(ퟔ좻뿆톧냦)JournalofHefeiUniversity(NaturalSciences)ꆡ2005쓪6퓂ꆡ뗚15뻭뗚2웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ퇇쪽웚좨뚨볛벰웤쳗웚놣횵닟싔탬ꆡ뮳1,뛅톩2,쳆ꆡ쇡2(1.낲믕듳톧쫽톧폫볆쯣뿆톧톧풺,뫏럊ꆡ230039;2.뫏럊릤튵듳톧샭톧풺,뫏럊ꆡ230009)햪ꆡ튪:퇇쪽웚좨쫇튻훖잿슷뺶틀삵웫좫,퓚쫐뎡컞쳗샻뗄볙짨쿂,샻폃닢뛈뇤뮻뫍랽램,쪹벸뫎욽뻹퇇쪽웚좨뚨볛뗄쟳뷢맽돌룼볓볲뮯,늢퓋폃췆맣뗄Clark릫쪽,룸돶쇋웤쳗웚놣횵닟싔ꆣ맘볼듊:닢뛈뇤뮻;;퇇쪽웚좨;Clark릫쪽;쳗웚놣횵닟싔훐춼럖샠뫅:컄쿗뇪쪶싫:A컄헂뇠뫅:1672-162X(2005)02-0009-04퇇쪽웚좨쫇튻훖잿슷뺶틀삵웚좨,웤퓚떽웚죕T쪱뗄쫕틦늻뷶좡뻶폚뇪뗄닺떽웚죕뗄볛룱,뮹폫헻룶웚좨폐킧웚[0,T]쓚쒳뛎쪱볤뇪뗄닺쯹뺭샺뗄볛룱뗄욽뻹횵폐맘,튻훖캪쯣쫵욽뻹횵,쇭튻훖캪벸뫎욽뻹횵,틲듋쿠뛔폚뇪ힼ얷쪽웚좨뛸퇔웤뚨볛벰쳗웚놣횵튪뢴퓓뗄뛠,맘폚웤뚨볛컊쳢컄[1ꆫ2]럖뇰쳖싛쇋폐만뚨횴탐볛룱뗄쯣쫵욽뻹뫍벸뫎욽뻹퇇쪽웚좨쟩탎,컄[3]쳖싛쇋웤쳗웚놣횵닟싔뗄릹퓬,놾컄듓룅싊싛뗄뷇뛈샻폃컄[4ꆫ5]훐뗄닢뛈뇤뮻벰랽램,늻뷶볲뮯쇋뻟폐뢡뚯횴탐볛룱뗄퇇쪽웚좨뚨볛맽돌,늢쪹웤쳗웚놣횵닟싔뗄릹퓬룼캪볲뇣ꆣ1ꆡ풤놸횪쪶짨(ꚸ,F,P,{Ft})캪듸ꛒ-쇷뗄룅싊뿕볤,{Ft,0ꇜtꇜT}캪뇪ힼ늼샊퓋뚯{wt,0ꇜtꇜT}닺짺뗄ퟔ좻ꛒ-쇷,볙뚨쫐뎡훐횻몬폐솽훖닺,럧쿕닺막욱뫍컞럧쿕닺햮좯,웤볛룱맽돌럖뇰죧쿂:dS=uSdt+ꛒSdw,dB=rBdt,Stttttt0=S(0),B0=1(1)웤훐wt뚨틥죧짏,u캪뇪뗄닺뗄쮲쪱웚췻쫕틦싊,ꛒ캪늨뚯싊,r캪컞럧쿕샻싊,캪쳖싛랽뇣헢샯짨u,ꛒ,r뻹캪뎣쫽,뛔폚럇뎣쫽쟩탎평놾컄뿉샠쯆쳖싛ꆣ짨쿫쒳튻춶헟뗄돵쪼놾V0=x,웤훐튻늿럖ꛐ00B0듦폚틸탐,튻늿럖ꛐ10S0춶폚쫐뎡,돆ꛐt=0(ꛐt,ꛐ1)t,0ꇜtꇜT캪춶닟싔,쫇횸뛔폚쎿룶ꛐ0t,ꛐ1t쫇뿉쇏맽돌ꆣ뚨틥1ꆡ춶닟싔{ꛐ0t,ꛐ1t,0ꇜtꇜT}돆캪ퟔ죚닟싔,죧맻웤닆뢻맽돌Vt=ꛐ1tSt+ꛐ0tB(t2)ꆡꆡ싺ퟣ랽돌:dVt=ꛐ1tdSt+ꛐ0tdB(t3)웤훐ꛐ1t,ꛐ0t뇭쪾춶헟t쪱쯹돖폐뗄막욱쫽뫍햮좯쫽(헢샯짨막욱컞뫬샻횧뢶)ꆣ뾼싇퓚쪱볤[0,T]쓚,볙뚨킡뗄춶헟늻믡뛔쫐뎡닺짺펰쿬,볇웤t쪱뗄닆뢻캪Vt,돵쪼횵캪V0=x,웤훐춶폚막욱뗄닆뢻캪ꛐ1tSt,퓲춶폚햮좯뗄닆뢻캪Vt-ꛐ1tSt,평(1),(2),(3)뗃웤닆뢻맽돌싺ퟣ죧쿂뗄쯦믺캢럖랽돌:dVt=ꛐ1tdSt+(Vt-ꛐ1tS)trdt=[(ꛌ-r)ꛐ1tSt+rVt]dt+ꛐ1tSꛒtdwtꆡꆡ쿂쏦뾼싇틔St캪볆볛떥캻뗄닺뚨볛:쇮Yt=Bt/St,평Ito릫쪽뗃:dYt=Yt{(r-ꛌ+ꛒ2)dt-ꛒdwt}=-ꛒYdw^t헢샯ꛈ=(ꛌ-r-ꛒ2)/ꛒ,dw^t=dwt+ꛈdt뚨틥탂뗄룅싊닢뛈Q^dQ^:|F,평Girsanov뚨샭횪{w^t,0ꇜtꇜT}캪Q^쿂뗄뇪dPt=exp1-ꛈwt-ꛈ2t2ힼ늼샊퓋뚯,퓲닆뢻맽돌Vt쿠뛔폚St뗄볛횵쯹싺ퟣ뗄캢럖랽돌캪:쫕룥죕웚:2004-12-27ꆡꆡ탞믘죕웚:2005-03-10ퟷ헟볲뷩:탬뮳(19762),쓐,낲믕뎤럡죋,낲믕듳톧쫽톧폫볆쯣뿆톧톧풺훺뷌;뛅톩(1947-),쓐,낲믕쿘죋,뷌쫚,퇐뺿랽쿲:춳볆럖컶폫럧쿕뻶닟;쳆쇡(19792),얮,낲믕뢷쓏죋,뫏럊릤튵듳톧샭톧풺퓚뛁퇐뺿짺ꆣ
10뫏럊톧풺톧놨(ퟔ좻뿆톧냦)뗚15뻭Vdt=dVtꆤ1=1dVt+1Vtd+ꆴ1dVt,dꆵSSSStStttt헻샭뗃ꆡVdt=ꛒꛐ1Vtdw^tt-StSt벴ꆡVtV=0+Sꇒtꛒꛐ1Vu0t-dw^u(4)tS0Su평뗄뚨틥벰늼샊퓋뚯뗄탔훊뗃죧쿂뷡싛:뚨샭1ꆡퟔ죚붻틗닟싔닆뢻맽돌쿠뛔폚막욱뗄볛룱맽돌Vt쫇Q^닢뛈쿂뗄ꆣSt평컞쳗샻뚨볛샭싛[6]횪퓚틔St캪볇볛떥캻쪱죎틢닺뗄볛횵뚼뗈폚퓚닢뛈Q^쿂웤캴살쳹쿖웚췻횵벴Vt=VEQ^TSꆤ|F(5)ttST2ꆡ벸뫎욽뻹퇇쪽웚좨뚨볛볇t쪱뿌뻟폐뢡뚯쟃뚨볛룱뗄퇇쪽뾴뗸웚좨뗄볛룱캪Pt,웤훐tdJtJJtJt=exp1lnSdt,=t(lnSt-lnJ)tt=1-JtlntꇒdtttSt0ꆡꆡ볇웤퓚떽웚죕T쪱뗄볛룱캪P+T=(JT-ST),평풤놸횪쪶횪웤t쪱뗄볛룱캪^P=SEQPTtt/F,tST+평폚P+TT/ST=(JT-ST)/ST=J-1,폻쟳PT퓚Q^쿂뗄쳵볾웚췻,횻탨쟳돶JT퓚닢뛈Q^쿂뗄럖늼벴SSSTTT뿉,헢샯룹뻝막볛맽돌뗄뛔쫽헽첬탔,쫗쿈뾼싇JT뛔쫽뗄럖늼ꆣST뚨샭T2ꆡJlnꆫN(ꛌ(t),ꛒ2(t))STJttlnr+1ꛒ2웤훐ꛌSt222ꛒ233(T-t)(t)=-(T-t),ꛒ2(t)=T2T23T횤쏷:ꆡ쇮Jt=ꛎt,퓲평Ito릫쪽뗃,Stdꛎ1t=Jdt=ꛎt-r-lnꛎdt-ꛒdw^tSttd11lnꛎ=dt-ꛒdw^t-ꛒ2t-r-lnꛎtt2평쯦믺캢럖랽돌샭싛[7ꆫ8]뿉뗃:r+1ꛒ2t222ꛒlnꛎtlnꛎT=-(T-t)-T2TTꇒTsdw^stnꛎr+1ꛒJ2t1tlnr+ꛒ2t2EQ^22St222(lnꛎtlT)=-(T-t)=-(T-t)=ꛌ(t)T2TT2Tꛒ233VQ^ar(lnꛎT)=2ETꇒT2ꛒ2(-t)sds=T2=ꛒ2(t)횤뇏t3T퓚틑횪럖늼뗄쟩뿶쿂틗쟳돶웤웚췻뇭듯쪽ꆣ뚨샭3ꆡPt=Stexp(ꛌ(t)+1ꛒ2(t))N(d1)-N(d2)2
뗚2웚탬뮳,뗈:퇇쪽웚좨뚨볛벰웤쳗웚놣횵닟싔11벴캪뻟폐뢡뚯횴탐볛룱뗄벸뫎욽뻹퇇쪽뾴뗸웚좨뗄뚨볛릫쪽ꆣ웤훐ꛌ(d1=t)+ꛒ2(t)ꛒ,d2=d1-ꛒ(t),ꛒ(t)=ꛒꆪ2(t)(t)횤쏷:쇮y=lnꛎ,퓲EQ^(yttT)=u(t),Var(yT)=ꛒ2(t)P=Py(t,ꛎ)=P(t,y)=SEQ^T+[(e-1)|F]tttttꇞEQ^y[(eT+-1)|F]=tꇒy(eT-1)f(yT)dyT=0ꇒꇞ22y(yT-ꛌ(t))1(yT-ꛌ(t))eT1exp-02ꛐꛒdyT-exp-dyT(t)2ꛒ2ꇒꇞ0(t)2ꛐꛒ(t)2ꛒ2(t)=exp(ꛌ(t)+1ꛒ2(t))Nꛌ(t)+ꛒ2(t)2ꛒ-Nꛌ(t))ꛒꆡꆡ횤뇏(t(t)ꆡꆡ뛔폚뾴헇웚좨벰뾴뗸뾴헇욽볛릫쪽샠쯆뿉뗃ꆣ3ꆡ쳗웚놣횵닟싔룃웚좨뗄쳗웚놣횵닟싔횸춶헟폃돵쪼닆뢻V0,닉폃싺ퟣ뿉믽쳵볾벰죝탭쳵볾뗄ퟔ죚닟싔(ꛐ0t,ꛐ1)t,쪹뗃평(4)쪽좷뚨뗄닆뢻맽돌싺ퟣVT=PT(.)캪쪹쫐뎡늻듦퓚쳗샻믺믡,틑횤쏷뇘탫폐V0=S0^EQPTꆣST뚨샭4ꆡ웚좨PT뗄쳗웚놣횵닟싔캪:퓚죎튻쪱뿌t돖폐막욱뗄쫐횵캪ꛐ1S=T-tt(Vt)-SNꛌttTtTtꛒ(t)웤훐V쫇룃웚좨쯹뛔펦뗄볛횵맽돌,벴춶헟뗄닆뢻맽돌,V0=EQ^PT,퓲돖폐햮좯뗄쫐횵캪V-ꛐ1SꆣttttST횤쏷:맘폚Banach뿕볤Dp,1벰룃뿕볤짏뗄쳝뛈쯣ퟓD뫍췆맣뗄Clark릫쪽,닎볻컄쿗[3],헢샯횱뷓샻폃웤뷡싛ꆣ평VT=PT벰(4),돖폐뗄막욱럝뛮{ꛐ1t,0ꇜtꇜT}싺ퟣ:TPT=EQ^PT+ꛒSTSꇒꛐ1Pt-dw^(t6)tT0St폫룃닟싔뛔펦뗄닆뢻맽돌믲헟쮵웚좨뗄볛횵맽돌싺ퟣ:Vt=EQ^PT|Fꆡ(.)SttST평컄쿗[3]훐틽샭3뗃P^T=EQPT+EQDPTtSTSꇒT|F(tdw^t7)0TST뇈뷏(6)폫(7)뗃EQ^DPT1Pt|F=ꛒ(8)ttꛐt-STSt쇮ꆡgT=JT-ST평컄쿗[3]훐틽샭2,4,뗃DgTJTt=Dt-1=tt-ꛒgT-ꛒSTSTSTTTDP+TgTTt=Dttt=-ꛒPT-ꛒIgSTS>0STSTTTT
12뫏럊톧풺톧놨(ퟔ좻뿆톧냦)뗚15뻭(8)쪽헻샭뗃ꛒꛐ1Ptt-=EQ^t-ꛒPTt-ꛒIgTStTS>0|FTTSTt=t-ꛒPttgT-ꛒQ^T>0|FSttTST=t-ꛒPtt-ꛒꛌ(Nt)TStTꛒ(t)ꛐ1t=tPttꛌ(t--Nt)Pꛒ+TSTSt(t)t=T-tVttꛌ(t)-NTStTꛒ(t)4ꆡ뷡쫸폯퇇쪽웚좨뗄뚨볛컊쳢튻횱쫇샭싛뷧뫍쪵컱뷧쯹맘힢뗄훘뗣,평폚뻟놸슷뺶틀삵쳘헷,쪹뗃퇇쪽웚좨뗄뚨볛쒣탍폫뇪ힼ웚좨뗄뚨볛쒣탍쿠뇈돊쿖돶뷏듳닮틬,듓뛸쪹퇇쪽웚좨뗄뚨볛컊쳢뇈얷쪽웚좨뗄뚨볛룼캪뢴퓓,쳗웚놣횵컊쳢펦폃뎣맦뗄랽램룼쫇쓑틔뷢뻶,죧뫎헒떽ퟮ캪쳹뷼웤쪵볊쫐뎡볛룱뗄뚨볛쒣탍벰쓜릻췪좫뛔돥웤럧쿕뗄쳗웚놣횵닟싔쫇횵뗃뷸튻늽쮼뾼뗄컊쳢ꆣ닎뾼컄쿗:[1]ꆡ[M].NewYork:Springer2Verlag,1998:288ꆫ297.[2]ꆡ붪샱짐.웚좨뚨볛뗄쫽톧쒣탍뫍랽램[M].놱뺩:룟뗈뷌폽돶냦짧,2003:277ꆫ290.[3]ꆡ퇮헑뻼,ퟞ뷝훐.튻훖퇇쪽웚좨뗄쳗웚놣횵닟싔[J].펦폃쫽톧톧놨,2001,24(1):56ꆫ60.[4]ꆡ[J].(6):183ꆫ194.[5]ꆡ잮쿾쯉.쳸삩즢쒣탍훐뗄닢뛈뇤뮻폫웚좨뚨볛[J].펦폃룅싊춳볆,2004,20(1):91ꆫ99.[6]ꆡHarrisonJM,[J].JournalofEconomicTheory,1979(20):381ꆫ408.[7]ꆡ믆횾풶.쯦믺럖컶톧믹뒡[M].뗚2냦,놱뺩:뿆톧돶냦짧,2001:133ꆫ189.[8]ꆡ릨맢슳.쯦믺캢럖랽돌틽싛[M].놱뺩:놱뺩듳톧돶냦짧,1987:1ꆫ70.[퓰죎뇠킣:헅폀뻼]AsianOptionPricinganditsHedgingStrategyXUH1uai,DUX2ue2qiao,TANGL2ing(,AnhuiUniversity,Hefeiꆡ230039,China;,HefeiUniversityofTechnology,Hefei230009,China)Abstracts:Basedonthehypothesisofthemarketbeingnon2arbitrage,usingthemethodsofchangingmeasureandmartingale,thispapersimplifiesthesolvingprocessoftheasianoptionpricingwithgeo2metricaveraging,byageneralizedclarkformula,:changeofmeasure;martingale;asianoption;clarkformula;ahedgingstrategy
