆢ떽웚웚쿞ꆢ욱쾢ꆢ쏦횵쿂뗄떽웚쫕틦싊Table4ꆡ룱뗄쿂붵뛸쿂붵;Theincomerateatdifferentbondprice,term,b.떱욱쾢싊튻뚨쪱,떽웚쫕틦싊폫햮좯볛룱뗄couponandfacevalue탲욱쾢떽웚웚쏦횵m/떽웚쫕틦햮좯볛룱뇤뮯맘쾵캪햮좯볛룱짏짽퓲떽웚쫕틦싊쿂붵,햮좯뫅볛룱쿂붵퓲떽웚쫕틦싊짏짽ꆣC/풪쿞n/a풪싊yq/풪4)햮좯떽웚웚쿞뫍떽웚쫕틦싊뛔햮좯볛룱뗄펰124241630010211430100247381790010281720100쿬ꆣ349491750010321580100짨햮좯떽웚웚쿞평n1뇤캪n2,떽웚쫕틦싊평426471470010871980100545431130010241120100y1뇤캪y2,퓲햮좯볛룱뗄뇤뮯뿉럖뷢캪:622181270010191230100q(n1,y1)-q(n2,y2)=q(n1,y1)-q(n1,y2)+734361090010161550100834131990010341640100q(n1,y2)-q(n2,y2)=q(n1,y1)-917491470010571840100q(n2,y1)+q(n2,y1)-q(n2,y2)(5)10ꆡ45171160010441090100쪽(5)뇭쏷,햮좯볛룱뗄뇤뮯뿉틔럖뷢캪솽룶늿2ꆡ럖컶룷닎쫽뛔햮좯볛룱펰쿬뗄폐킧랽램럖,헢솽늿럖럖뇰쫇떽웚쫕틦싊뗄뇤뮯뫍햮좯떽웚뛔햮좯볛룱릫쪽뷸탐럖뷢웚쿞뗄뇤뮯뛸틽웰뗄ꆣmrmq=ꇆn+3ꆡ뷡쫸폯i(i=1(1+y)1+n=y)놾컄훐듓쫽톧뷇뛈돶랢뛔햮좯쫐뎡볛룱폫욱쏦1m1-r(1+ny)m쫕틦싊ꆢ떽웚쫕틦싊틔벰떽웚웚쿞룷닎쫽횮볤뗄맘+1+y1(1+n=y)1쾵,룸돶쇋퇏룱뗄싛횤,늢샻폃볆쯣믺뷸탐쫽뻝뒦샭-1+y벰솿뮯럖컶;쳡돶쇋럖컶룷닎쫽뛔햮좯볛룱펰쿬뗄mrmrm-=폐킧랽램,뛔횸떼뷰죚쫐뎡폐튻뚨쿖쪵틢틥ꆣyy(1+n+y)(1+ny)mrm(y-r)+y닎뾼컄쿗y(1+n(4)y)뛔쪽(4)뷸탐쫽톧럖컶,늢샻폃뇭1ꆫ4뗄솿뮯\[1\]ꆡ믆ꆡ듯.믵뇒틸탐톧\[M\]놱.뺩:훐맺죋쏱듳톧돶냦짧,뷡맻ꆫ108,뗃돶틔쿂뷡싛ꆣ1\[2\]ꆡ튶폀룕.만뚨쫕죫횤좯룅싛\[M\]커.몺:커몺듳톧돶냦)떽웚웚쿞뛔햮좯볛룱뗄펰쿬ꆣ짧,ꆫ102a.떱y>r,벴떽웚쫕틦싊듳폚욱쾢싊쪱,쯦ퟅ햮좯떽웚웚쿞n뗄퓶볓,웤햮좯볛룱q훰붥쿂붵\[3\]ꆡ\[M\].NewYork:John;Wiley&SonsInc,ꆫ8b.떱y<r,벴떽웚쫕틦싊킡폚욱쾢싊쪱,쯦ퟅ햮좯떽웚웚쿞n뗄퓶볓,웤햮좯볛룱q훰붥짏짽\[4\]ꆡ(Reviewediton);\[M\].London:PitmanPublishign,ꆫ139c.떱y=r쪱,뛔폚죎틢뗄햮좯떽웚웚쿞n,햮\[5\]ꆡ\[M\].3rd좯볛룱q뻹캪뚨횵;:McGraw2HillInc,ꆫ120d.떱nꇺꇞ쪱,햮좯볛룱캪mr/yꆣ' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
